Update libsecp256k1

crypto/secp256k1/libsecp256k1/.gitignore

@@ -0,0 +1,41 @@
+bench_inv
+bench_ecdh
+bench_sign
+bench_verify
+bench_schnorr_verify
+bench_recover
+bench_internal
+tests
+gen_context
+*.exe
+*.so
+*.a
+!.gitignore
+
+Makefile
+configure
+.libs/
+Makefile.in
+aclocal.m4
+autom4te.cache/
+config.log
+config.status
+*.tar.gz
+*.la
+libtool
+.deps/
+.dirstamp
+build-aux/
+*.lo
+*.o
+*~
+src/libsecp256k1-config.h
+src/libsecp256k1-config.h.in
+src/ecmult_static_context.h
+m4/libtool.m4
+m4/ltoptions.m4
+m4/ltsugar.m4
+m4/ltversion.m4
+m4/lt~obsolete.m4
+src/stamp-h1
+libsecp256k1.pc

crypto/secp256k1/libsecp256k1/.travis.yml

@@ -0,0 +1,62 @@
+language: c
+sudo: false
+addons:
+  apt:
+    packages: libgmp-dev
+compiler:
+  - clang
+  - gcc
+env:
+  global:
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  schnorr=NO  RECOVERY=NO
+  matrix:
+    - SCALAR=32bit    RECOVERY=yes
+    - SCALAR=32bit    FIELD=32bit       ECDH=yes
+    - SCALAR=64bit
+    - FIELD=64bit     RECOVERY=yes
+    - FIELD=64bit     ENDOMORPHISM=yes
+    - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes
+    - FIELD=64bit                       ASM=x86_64
+    - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
+    - FIELD=32bit     SCHNORR=yes
+    - FIELD=32bit     ENDOMORPHISM=yes
+    - BIGNUM=no
+    - BIGNUM=no       ENDOMORPHISM=yes SCHNORR=yes  RECOVERY=yes
+    - BIGNUM=no       STATICPRECOMPUTATION=no
+    - BUILD=distcheck
+    - EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
+matrix:
+  fast_finish: true
+  include:
+    - compiler: clang
+      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+            - libgmp-dev:i386
+    - compiler: clang
+      env: HOST=i686-linux-gnu
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+    - compiler: gcc
+      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+    - compiler: gcc
+      env: HOST=i686-linux-gnu
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+            - libgmp-dev:i386
+before_script: ./autogen.sh
+script:
+ - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
+ - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
+ - ./configure --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+os: linux

crypto/secp256k1/libsecp256k1/Makefile.am

@@ -19,6 +19,8 @@ noinst_HEADERS += src/eckey.h
 noinst_HEADERS += src/eckey_impl.h
 noinst_HEADERS += src/ecmult.h
 noinst_HEADERS += src/ecmult_impl.h
+noinst_HEADERS += src/ecmult_const.h
+noinst_HEADERS += src/ecmult_const_impl.h
 noinst_HEADERS += src/ecmult_gen.h
 noinst_HEADERS += src/ecmult_gen_impl.h
 noinst_HEADERS += src/num.h
@@ -43,19 +45,16 @@ pkgconfigdir = $(libdir)/pkgconfig
 pkgconfig_DATA = libsecp256k1.pc
 
 libsecp256k1_la_SOURCES = src/secp256k1.c
-libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include $(SECP_INCLUDES)
+libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
 libsecp256k1_la_LIBADD = $(SECP_LIBS)
 
 
 noinst_PROGRAMS =
 if USE_BENCHMARK
-noinst_PROGRAMS += bench_verify bench_recover bench_sign bench_internal
+noinst_PROGRAMS += bench_verify bench_sign bench_internal
 bench_verify_SOURCES = src/bench_verify.c
 bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
 bench_verify_LDFLAGS = -static
-bench_recover_SOURCES = src/bench_recover.c
-bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
-bench_recover_LDFLAGS = -static
 bench_sign_SOURCES = src/bench_sign.c
 bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS)
 bench_sign_LDFLAGS = -static
@@ -68,10 +67,44 @@ endif
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
-tests_CPPFLAGS = -DVERIFY $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+tests_CPPFLAGS = -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
 tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS)
 tests_LDFLAGS = -static
 TESTS = tests
 endif
 
-EXTRA_DIST = autogen.sh
+if USE_ECMULT_STATIC_PRECOMPUTATION
+CPPFLAGS_FOR_BUILD +=-I$(top_srcdir)/
+CFLAGS_FOR_BUILD += -Wall -Wextra -Wno-unused-function
+
+gen_context_OBJECTS = gen_context.o
+gen_context_BIN = gen_context$(BUILD_EXEEXT)
+gen_%.o: src/gen_%.c
+	$(CC_FOR_BUILD) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@
+
+$(gen_context_BIN): $(gen_context_OBJECTS)
+	$(CC_FOR_BUILD) $^ -o $@
+
+$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h
+$(tests_OBJECTS): src/ecmult_static_context.h
+$(bench_internal_OBJECTS): src/ecmult_static_context.h
+
+src/ecmult_static_context.h: $(gen_context_BIN)
+	./$(gen_context_BIN)
+
+CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h
+endif
+
+EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h
+
+if ENABLE_MODULE_ECDH
+include src/modules/ecdh/Makefile.am.include
+endif
+
+if ENABLE_MODULE_SCHNORR
+include src/modules/schnorr/Makefile.am.include
+endif
+
+if ENABLE_MODULE_RECOVERY
+include src/modules/recovery/Makefile.am.include
+endif

crypto/secp256k1/libsecp256k1/configure.ac

@@ -17,25 +17,19 @@ PKG_PROG_PKG_CONFIG
 AC_PATH_TOOL(AR, ar)
 AC_PATH_TOOL(RANLIB, ranlib)
 AC_PATH_TOOL(STRIP, strip)
+AX_PROG_CC_FOR_BUILD
 
 if test "x$CFLAGS" = "x"; then
   CFLAGS="-O3 -g"
 fi
 
+AM_PROG_CC_C_O
+
 AC_PROG_CC_C89
 if test x"$ac_cv_prog_cc_c89" = x"no"; then
   AC_MSG_ERROR([c89 compiler support required])
 fi
 
-case $host in
-  *mingw*)
-     use_pkgconfig=no
-     ;;
-   *)
-     use_pkgconfig=yes
-     ;;
-esac
-
 case $host_os in
   *darwin*)
      if  test x$cross_compiling != xyes; then
@@ -80,6 +74,14 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
       CFLAGS="$saved_CFLAGS"
     ])
 
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS -fvisibility=hidden"
+AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
 
 AC_ARG_ENABLE(benchmark,
     AS_HELP_STRING([--enable-benchmark],[compile benchmark (default is no)]),
@@ -95,6 +97,26 @@ AC_ARG_ENABLE(endomorphism,
     AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
     [use_endomorphism=$enableval],
     [use_endomorphism=no])
+    
+AC_ARG_ENABLE(ecmult_static_precomputation,
+    AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing (default is yes)]),
+    [use_ecmult_static_precomputation=$enableval],
+    [use_ecmult_static_precomputation=yes])
+
+AC_ARG_ENABLE(module_ecdh,
+    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (default is no)]),
+    [enable_module_ecdh=$enableval],
+    [enable_module_ecdh=no])
+
+AC_ARG_ENABLE(module_schnorr,
+    AS_HELP_STRING([--enable-module-schnorr],[enable Schnorr signature module (default is no)]),
+    [enable_module_schnorr=$enableval],
+    [enable_module_schnorr=no])
+
+AC_ARG_ENABLE(module_recovery,
+    AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module (default is no)]),
+    [enable_module_recovery=$enableval],
+    [enable_module_recovery=no])
 
 AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
 [Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
@@ -305,6 +327,22 @@ if test x"$use_endomorphism" = x"yes"; then
   AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
 fi
 
+if test x"$use_ecmult_static_precomputation" = x"yes"; then
+  AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
+fi
+
+if test x"$enable_module_ecdh" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module])
+fi
+
+if test x"$enable_module_schnorr" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_SCHNORR, 1, [Define this symbol to enable the Schnorr signature module])
+fi
+
+if test x"$enable_module_recovery" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_RECOVERY, 1, [Define this symbol to enable the ECDSA pubkey recovery module])
+fi
+
 AC_C_BIGENDIAN()
 
 AC_MSG_NOTICE([Using assembly optimizations: $set_asm])
@@ -312,6 +350,10 @@ AC_MSG_NOTICE([Using field implementation: $set_field])
 AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
 AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
 AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
+AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
+
+AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
+AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
 
 AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
 AC_CONFIG_FILES([Makefile libsecp256k1.pc])
@@ -321,6 +363,10 @@ AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
 AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
 AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
+AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$use_ecmult_static_precomputation" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_SCHNORR], [test x"$enable_module_schnorr" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
 
 dnl make sure nothing new is exported so that we don't break the cache
 PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"

crypto/secp256k1/libsecp256k1/include/secp256k1.h

@@ -0,0 +1,547 @@
+#ifndef _SECP256K1_
+# define _SECP256K1_
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+#include <stddef.h>
+
+/* These rules specify the order of arguments in API calls:
+ *
+ * 1. Context pointers go first, followed by output arguments, combined
+ *    output/input arguments, and finally input-only arguments.
+ * 2. Array lengths always immediately the follow the argument whose length
+ *    they describe, even if this violates rule 1.
+ * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated
+ *    later go first. This means: signatures, public nonces, private nonces,
+ *    messages, public keys, secret keys, tweaks.
+ * 4. Arguments that are not data pointers go last, from more complex to less
+ *    complex: function pointers, algorithm names, messages, void pointers,
+ *    counts, flags, booleans.
+ * 5. Opaque data pointers follow the function pointer they are to be passed to.
+ */
+
+/** Opaque data structure that holds context information (precomputed tables etc.).
+ *
+ *  The purpose of context structures is to cache large precomputed data tables
+ *  that are expensive to construct, and also to maintain the randomization data
+ *  for blinding.
+ *
+ *  Do not create a new context object for each operation, as construction is
+ *  far slower than all other API calls (~100 times slower than an ECDSA
+ *  verification).
+ *
+ *  A constructed context can safely be used from multiple threads
+ *  simultaneously, but API call that take a non-const pointer to a context
+ *  need exclusive access to it. In particular this is the case for
+ *  secp256k1_context_destroy and secp256k1_context_randomize.
+ *
+ *  Regarding randomization, either do it once at creation time (in which case
+ *  you do not need any locking for the other calls), or use a read-write lock.
+ */
+typedef struct secp256k1_context_struct secp256k1_context;
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
+ *
+ *  Furthermore, it is guaranteed that identical public keys (ignoring
+ *  compression) will have identical representation, so they can be memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_pubkey;
+
+/** Opaque data structured that holds a parsed ECDSA signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_serialize_* functions.
+ *
+ *  Furthermore, it is guaranteed to identical signatures will have identical
+ *  representation, so they can be memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_ecdsa_signature;
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
+ * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
+ * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
+ *          key32:     pointer to a 32-byte secret key (will not be NULL)
+ *          algo16:    pointer to a 16-byte array describing the signature
+ *                     algorithm (will be NULL for ECDSA for compatibility).
+ *          data:      Arbitrary data pointer that is passed through.
+ *          attempt:   how many iterations we have tried to find a nonce.
+ *                     This will almost always be 0, but different attempt values
+ *                     are required to result in a different nonce.
+ *
+ * Except for test cases, this function should compute some cryptographic hash of
+ * the message, the algorithm, the key and the attempt.
+ */
+typedef int (*secp256k1_nonce_function)(
+    unsigned char *nonce32,
+    const unsigned char *msg32,
+    const unsigned char *key32,
+    const unsigned char *algo16,
+    void *data,
+    unsigned int attempt
+);
+
+# if !defined(SECP256K1_GNUC_PREREQ)
+#  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) \
+ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
+#  else
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) 0
+#  endif
+# endif
+
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(2,7)
+#   define SECP256K1_INLINE __inline__
+#  elif (defined(_MSC_VER))
+#   define SECP256K1_INLINE __inline
+#  else
+#   define SECP256K1_INLINE
+#  endif
+# else
+#  define SECP256K1_INLINE inline
+# endif
+
+#ifndef SECP256K1_API
+# if defined(_WIN32)
+#  ifdef SECP256K1_BUILD
+#   define SECP256K1_API __declspec(dllexport)
+#  else
+#   define SECP256K1_API
+#  endif
+# elif defined(__GNUC__) && defined(SECP256K1_BUILD)
+#  define SECP256K1_API __attribute__ ((visibility ("default")))
+# else
+#  define SECP256K1_API
+# endif
+#endif
+
+/**Warning attributes
+  * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
+  * some paranoid null checks. */
+# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
+# else
+#  define SECP256K1_WARN_UNUSED_RESULT
+# endif
+# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_ARG_NONNULL(_x)  __attribute__ ((__nonnull__(_x)))
+# else
+#  define SECP256K1_ARG_NONNULL(_x)
+# endif
+
+/** Flags to pass to secp256k1_context_create. */
+# define SECP256K1_CONTEXT_VERIFY (1 << 0)
+# define SECP256K1_CONTEXT_SIGN   (1 << 1)
+
+/** Flag to pass to secp256k1_ec_pubkey_serialize and secp256k1_ec_privkey_export. */
+# define SECP256K1_EC_COMPRESSED  (1 << 0)
+
+/** Create a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  In:      flags: which parts of the context to initialize.
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_create(
+    unsigned int flags
+) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Copies a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  Args:    ctx: an existing context to copy (cannot be NULL)
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_clone(
+    const secp256k1_context* ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Destroy a secp256k1 context object.
+ *
+ *  The context pointer may not be used afterwards.
+ *  Args:   ctx: an existing context to destroy (cannot be NULL)
+ */
+SECP256K1_API void secp256k1_context_destroy(
+    secp256k1_context* ctx
+);
+
+/** Set a callback function to be called when an illegal argument is passed to
+ *  an API call. It will only trigger for violations that are mentioned
+ *  explicitly in the header.
+ *
+ *  The philosophy is that these shouldn't be dealt with through a
+ *  specific return value, as calling code should not have branches to deal with
+ *  the case that this code itself is broken.
+ *
+ *  On the other hand, during debug stage, one would want to be informed about
+ *  such mistakes, and the default (crashing) may be inadvisable.
+ *  When this callback is triggered, the API function called is guaranteed not
+ *  to cause a crash, though its return value and output arguments are
+ *  undefined.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an illegal argument is
+ *              passed to the API, taking a message and an opaque pointer
+ *              (NULL restores a default handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_illegal_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Set a callback function to be called when an internal consistency check
+ *  fails. The default is crashing.
+ *
+ *  This can only trigger in case of a hardware failure, miscompilation,
+ *  memory corruption, serious bug in the library, or other error would can
+ *  otherwise result in undefined behaviour. It will not trigger due to mere
+ *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
+ *  for that). After this callback returns, anything may happen, including
+ *  crashing.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an interal error occurs,
+ *              taking a message and an opaque pointer (NULL restores a default
+ *              handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_error_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Parse a variable-length public key into the pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *  Args: ctx:      a secp256k1 context object.
+ *  Out:  pubkey:   pointer to a pubkey object. If 1 is returned, it is set to a
+ *                  parsed version of input. If not, its value is undefined.
+ *  In:   input:    pointer to a serialized public key
+ *        inputlen: length of the array pointed to by input
+ *
+ *  This function supports parsing compressed (33 bytes, header byte 0x02 or
+ *  0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header
+ *  byte 0x06 or 0x07) format public keys.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey* pubkey,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a pubkey object into a serialized byte sequence.
+ *
+ *  Returns: 1 always.
+ *  Args: ctx:        a secp256k1 context object.
+ *  Out:  output:     a pointer to a 65-byte (if compressed==0) or 33-byte (if
+ *                    compressed==1) byte array to place the serialized key in.
+ *        outputlen:  a pointer to an integer which will contain the serialized
+ *                    size.
+ *  In:   pubkey:     a pointer to a secp256k1_pubkey containing an initialized
+ *                    public key.
+ *        flags:      SECP256K1_EC_COMPRESSED if serialization should be in
+ *                    compressed format.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_pubkey* pubkey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Parse a DER ECDSA signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  Note that this function also supports some violations of DER and even BER.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in DER format.
+ *
+ *  Returns: 1 if enough space was available to serialize, 0 otherwise
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output:    a pointer to an array to store the DER serialization
+ *  In/Out: outputlen: a pointer to a length integer. Initially, this integer
+ *                     should be set to the length of output. After the call
+ *                     it will be set to the length of the serialization (even
+ *                     if 0 was returned).
+ *  In:     sig:       a pointer to an initialized signature object
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_der(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify an ECDSA signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig:       the signature being verified (cannot be NULL)
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           pubkey:    pointer to an initialized public key to verify with (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
+ * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
+ * extra entropy.
+ */
+extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979;
+
+/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
+extern const secp256k1_nonce_function secp256k1_nonce_function_default;
+
+/** Create an ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *
+ * The sig always has an s value in the lower half of the range (From 0x1
+ * to 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
+ * inclusive), unlike many other implementations.
+ *
+ * With ECDSA a third-party can can forge a second distinct signature
+ * of the same message given a single initial signature without knowing
+ * the key by setting s to its additive inverse mod-order, 'flipping' the
+ * sign of the random point R which is not included in the signature.
+ * Since the forgery is of the same message this isn't universally
+ * problematic, but in systems where message malleability or uniqueness
+ * of signatures is important this can cause issues.  This forgery can be
+ * blocked by all verifiers forcing signers to use a canonical form. The
+ * lower-S form reduces the size of signatures slightly on average when
+ * variable length encodings (such as DER) are used and is cheap to
+ * verify, making it a good choice. Security of always using lower-S is
+ * assured because anyone can trivially modify a signature after the
+ * fact to enforce this property.  Adjusting it inside the signing
+ * function avoids the need to re-serialize or have curve specific
+ * constants outside of the library.  By always using a canonical form
+ * even in applications where it isn't needed it becomes possible to
+ * impose a requirement later if a need is discovered.
+ * No other forms of ECDSA malleability are known and none seem likely,
+ * but there is no formal proof that ECDSA, even with this additional
+ * restriction, is free of other malleability.  Commonly used serialization
+ * schemes will also accept various non-unique encodings, so care should
+ * be taken when this property is required for an application.
+ */
+SECP256K1_API int secp256k1_ecdsa_sign(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify an ECDSA secret key.
+ *
+ *  Returns: 1: secret key is valid
+ *           0: secret key is invalid
+ *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
+    const secp256k1_context* ctx,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Compute the public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key stores
+ *           0: secret was invalid, try again
+ *  Args:   ctx:        pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:    pubkey:     pointer to the created public key (cannot be NULL)
+ *  In:     seckey:     pointer to a 32-byte private key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Export a private key in BER format.
+ *
+ *  Returns: 1 if the private key was valid.
+ *  Args: ctx:        pointer to a context object, initialized for signing (cannot
+ *                    be NULL)
+ *  Out: privkey:     pointer to an array for storing the private key in BER.
+ *                    Should have space for 279 bytes, and cannot be NULL.
+ *       privkeylen:  Pointer to an int where the length of the private key in
+ *                    privkey will be stored.
+ *  In:  seckey:      pointer to a 32-byte secret key to export.
+ *       flags:       SECP256K1_EC_COMPRESSED if the key should be exported in
+ *                    compressed format.
+ *
+ *  This function is purely meant for compatibility with applications that
+ *  require BER encoded keys. When working with secp256k1-specific code, the
+ *  simple 32-byte private keys are sufficient.
+ *
+ *  Note that this function does not guarantee correct DER output. It is
+ *  guaranteed to be parsable by secp256k1_ec_privkey_import.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_export(
+    const secp256k1_context* ctx,
+    unsigned char *privkey,
+    size_t *privkeylen,
+    const unsigned char *seckey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Import a private key in DER format.
+ * Returns: 1 if a private key was extracted.
+ * Args: ctx:        pointer to a context object (cannot be NULL).
+ * Out:  seckey:     pointer to a 32-byte array for storing the private key.
+ *                   (cannot be NULL).
+ * In:   privkey:    pointer to a private key in DER format (cannot be NULL).
+ *       privkeylen: length of the DER private key pointed to be privkey.
+ *
+ * This function will accept more than just strict DER, and even allow some BER
+ * violations. The public key stored inside the DER-encoded private key is not
+ * verified for correctness, nor are the curve parameters. Use this function
+ * only if you know in advance it is supposed to contain a secp256k1 private
+ * key.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_import(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *privkey,
+    size_t privkeylen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a private key by adding tweak to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting private key
+ *          would be invalid (only when the tweak is the complement of the
+ *          private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object (cannot be NULL).
+ * In/Out:  seckey: pointer to a 32-byte private key.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by adding tweak times the generator to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting public key
+ *          would be invalid (only when the tweak is the complement of the
+ *          corresponding private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                  (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key object.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a private key by multiplying it by a tweak.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:   ctx:    pointer to a context object (cannot be NULL).
+ * In/Out: seckey: pointer to a 32-byte private key.
+ * In:     tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by multiplying it by a tweak value.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                 (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key obkect.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Updates the context randomization.
+ *  Returns: 1: randomization successfully updated
+ *           0: error
+ *  Args:    ctx:       pointer to a context object (cannot be NULL)
+ *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
+    secp256k1_context* ctx,
+    const unsigned char *seed32
+) SECP256K1_ARG_NONNULL(1);
+
+/** Add a number of public keys together.
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *  Args:   ctx:        pointer to a context object
+ *  Out:    out:        pointer to pubkey for placing the resulting public key
+ *                      (cannot be NULL)
+ *  In:     ins:        pointer to array of pointers to public keys (cannot be NULL)
+ *          n:          the number of public keys to add together (must be at least 1)
+ *  Use secp256k1_ec_pubkey_compress and secp256k1_ec_pubkey_decompress if the
+ *  uncompressed format is needed.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *out,
+    const secp256k1_pubkey * const * ins,
+    int n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif

crypto/secp256k1/libsecp256k1/include/secp256k1_ecdh.h

@@ -0,0 +1,30 @@
+#ifndef _SECP256K1_ECDH_
+# define _SECP256K1_ECDH_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Compute an EC Diffie-Hellman secret in constant time
+ *  Returns: 1: exponentiation was successful
+ *           0: scalar was invalid (zero or overflow)
+ *  Args:    ctx:      pointer to a context object (cannot be NULL)
+ *  Out:     result:   a 32-byte array which will be populated by an ECDH
+ *                     secret computed from the point and scalar
+ *  In:      point:    pointer to a public point
+ *           scalar:   a 32-byte scalar with which to multiply the point
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh(
+  const secp256k1_context* ctx,
+  unsigned char *result,
+  const secp256k1_pubkey *point,
+  const unsigned char *scalar
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif

crypto/secp256k1/libsecp256k1/include/secp256k1_recovery.h

@@ -0,0 +1,110 @@
+#ifndef _SECP256K1_RECOVERY_
+# define _SECP256K1_RECOVERY_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Opaque data structured that holds a parsed ECDSA signature,
+ *  supporting pubkey recovery.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 65 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ *
+ *  Furthermore, it is guaranteed that identical signatures (including their
+ *  recoverability) will have identical representation, so they can be
+ *  memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[65];
+} secp256k1_ecdsa_recoverable_signature;
+
+/** Parse a compact ECDSA signature (64 bytes + recovery id).
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise
+ *  Args: ctx:     a secp256k1 context object
+ *  Out:  sig:     a pointer to a signature object
+ *  In:   input64: a pointer to a 64-byte compact signature
+ *        recid:   the recovery id (0, 1, 2 or 3)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature* sig,
+    const unsigned char *input64,
+    int recid
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Convert a recoverable signature into a normal signature.
+ *
+ *  Returns: 1
+ *  Out: sig:    a pointer to a normal signature (cannot be NULL).
+ *  In:  sigin:  a pointer to a recoverable signature (cannot be NULL).
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const secp256k1_ecdsa_recoverable_signature* sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
+ *
+ *  Returns: 1
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  output64: a pointer to a 64-byte array of the compact signature (cannot be NULL)
+ *        recid:    a pointer to an integer to hold the recovery id (can be NULL).
+ *  In:   sig:      a pointer to an initialized signature object (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    int *recid,
+    const secp256k1_ecdsa_recoverable_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
+
+/** Create a recoverable ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an ECDSA public key from a signature.
+ *
+ *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to the recoved public key (cannot be NULL)
+ *  In:      sig:        pointer to initialized signature that supports pubkey recovery (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif

crypto/secp256k1/libsecp256k1/include/secp256k1_schnorr.h

@@ -0,0 +1,173 @@
+#ifndef _SECP256K1_SCHNORR_
+# define _SECP256K1_SCHNORR_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Create a signature using a custom EC-Schnorr-SHA256 construction. It
+ *  produces non-malleable 64-byte signatures which support public key recovery
+ *  batch validation, and multiparty signing.
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was
+ *              invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing
+ *                   (cannot be NULL)
+ *  Out:     sig64:  pointer to a 64-byte array where the signature will be
+ *                   placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL,
+ *                   secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation
+ *                   function (can be NULL)
+ */
+SECP256K1_API int secp256k1_schnorr_sign(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char *msg32,
+  const unsigned char *seckey,
+  secp256k1_nonce_function noncefp,
+  const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify a signature created by secp256k1_schnorr_sign.
+ *  Returns: 1: correct signature
+ *           0: incorrect signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig64:     the 64-byte signature being verified (cannot be NULL)
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           pubkey:    the public key to verify with (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_verify(
+  const secp256k1_context* ctx,
+  const unsigned char *sig64,
+  const unsigned char *msg32,
+  const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an EC public key from a Schnorr signature created using
+ *  secp256k1_schnorr_sign.
+ *  Returns: 1: public key successfully recovered (which guarantees a correct
+ *           signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for
+ *                       verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to a pubkey to set to the recovered public key
+ *                       (cannot be NULL).
+ *  In:      sig64:      signature as 64 byte array (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot
+ *                       be NULL)
+ */
+SECP256K1_API int secp256k1_schnorr_recover(
+  const secp256k1_context* ctx,
+  secp256k1_pubkey *pubkey,
+  const unsigned char *sig64,
+  const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Generate a nonce pair deterministically for use with
+ *  secp256k1_schnorr_partial_sign.
+ *  Returns: 1: valid nonce pair was generated.
+ *           0: otherwise (nonce generation function failed)
+ *  Args:    ctx:         pointer to a context object, initialized for signing
+ *                        (cannot be NULL)
+ *  Out:     pubnonce:    public side of the nonce (cannot be NULL)
+ *           privnonce32: private side of the nonce (32 byte) (cannot be NULL)
+ *  In:      msg32:       the 32-byte message hash assumed to be signed (cannot
+ *                        be NULL)
+ *           sec32:       the 32-byte private key (cannot be NULL)
+ *           noncefp:     pointer to a nonce generation function. If NULL,
+ *                        secp256k1_nonce_function_default is used
+ *           noncedata:   pointer to arbitrary data used by the nonce generation
+ *                        function (can be NULL)
+ *
+ *  Do not use the output as a private/public key pair for signing/validation.
+ */
+SECP256K1_API int secp256k1_schnorr_generate_nonce_pair(
+  const secp256k1_context* ctx,
+  secp256k1_pubkey *pubnonce,
+  unsigned char *privnonce32,
+  const unsigned char *msg32,
+  const unsigned char *sec32,
+  secp256k1_nonce_function noncefp,
+  const void* noncedata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Produce a partial Schnorr signature, which can be combined using
+ *  secp256k1_schnorr_partial_combine, to end up with a full signature that is
+ *  verifiable using secp256k1_schnorr_verify.
+ *  Returns: 1: signature created succesfully.
+ *           0: no valid signature exists with this combination of keys, nonces
+ *              and message (chance around 1 in 2^128)
+ *          -1: invalid private key, nonce, or public nonces.
+ *  Args: ctx:             pointer to context object, initialized for signing (cannot
+ *                         be NULL)
+ *  Out:  sig64:           pointer to 64-byte array to put partial signature in
+ *  In:   msg32:           pointer to 32-byte message to sign
+ *        sec32:           pointer to 32-byte private key
+ *        pubnonce_others: pointer to pubkey containing the sum of the other's
+ *                         nonces (see secp256k1_ec_pubkey_combine)
+ *        secnonce32:      pointer to 32-byte array containing our nonce
+ *
+ * The intended procedure for creating a multiparty signature is:
+ * - Each signer S[i] with private key x[i] and public key Q[i] runs
+ *   secp256k1_schnorr_generate_nonce_pair to produce a pair (k[i],R[i]) of
+ *   private/public nonces.
+ * - All signers communicate their public nonces to each other (revealing your
+ *   private nonce can lead to discovery of your private key, so it should be
+ *   considered secret).
+ * - All signers combine all the public nonces they received (excluding their
+ *   own) using secp256k1_ec_pubkey_combine to obtain an
+ *   Rall[i] = sum(R[0..i-1,i+1..n]).
+ * - All signers produce a partial signature using
+ *   secp256k1_schnorr_partial_sign, passing in their own private key x[i],
+ *   their own private nonce k[i], and the sum of the others' public nonces
+ *   Rall[i].
+ * - All signers communicate their partial signatures to each other.
+ * - Someone combines all partial signatures using
+ *   secp256k1_schnorr_partial_combine, to obtain a full signature.
+ * - The resulting signature is validatable using secp256k1_schnorr_verify, with
+ *   public key equal to the result of secp256k1_ec_pubkey_combine of the
+ *   signers' public keys (sum(Q[0..n])).
+ *
+ *  Note that secp256k1_schnorr_partial_combine and secp256k1_ec_pubkey_combine
+ *  function take their arguments in any order, and it is possible to
+ *  pre-combine several inputs already with one call, and add more inputs later
+ *  by calling the function again (they are commutative and associative).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_sign(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char *msg32,
+  const unsigned char *sec32,
+  const secp256k1_pubkey *pubnonce_others,
+  const unsigned char *secnonce32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
+
+/** Combine multiple Schnorr partial signatures.
+ * Returns: 1: the passed signatures were succesfully combined.
+ *          0: the resulting signature is not valid (chance of 1 in 2^256)
+ *         -1: some inputs were invalid, or the signatures were not created
+ *             using the same set of nonces
+ * Args:   ctx:      pointer to a context object
+ * Out:    sig64:    pointer to a 64-byte array to place the combined signature
+ *                   (cannot be NULL)
+ * In:     sig64sin: pointer to an array of n pointers to 64-byte input
+ *                   signatures
+ *         n:        the number of signatures to combine (at least 1)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_combine(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char * const * sig64sin,
+  int n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif

crypto/secp256k1/libsecp256k1/src/basic-config.h

@@ -0,0 +1,32 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_BASIC_CONFIG_
+#define _SECP256K1_BASIC_CONFIG_
+
+#ifdef USE_BASIC_CONFIG
+
+#undef USE_ASM_X86_64
+#undef USE_ENDOMORPHISM
+#undef USE_FIELD_10X26
+#undef USE_FIELD_5X52
+#undef USE_FIELD_INV_BUILTIN
+#undef USE_FIELD_INV_NUM
+#undef USE_NUM_GMP
+#undef USE_NUM_NONE
+#undef USE_SCALAR_4X64
+#undef USE_SCALAR_8X32
+#undef USE_SCALAR_INV_BUILTIN
+#undef USE_SCALAR_INV_NUM
+
+#define USE_NUM_NONE 1
+#define USE_FIELD_INV_BUILTIN 1
+#define USE_SCALAR_INV_BUILTIN 1
+#define USE_FIELD_10X26 1
+#define USE_SCALAR_8X32 1
+
+#endif // USE_BASIC_CONFIG
+#endif // _SECP256K1_BASIC_CONFIG_

crypto/secp256k1/libsecp256k1/src/bench.h

@@ -20,7 +20,9 @@ static double gettimedouble(void) {
 void print_number(double x) {
     double y = x;
     int c = 0;
-    if (y < 0.0) y = -y;
+    if (y < 0.0) {
+        y = -y;
+    }
     while (y < 100.0) {
         y *= 10.0;
         c++;
@@ -35,20 +37,28 @@ void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), v
     double max = 0.0;
     for (i = 0; i < count; i++) {
         double begin, total;
-        if (setup) setup(data);
+        if (setup != NULL) {
+            setup(data);
+        }
         begin = gettimedouble();
         benchmark(data);
         total = gettimedouble() - begin;
-        if (teardown) teardown(data);
-        if (total < min) min = total;
-        if (total > max) max = total;
+        if (teardown != NULL) {
+            teardown(data);
+        }
+        if (total < min) {
+            min = total;
+        }
+        if (total > max) {
+            max = total;
+        }
         sum += total;
     }
     printf("%s: min ", name);
     print_number(min * 1000000.0 / iter);
     printf("us / avg ");
     print_number((sum / count) * 1000000.0 / iter);
-    printf("us / avg ");
+    printf("us / max ");
     print_number(max * 1000000.0 / iter);
     printf("us\n");
 }

crypto/secp256k1/libsecp256k1/src/bench_ecdh.c

@@ -0,0 +1,53 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_ecdh.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char scalar[32];
+} bench_ecdh_t;
+
+static void bench_ecdh_setup(void* arg) {
+    int i;
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+
+    data->ctx = secp256k1_context_create(0);
+    for (i = 0; i < 32; i++) {
+        data->scalar[i] = i + 1;
+    }
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+static void bench_ecdh(void* arg) {
+    int i;
+    unsigned char res[32];
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar) == 1);
+    }
+}
+
+int main(void) {
+    bench_ecdh_t data;
+
+    run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, 20000);
+    return 0;
+}

crypto/secp256k1/libsecp256k1/src/bench_internal.c

@@ -13,15 +13,17 @@
 #include "field_impl.h"
 #include "group_impl.h"
 #include "scalar_impl.h"
+#include "ecmult_const_impl.h"
 #include "ecmult_impl.h"
 #include "bench.h"
+#include "secp256k1.c"
 
 typedef struct {
-    secp256k1_scalar_t scalar_x, scalar_y;
-    secp256k1_fe_t fe_x, fe_y;
-    secp256k1_ge_t ge_x, ge_y;
-    secp256k1_gej_t gej_x, gej_y;
-    unsigned char data[32];
+    secp256k1_scalar scalar_x, scalar_y;
+    secp256k1_fe fe_x, fe_y;
+    secp256k1_ge ge_x, ge_y;
+    secp256k1_gej gej_x, gej_y;
+    unsigned char data[64];
     int wnaf[256];
 } bench_inv_t;
 
@@ -51,6 +53,7 @@ void bench_setup(void* arg) {
     secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
     secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
     memcpy(data->data, init_x, 32);
+    memcpy(data->data + 32, init_y, 32);
 }
 
 void bench_scalar_add(void* arg) {
@@ -95,8 +98,8 @@ void bench_scalar_split(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_scalar_t l, r;
-        secp256k1_scalar_split_lambda_var(&l, &r, &data->scalar_x);
+        secp256k1_scalar l, r;
+        secp256k1_scalar_split_lambda(&l, &r, &data->scalar_x);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
@@ -193,7 +196,7 @@ void bench_group_double_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_double_var(&data->gej_x, &data->gej_x);
+        secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL);
     }
 }
 
@@ -202,7 +205,7 @@ void bench_group_add_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y);
+        secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL);
     }
 }
 
@@ -220,7 +223,7 @@ void bench_group_add_affine_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y);
+        secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL);
     }
 }
 
@@ -229,7 +232,17 @@ void bench_ecmult_wnaf(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_ecmult_wnaf(data->wnaf, &data->scalar_x, WINDOW_A);
+        secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_wnaf_const(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
@@ -265,11 +278,27 @@ void bench_rfc6979_hmac_sha256(void* arg) {
     secp256k1_rfc6979_hmac_sha256_t rng;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 32, data->data, 32, NULL, 0);
+        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
         secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
     }
 }
 
+void bench_context_verify(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 20; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
+    }
+}
+
+void bench_context_sign(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 200; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
+    }
+}
+
 
 int have_flag(int argc, char** argv, char *flag) {
     char** argm = argv + argc;
@@ -278,7 +307,9 @@ int have_flag(int argc, char** argv, char *flag) {
         return 1;
     }
     while (argv != NULL && argv != argm) {
-        if (strcmp(*argv, flag) == 0) return 1;
+        if (strcmp(*argv, flag) == 0) {
+            return 1;
+        }
         argv++;
     }
     return 0;
@@ -309,10 +340,15 @@ int main(int argc, char **argv) {
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, 200000);
 
+    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
+
     return 0;
 }

crypto/secp256k1/libsecp256k1/src/bench_recover.c

@@ -1,14 +1,16 @@
 /**********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                   *
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
 #include "include/secp256k1.h"
+#include "include/secp256k1_recovery.h"
 #include "util.h"
 #include "bench.h"
 
 typedef struct {
+    secp256k1_context *ctx;
     unsigned char msg[32];
     unsigned char sig[64];
 } bench_recover_t;
@@ -16,16 +18,20 @@ typedef struct {
 void bench_recover(void* arg) {
     int i;
     bench_recover_t *data = (bench_recover_t*)arg;
-    unsigned char pubkey[33];
+    secp256k1_pubkey pubkey;
+    unsigned char pubkeyc[33];
 
     for (i = 0; i < 20000; i++) {
         int j;
-        int pubkeylen = 33;
-        CHECK(secp256k1_ecdsa_recover_compact(data->msg, data->sig, pubkey, &pubkeylen, 1, i % 2));
+        size_t pubkeylen = 33;
+        secp256k1_ecdsa_recoverable_signature sig;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2));
+        CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
         for (j = 0; j < 32; j++) {
             data->sig[j + 32] = data->msg[j];    /* Move former message to S. */
             data->msg[j] = data->sig[j];         /* Move former R to message. */
-            data->sig[j] = pubkey[j + 1];        /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
+            data->sig[j] = pubkeyc[j + 1];       /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
         }
     }
 }
@@ -34,16 +40,21 @@ void bench_recover_setup(void* arg) {
     int i;
     bench_recover_t *data = (bench_recover_t*)arg;
 
-    for (i = 0; i < 32; i++) data->msg[i] = 1 + i;
-    for (i = 0; i < 64; i++) data->sig[i] = 65 + i;
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (i = 0; i < 64; i++) {
+        data->sig[i] = 65 + i;
+    }
 }
 
 int main(void) {
     bench_recover_t data;
-    secp256k1_start(SECP256K1_START_VERIFY);
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
 
     run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, 20000);
 
-    secp256k1_stop();
+    secp256k1_context_destroy(data.ctx);
     return 0;
 }

crypto/secp256k1/libsecp256k1/src/bench_schnorr_verify.c

@@ -0,0 +1,73 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_schnorr.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    unsigned char key[32];
+    unsigned char sig[64];
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+} benchmark_schnorr_sig_t;
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    benchmark_schnorr_sig_t sigs[64];
+    int numsigs;
+} benchmark_schnorr_verify_t;
+
+static void benchmark_schnorr_init(void* arg) {
+    int i, k;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (k = 0; k < data->numsigs; k++) {
+        secp256k1_pubkey pubkey;
+        for (i = 0; i < 32; i++) {
+            data->sigs[k].key[i] = 33 + i + k;
+        }
+        secp256k1_schnorr_sign(data->ctx, data->sigs[k].sig, data->msg, data->sigs[k].key, NULL, NULL);
+        data->sigs[k].pubkeylen = 33;
+        CHECK(secp256k1_ec_pubkey_create(data->ctx, &pubkey, data->sigs[k].key));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
+    }
+}
+
+static void benchmark_schnorr_verify(void* arg) {
+    int i;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 20000 / data->numsigs; i++) {
+        secp256k1_pubkey pubkey;
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->sigs[0].pubkey, data->sigs[0].pubkeylen));
+        CHECK(secp256k1_schnorr_verify(data->ctx, data->sigs[0].sig, data->msg, &pubkey) == ((i & 0xFF) == 0));
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+    }
+}
+
+
+
+int main(void) {
+    benchmark_schnorr_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    data.numsigs = 1;
+    run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}

crypto/secp256k1/libsecp256k1/src/bench_sign.c

@@ -9,6 +9,7 @@
 #include "bench.h"
 
 typedef struct {
+    secp256k1_context* ctx;
     unsigned char msg[32];
     unsigned char key[32];
 } bench_sign_t;
@@ -17,32 +18,39 @@ static void bench_sign_setup(void* arg) {
     int i;
     bench_sign_t *data = (bench_sign_t*)arg;
 
-    for (i = 0; i < 32; i++) data->msg[i] = i + 1;
-    for (i = 0; i < 32; i++) data->key[i] = i + 65;
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = i + 1;
+    }
+    for (i = 0; i < 32; i++) {
+        data->key[i] = i + 65;
+    }
 }
 
 static void bench_sign(void* arg) {
     int i;
     bench_sign_t *data = (bench_sign_t*)arg;
 
-    unsigned char sig[64];
+    unsigned char sig[74];
     for (i = 0; i < 20000; i++) {
+        size_t siglen = 74;
         int j;
-        int recid = 0;
-        CHECK(secp256k1_ecdsa_sign_compact(data->msg, sig, data->key, NULL, NULL, &recid));
+        secp256k1_ecdsa_signature signature;
+        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
+        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
         for (j = 0; j < 32; j++) {
-            data->msg[j] = sig[j];             /* Move former R to message. */
-            data->key[j] = sig[j + 32];        /* Move former S to key.     */
+            data->msg[j] = sig[j];
+            data->key[j] = sig[j + 32];
         }
     }
 }
 
 int main(void) {
     bench_sign_t data;
-    secp256k1_start(SECP256K1_START_SIGN);
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
 
     run_benchmark("ecdsa_sign", bench_sign, bench_sign_setup, NULL, &data, 10, 20000);
 
-    secp256k1_stop();
+    secp256k1_context_destroy(data.ctx);
     return 0;
 }

crypto/secp256k1/libsecp256k1/src/bench_verify.c

@@ -12,12 +12,13 @@
 #include "bench.h"
 
 typedef struct {
+    secp256k1_context *ctx;
     unsigned char msg[32];
     unsigned char key[32];
     unsigned char sig[72];
-    int siglen;
+    size_t siglen;
     unsigned char pubkey[33];
-    int pubkeylen;
+    size_t pubkeylen;
 } benchmark_verify_t;
 
 static void benchmark_verify(void* arg) {
@@ -25,10 +26,14 @@ static void benchmark_verify(void* arg) {
     benchmark_verify_t* data = (benchmark_verify_t*)arg;
 
     for (i = 0; i < 20000; i++) {
+        secp256k1_pubkey pubkey;
+        secp256k1_ecdsa_signature sig;
         data->sig[data->siglen - 1] ^= (i & 0xFF);
         data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
         data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-        CHECK(secp256k1_ecdsa_verify(data->msg, data->sig, data->siglen, data->pubkey, data->pubkeylen) == (i == 0));
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
+        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
         data->sig[data->siglen - 1] ^= (i & 0xFF);
         data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
         data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
@@ -37,19 +42,26 @@ static void benchmark_verify(void* arg) {
 
 int main(void) {
     int i;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
     benchmark_verify_t data;
 
-    secp256k1_start(SECP256K1_START_VERIFY | SECP256K1_START_SIGN);
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
 
-    for (i = 0; i < 32; i++) data.msg[i] = 1 + i;
-    for (i = 0; i < 32; i++) data.key[i] = 33 + i;
+    for (i = 0; i < 32; i++) {
+        data.msg[i] = 1 + i;
+    }
+    for (i = 0; i < 32; i++) {
+        data.key[i] = 33 + i;
+    }
     data.siglen = 72;
-    secp256k1_ecdsa_sign(data.msg, data.sig, &data.siglen, data.key, NULL, NULL);
-    data.pubkeylen = 33;
-    CHECK(secp256k1_ec_pubkey_create(data.pubkey, &data.pubkeylen, data.key, 1));
+    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
+    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
+    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
+    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
 
     run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, 20000);
 
-    secp256k1_stop();
+    secp256k1_context_destroy(data.ctx);
     return 0;
 }

crypto/secp256k1/libsecp256k1/src/ecdsa.h

@@ -0,0 +1,22 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECDSA_
+#define _SECP256K1_ECDSA_
+
+#include <stddef.h>
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult.h"
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
+static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid);
+
+#endif

crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h

@@ -28,7 +28,7 @@
  *  sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
  *   'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
  */
-static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
     0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
     0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
 );
@@ -42,16 +42,16 @@ static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CON
  *  sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
  *   '14551231950b75fc4402da1722fc9baee'
  */
-static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
     0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
 );
 
-static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
     unsigned char ra[32] = {0}, sa[32] = {0};
     const unsigned char *rp;
     const unsigned char *sp;
-    int lenr;
-    int lens;
+    size_t lenr;
+    size_t lens;
     int overflow;
     if (sig[0] != 0x30) {
         return 0;
@@ -98,26 +98,27 @@ static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned ch
     memcpy(ra + 32 - lenr, rp, lenr);
     memcpy(sa + 32 - lens, sp, lens);
     overflow = 0;
-    secp256k1_scalar_set_b32(&r->r, ra, &overflow);
+    secp256k1_scalar_set_b32(rr, ra, &overflow);
     if (overflow) {
         return 0;
     }
-    secp256k1_scalar_set_b32(&r->s, sa, &overflow);
+    secp256k1_scalar_set_b32(rs, sa, &overflow);
     if (overflow) {
         return 0;
     }
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a) {
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
     unsigned char r[33] = {0}, s[33] = {0};
     unsigned char *rp = r, *sp = s;
-    int lenR = 33, lenS = 33;
-    secp256k1_scalar_get_b32(&r[1], &a->r);
-    secp256k1_scalar_get_b32(&s[1], &a->s);
+    size_t lenR = 33, lenS = 33;
+    secp256k1_scalar_get_b32(&r[1], ar);
+    secp256k1_scalar_get_b32(&s[1], as);
     while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
     while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
     if (*size < 6+lenS+lenR) {
+        *size = 6 + lenS + lenR;
         return 0;
     }
     *size = 6 + lenS + lenR;
@@ -132,26 +133,26 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const se
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message) {
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
     unsigned char c[32];
-    secp256k1_scalar_t sn, u1, u2;
-    secp256k1_fe_t xr;
-    secp256k1_gej_t pubkeyj;
-    secp256k1_gej_t pr;
+    secp256k1_scalar sn, u1, u2;
+    secp256k1_fe xr;
+    secp256k1_gej pubkeyj;
+    secp256k1_gej pr;
 
-    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
         return 0;
     }
 
-    secp256k1_scalar_inverse_var(&sn, &sig->s);
+    secp256k1_scalar_inverse_var(&sn, sigs);
     secp256k1_scalar_mul(&u1, &sn, message);
-    secp256k1_scalar_mul(&u2, &sn, &sig->r);
+    secp256k1_scalar_mul(&u2, &sn, sigr);
     secp256k1_gej_set_ge(&pubkeyj, pubkey);
-    secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
+    secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
     if (secp256k1_gej_is_infinity(&pr)) {
         return 0;
     }
-    secp256k1_scalar_get_b32(c, &sig->r);
+    secp256k1_scalar_get_b32(c, sigr);
     secp256k1_fe_set_b32(&xr, c);
 
     /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
@@ -186,19 +187,19 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const se
     return 0;
 }
 
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid) {
+static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
     unsigned char brx[32];
-    secp256k1_fe_t fx;
-    secp256k1_ge_t x;
-    secp256k1_gej_t xj;
-    secp256k1_scalar_t rn, u1, u2;
-    secp256k1_gej_t qj;
+    secp256k1_fe fx;
+    secp256k1_ge x;
+    secp256k1_gej xj;
+    secp256k1_scalar rn, u1, u2;
+    secp256k1_gej qj;
 
-    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
         return 0;
     }
 
-    secp256k1_scalar_get_b32(brx, &sig->r);
+    secp256k1_scalar_get_b32(brx, sigr);
     VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
     if (recid & 2) {
         if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
@@ -210,29 +211,29 @@ static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256
         return 0;
     }
     secp256k1_gej_set_ge(&xj, &x);
-    secp256k1_scalar_inverse_var(&rn, &sig->r);
+    secp256k1_scalar_inverse_var(&rn, sigr);
     secp256k1_scalar_mul(&u1, &rn, message);
     secp256k1_scalar_negate(&u1, &u1);
-    secp256k1_scalar_mul(&u2, &rn, &sig->s);
-    secp256k1_ecmult(&qj, &xj, &u2, &u1);
+    secp256k1_scalar_mul(&u2, &rn, sigs);
+    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
     secp256k1_ge_set_gej_var(pubkey, &qj);
     return !secp256k1_gej_is_infinity(&qj);
 }
 
-static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid) {
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
     unsigned char b[32];
-    secp256k1_gej_t rp;
-    secp256k1_ge_t r;
-    secp256k1_scalar_t n;
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    secp256k1_scalar n;
     int overflow = 0;
 
-    secp256k1_ecmult_gen(&rp, nonce);
+    secp256k1_ecmult_gen(ctx, &rp, nonce);
     secp256k1_ge_set_gej(&r, &rp);
     secp256k1_fe_normalize(&r.x);
     secp256k1_fe_normalize(&r.y);
     secp256k1_fe_get_b32(b, &r.x);
-    secp256k1_scalar_set_b32(&sig->r, b, &overflow);
-    if (secp256k1_scalar_is_zero(&sig->r)) {
+    secp256k1_scalar_set_b32(sigr, b, &overflow);
+    if (secp256k1_scalar_is_zero(sigr)) {
         /* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature. */
         secp256k1_gej_clear(&rp);
         secp256k1_ge_clear(&r);
@@ -241,18 +242,18 @@ static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_
     if (recid) {
         *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
     }
-    secp256k1_scalar_mul(&n, &sig->r, seckey);
+    secp256k1_scalar_mul(&n, sigr, seckey);
     secp256k1_scalar_add(&n, &n, message);
-    secp256k1_scalar_inverse(&sig->s, nonce);
-    secp256k1_scalar_mul(&sig->s, &sig->s, &n);
+    secp256k1_scalar_inverse(sigs, nonce);
+    secp256k1_scalar_mul(sigs, sigs, &n);
     secp256k1_scalar_clear(&n);
     secp256k1_gej_clear(&rp);
     secp256k1_ge_clear(&r);
-    if (secp256k1_scalar_is_zero(&sig->s)) {
+    if (secp256k1_scalar_is_zero(sigs)) {
         return 0;
     }
-    if (secp256k1_scalar_is_high(&sig->s)) {
-        secp256k1_scalar_negate(&sig->s, &sig->s);
+    if (secp256k1_scalar_is_high(sigs)) {
+        secp256k1_scalar_negate(sigs, sigs);
         if (recid) {
             *recid ^= 1;
         }

crypto/secp256k1/libsecp256k1/src/eckey.h

@@ -0,0 +1,28 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECKEY_
+#define _SECP256K1_ECKEY_
+
+#include <stddef.h>
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, unsigned int flags);
+
+static int secp256k1_eckey_privkey_parse(secp256k1_scalar *key, const unsigned char *privkey, size_t privkeylen);
+static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context *ctx, unsigned char *privkey, size_t *privkeylen, const secp256k1_scalar *key, unsigned int flags);
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+
+#endif

crypto/secp256k1/libsecp256k1/src/eckey_impl.h

@@ -14,12 +14,12 @@
 #include "group.h"
 #include "ecmult_gen.h"
 
-static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size) {
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
     if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
-        secp256k1_fe_t x;
+        secp256k1_fe x;
         return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == 0x03);
     } else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
-        secp256k1_fe_t x, y;
+        secp256k1_fe x, y;
         if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
             return 0;
         }
@@ -33,14 +33,14 @@ static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned cha
     }
 }
 
-static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed) {
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, unsigned int flags) {
     if (secp256k1_ge_is_infinity(elem)) {
         return 0;
     }
     secp256k1_fe_normalize_var(&elem->x);
     secp256k1_fe_normalize_var(&elem->y);
     secp256k1_fe_get_b32(&pub[1], &elem->x);
-    if (compressed) {
+    if (flags & SECP256K1_EC_COMPRESSED) {
         *size = 33;
         pub[0] = 0x02 | (secp256k1_fe_is_odd(&elem->y) ? 0x01 : 0x00);
     } else {
@@ -51,7 +51,7 @@ static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char
     return 1;
 }
 
-static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen) {
+static int secp256k1_eckey_privkey_parse(secp256k1_scalar *key, const unsigned char *privkey, size_t privkeylen) {
     unsigned char c[32] = {0};
     const unsigned char *end = privkey + privkeylen;
     int lenb = 0;
@@ -94,13 +94,13 @@ static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned
     return !overflow;
 }
 
-static int secp256k1_eckey_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed) {
-    secp256k1_gej_t rp;
-    secp256k1_ge_t r;
-    int pubkeylen = 0;
-    secp256k1_ecmult_gen(&rp, key);
+static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context *ctx, unsigned char *privkey, size_t *privkeylen, const secp256k1_scalar *key, unsigned int flags) {
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    size_t pubkeylen = 0;
+    secp256k1_ecmult_gen(ctx, &rp, key);
     secp256k1_ge_set_gej(&r, &rp);
-    if (compressed) {
+    if (flags & SECP256K1_EC_COMPRESSED) {
         static const unsigned char begin[] = {
             0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
         };
@@ -154,7 +154,7 @@ static int secp256k1_eckey_privkey_serialize(unsigned char *privkey, int *privke
     return 1;
 }
 
-static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
     secp256k1_scalar_add(key, key, tweak);
     if (secp256k1_scalar_is_zero(key)) {
         return 0;
@@ -162,12 +162,12 @@ static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp
     return 1;
 }
 
-static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
-    secp256k1_gej_t pt;
-    secp256k1_scalar_t one;
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    secp256k1_scalar one;
     secp256k1_gej_set_ge(&pt, key);
     secp256k1_scalar_set_int(&one, 1);
-    secp256k1_ecmult(&pt, &pt, &one, tweak);
+    secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
 
     if (secp256k1_gej_is_infinity(&pt)) {
         return 0;
@@ -176,7 +176,7 @@ static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge_t *key, const secp256k1
     return 1;
 }
 
-static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
     if (secp256k1_scalar_is_zero(tweak)) {
         return 0;
     }
@@ -185,16 +185,16 @@ static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp
     return 1;
 }
 
-static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
-    secp256k1_scalar_t zero;
-    secp256k1_gej_t pt;
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar zero;
+    secp256k1_gej pt;
     if (secp256k1_scalar_is_zero(tweak)) {
         return 0;
     }
 
     secp256k1_scalar_set_int(&zero, 0);
     secp256k1_gej_set_ge(&pt, key);
-    secp256k1_ecmult(&pt, &pt, tweak, &zero);
+    secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero);
     secp256k1_ge_set_gej(key, &pt);
     return 1;
 }

crypto/secp256k1/libsecp256k1/src/ecmult.h

@@ -0,0 +1,31 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_
+#define _SECP256K1_ECMULT_
+
+#include "num.h"
+#include "group.h"
+
+typedef struct {
+    /* For accelerating the computation of a*P + b*G: */
+    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
+#endif
+} secp256k1_ecmult_context;
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
+
+/** Double multiply: R = na*A + ng*G */
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+
+#endif

crypto/secp256k1/libsecp256k1/src/ecmult_const.h

@@ -1,19 +1,15 @@
 /**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Copyright (c) 2015 Andrew Poelstra                                 *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
-#ifndef _SECP256K1_ECMULT_GEN_
-#define _SECP256K1_ECMULT_GEN_
+#ifndef _SECP256K1_ECMULT_CONST_
+#define _SECP256K1_ECMULT_CONST_
 
 #include "scalar.h"
 #include "group.h"
 
-static void secp256k1_ecmult_gen_start(void);
-static void secp256k1_ecmult_gen_stop(void);
-
-/** Multiply with the generator: R = a*G */
-static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
 
 #endif

crypto/secp256k1/libsecp256k1/src/ecmult_const_impl.h

@@ -0,0 +1,260 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_IMPL_
+#define _SECP256K1_ECMULT_CONST_IMPL_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+#ifdef USE_ENDOMORPHISM
+    #define WNAF_BITS 128
+#else
+    #define WNAF_BITS 256
+#endif
+#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+    int m; \
+    int abs_n = (n) * (((n) > 0) * 2 - 1); \
+    int idx_n = abs_n / 2; \
+    secp256k1_fe neg_y; \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+    for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+        /* This loop is used to avoid secret data in array indices. See
+         * the comment in ecmult_gen_impl.h for rationale. */ \
+        secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+        secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+    } \
+    (r)->infinity = 0; \
+    secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+    secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^{wi} * wnaf[i], i=0..return_val)
+ *  with the following guarantees:
+ *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ *  - each wnaf[i] is nonzero
+ *  - the number of words set is returned; this is always (WNAF_BITS + w - 1) / w
+ *
+ *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
+    int global_sign;
+    int skew = 0;
+    int word = 0;
+    /* 1 2 3 */
+    int u_last;
+    int u;
+
+#ifdef USE_ENDOMORPHISM
+    int flip;
+    int bit;
+    secp256k1_scalar neg_s;
+    int not_neg_one;
+    /* If we are using the endomorphism, we cannot handle even numbers by negating
+     * them, since we are working with 128-bit numbers whose negations would be 256
+     * bits, eliminating the performance advantage. Instead we use a technique from
+     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+     * or 2 (for odd) to the number we are encoding, then compensating after the
+     * multiplication. */
+    /* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */
+    flip = secp256k1_scalar_is_high(&s);
+    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+    bit = flip ^ (s.d[0] & 1);
+    /* We check for negative one, since adding 2 to it will cause an overflow */
+    secp256k1_scalar_negate(&neg_s, &s);
+    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+     * that we added two to it and flipped it. In fact for -1 these operations are
+     * identical. We only flipped, but since skewing is required (in the sense that
+     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+     * our flags to claim that we only skewed. */
+    global_sign = secp256k1_scalar_cond_negate(&s, flip);
+    global_sign *= not_neg_one * 2 - 1;
+    skew = 1 << bit;
+#else
+    /* Otherwise, we just negate to force oddness */
+    int is_even = secp256k1_scalar_is_even(&s);
+    global_sign = secp256k1_scalar_cond_negate(&s, is_even);
+#endif
+
+    /* 4 */
+    u_last = secp256k1_scalar_shr_int(&s, w);
+    while (word * w < WNAF_BITS) {
+        int sign;
+        int even;
+
+        /* 4.1 4.4 */
+        u = secp256k1_scalar_shr_int(&s, w);
+        /* 4.2 */
+        even = ((u & 1) == 0);
+        sign = 2 * (u_last > 0) - 1;
+        u += sign * even;
+        u_last -= sign * even * (1 << w);
+
+        /* 4.3, adapted for global sign change */
+        wnaf[word++] = u_last * global_sign;
+
+        u_last = u;
+    }
+    wnaf[word] = u * global_sign;
+
+    VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+    VERIFY_CHECK(word == WNAF_SIZE(w));
+    return skew;
+}
+
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int skew_1;
+    int skew_lam;
+    secp256k1_scalar q_1, q_lam;
+#else
+    int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)];
+#endif
+
+    int i;
+    secp256k1_scalar sc = *scalar;
+
+    /* build wnaf representation for q. */
+#ifdef USE_ENDOMORPHISM
+    /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+    /* no need for zero correction when using endomorphism since even
+     * numbers have one added to them anyway */
+    skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1);
+    skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
+#else
+    int is_zero = secp256k1_scalar_is_zero(scalar);
+    /* the wNAF ladder cannot handle zero, so bump this to one .. we will
+     * correct the result after the fact */
+    sc.d[0] += is_zero;
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc));
+
+    secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1);
+#endif
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_fe_normalize_weak(&pre_a[i].y);
+    }
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+#endif
+
+    /* first loop iteration (separated out so we can directly set r, rather
+     * than having it start at infinity, get doubled several times, then have
+     * its new value added to it) */
+#ifdef USE_ENDOMORPHISM
+    i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+
+    i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+    secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+    i = wnaf[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+#endif
+    /* remaining loop iterations */
+    for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
+        int n;
+        int j;
+        for (j = 0; j < WINDOW_A - 1; ++j) {
+            secp256k1_gej_double_nonzero(r, r, NULL);
+        }
+#ifdef USE_ENDOMORPHISM
+        n = wnaf_1[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+
+        n = wnaf_lam[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+        n = wnaf[i];
+        VERIFY_CHECK(n != 0);
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#endif
+    }
+
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
+
+#ifdef USE_ENDOMORPHISM
+    {
+        /* Correct for wNAF skew */
+        secp256k1_ge correction = *a;
+        secp256k1_ge_storage correction_1_stor;
+        secp256k1_ge_storage correction_lam_stor;
+        secp256k1_ge_storage a2_stor;
+        secp256k1_gej tmpj;
+        secp256k1_gej_set_ge(&tmpj, &correction);
+        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+        secp256k1_ge_set_gej(&correction, &tmpj);
+        secp256k1_ge_to_storage(&correction_1_stor, a);
+        secp256k1_ge_to_storage(&correction_lam_stor, a);
+        secp256k1_ge_to_storage(&a2_stor, &correction);
+
+        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+        secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+
+        /* Apply the correction */
+        secp256k1_ge_from_storage(&correction, &correction_1_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+
+        secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_ge_mul_lambda(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+    }
+#else
+    /* correct for zero */
+    r->infinity |= is_zero;
+#endif
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/ecmult_gen.h

@@ -0,0 +1,43 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_GEN_
+#define _SECP256K1_ECMULT_GEN_
+
+#include "scalar.h"
+#include "group.h"
+
+typedef struct {
+    /* For accelerating the computation of a*G:
+     * To harden against timing attacks, use the following mechanism:
+     * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
+     * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
+     *   * U_i = U * 2^i (for i=0..62)
+     *   * U_i = U * (1-2^63) (for i=63)
+     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
+     * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
+     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
+     * None of the resulting prec group elements have a known scalar, and neither do any of
+     * the intermediate sums while computing a*G.
+     */
+    secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
+    secp256k1_scalar blind;
+    secp256k1_gej initial;
+} secp256k1_ecmult_gen_context;
+
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
+
+/** Multiply with the generator: R = a*G */
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
+
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
+
+#endif

crypto/secp256k1/libsecp256k1/src/ecmult_gen_impl.h

@@ -0,0 +1,205 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
+#define _SECP256K1_ECMULT_GEN_IMPL_H_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_gen.h"
+#include "hash_impl.h"
+#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
+#include "ecmult_static_context.h"
+#endif
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    secp256k1_ge prec[1024];
+    secp256k1_gej gj;
+    secp256k1_gej nums_gej;
+    int i, j;
+#endif
+
+    if (ctx->prec != NULL) {
+        return;
+    }
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+
+    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
+    {
+        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
+        secp256k1_fe nums_x;
+        secp256k1_ge nums_ge;
+        VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
+        VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
+        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
+        /* Add G to make the bits in x uniformly distributed. */
+        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
+    }
+
+    /* compute prec. */
+    {
+        secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
+        secp256k1_gej gbase;
+        secp256k1_gej numsbase;
+        gbase = gj; /* 16^j * G */
+        numsbase = nums_gej; /* 2^j * nums. */
+        for (j = 0; j < 64; j++) {
+            /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
+            precj[j*16] = numsbase;
+            for (i = 1; i < 16; i++) {
+                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
+            }
+            /* Multiply gbase by 16. */
+            for (i = 0; i < 4; i++) {
+                secp256k1_gej_double_var(&gbase, &gbase, NULL);
+            }
+            /* Multiply numbase by 2. */
+            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
+            if (j == 62) {
+                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
+                secp256k1_gej_neg(&numsbase, &numsbase);
+                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
+            }
+        }
+        secp256k1_ge_set_all_gej_var(1024, prec, precj, cb);
+    }
+    for (j = 0; j < 64; j++) {
+        for (i = 0; i < 16; i++) {
+            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
+        }
+    }
+#else
+    (void)cb;
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
+#endif
+    secp256k1_ecmult_gen_blind(ctx, NULL);
+}
+
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
+    return ctx->prec != NULL;
+}
+
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
+    if (src->prec == NULL) {
+        dst->prec = NULL;
+    } else {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+        dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
+        memcpy(dst->prec, src->prec, sizeof(*dst->prec));
+#else
+        (void)cb;
+        dst->prec = src->prec;
+#endif
+        dst->initial = src->initial;
+        dst->blind = src->blind;
+    }
+}
+
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    free(ctx->prec);
+#endif
+    secp256k1_scalar_clear(&ctx->blind);
+    secp256k1_gej_clear(&ctx->initial);
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    secp256k1_ge add;
+    secp256k1_ge_storage adds;
+    secp256k1_scalar gnb;
+    int bits;
+    int i, j;
+    memset(&adds, 0, sizeof(adds));
+    *r = ctx->initial;
+    /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
+    secp256k1_scalar_add(&gnb, gn, &ctx->blind);
+    add.infinity = 0;
+    for (j = 0; j < 64; j++) {
+        bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
+        for (i = 0; i < 16; i++) {
+            /** This uses a conditional move to avoid any secret data in array indexes.
+             *   _Any_ use of secret indexes has been demonstrated to result in timing
+             *   sidechannels, even when the cache-line access patterns are uniform.
+             *  See also:
+             *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
+             *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
+             *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
+             *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
+             *    (http://www.tau.ac.il/~tromer/papers/cache.pdf)
+             */
+            secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
+        }
+        secp256k1_ge_from_storage(&add, &adds);
+        secp256k1_gej_add_ge(r, r, &add);
+    }
+    bits = 0;
+    secp256k1_ge_clear(&add);
+    secp256k1_scalar_clear(&gnb);
+}
+
+/* Setup blinding values for secp256k1_ecmult_gen. */
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+    secp256k1_scalar b;
+    secp256k1_gej gb;
+    secp256k1_fe s;
+    unsigned char nonce32[32];
+    secp256k1_rfc6979_hmac_sha256_t rng;
+    int retry;
+    unsigned char keydata[64] = {0};
+    if (seed32 == NULL) {
+        /* When seed is NULL, reset the initial point and blinding value. */
+        secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
+        secp256k1_gej_neg(&ctx->initial, &ctx->initial);
+        secp256k1_scalar_set_int(&ctx->blind, 1);
+    }
+    /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
+    secp256k1_scalar_get_b32(nonce32, &ctx->blind);
+    /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
+     *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
+     *   asking the caller for blinding values directly and expecting them to retry on failure.
+     */
+    memcpy(keydata, nonce32, 32);
+    if (seed32 != NULL) {
+        memcpy(keydata + 32, seed32, 32);
+    }
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+    memset(keydata, 0, sizeof(keydata));
+    /* Retry for out of range results to achieve uniformity. */
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        retry = !secp256k1_fe_set_b32(&s, nonce32);
+        retry |= secp256k1_fe_is_zero(&s);
+    } while (retry);
+    /* Randomize the projection to defend against multiplier sidechannels. */
+    secp256k1_gej_rescale(&ctx->initial, &s);
+    secp256k1_fe_clear(&s);
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        secp256k1_scalar_set_b32(&b, nonce32, &retry);
+        /* A blinding value of 0 works, but would undermine the projection hardening. */
+        retry |= secp256k1_scalar_is_zero(&b);
+    } while (retry);
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+    memset(nonce32, 0, 32);
+    secp256k1_ecmult_gen(ctx, &gb, &b);
+    secp256k1_scalar_negate(&b, &b);
+    ctx->blind = b;
+    ctx->initial = gb;
+    secp256k1_scalar_clear(&b);
+    secp256k1_gej_clear(&gb);
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/ecmult_impl.h

@@ -0,0 +1,389 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_IMPL_H_
+#define _SECP256K1_ECMULT_IMPL_H_
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+
+/* optimal for 128-bit and 256-bit exponents. */
+#define WINDOW_A 5
+
+/** larger numbers may result in slightly better performance, at the cost of
+    exponentially larger precomputed tables. */
+#ifdef USE_ENDOMORPHISM
+/** Two tables for window size 15: 1.375 MiB. */
+#define WINDOW_G 15
+#else
+/** One table for window size 16: 1.375 MiB. */
+#define WINDOW_G 16
+#endif
+
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
+
+/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
+ *  the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
+ *  contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
+ *  Prej's Z values are undefined, except for the last value.
+ */
+static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
+    secp256k1_gej d;
+    secp256k1_ge a_ge, d_ge;
+    int i;
+
+    VERIFY_CHECK(!a->infinity);
+
+    secp256k1_gej_double_var(&d, a, NULL);
+
+    /*
+     * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
+     * of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
+     */
+    d_ge.x = d.x;
+    d_ge.y = d.y;
+    d_ge.infinity = 0;
+
+    secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
+    prej[0].x = a_ge.x;
+    prej[0].y = a_ge.y;
+    prej[0].z = a->z;
+    prej[0].infinity = 0;
+
+    zr[0] = d.z;
+    for (i = 1; i < n; i++) {
+        secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
+    }
+
+    /*
+     * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
+     * the final point's z coordinate is actually used though, so just update that.
+     */
+    secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
+}
+
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ *  There are two versions of this function:
+ *  - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
+ *    resulting point set to a single constant Z denominator, stores the X and Y
+ *    coordinates as ge_storage points in pre, and stores the global Z in rz.
+ *    It only operates on tables sized for WINDOW_A wnaf multiples.
+ *  - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
+ *    resulting point set to actually affine points, and stores those in pre.
+ *    It operates on tables of any size, but uses heap-allocated temporaries.
+ *
+ *  To compute a*P + b*G, we compute a table for P using the first function,
+ *  and for G using the second (which requires an inverse, but it only needs to
+ *  happen once).
+ */
+static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+    secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
+    /* Bring them to the same Z denominator. */
+    secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
+}
+
+static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
+    secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
+    secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
+    secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
+    int i;
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
+    /* Convert them in batch to affine coordinates. */
+    secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
+    /* Convert them to compact storage form. */
+    for (i = 0; i < n; i++) {
+        secp256k1_ge_to_storage(&pre[i], &prea[i]);
+    }
+
+    free(prea);
+    free(prej);
+    free(zr);
+}
+
+/** The following two macro retrieves a particular odd multiple from a table
+ *  of precomputed multiples. */
+#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    if ((n) > 0) { \
+        *(r) = (pre)[((n)-1)/2]; \
+    } else { \
+        secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
+    } \
+} while(0)
+
+#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    if ((n) > 0) { \
+        secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
+    } else { \
+        secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
+        secp256k1_ge_neg((r), (r)); \
+    } \
+} while(0)
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
+    ctx->pre_g = NULL;
+#ifdef USE_ENDOMORPHISM
+    ctx->pre_g_128 = NULL;
+#endif
+}
+
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
+    secp256k1_gej gj;
+
+    if (ctx->pre_g != NULL) {
+        return;
+    }
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+
+    ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+
+    /* precompute the tables with odd multiples */
+    secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
+
+#ifdef USE_ENDOMORPHISM
+    {
+        secp256k1_gej g_128j;
+        int i;
+
+        ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+
+        /* calculate 2^128*generator */
+        g_128j = gj;
+        for (i = 0; i < 128; i++) {
+            secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
+        }
+        secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
+    }
+#endif
+}
+
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
+    if (src->pre_g == NULL) {
+        dst->pre_g = NULL;
+    } else {
+        size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
+        dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
+        memcpy(dst->pre_g, src->pre_g, size);
+    }
+#ifdef USE_ENDOMORPHISM
+    if (src->pre_g_128 == NULL) {
+        dst->pre_g_128 = NULL;
+    } else {
+        size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
+        dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
+        memcpy(dst->pre_g_128, src->pre_g_128, size);
+    }
+#endif
+}
+
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
+    return ctx->pre_g != NULL;
+}
+
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
+    free(ctx->pre_g);
+#ifdef USE_ENDOMORPHISM
+    free(ctx->pre_g_128);
+#endif
+    secp256k1_ecmult_context_init(ctx);
+}
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
+ *  with the following guarantees:
+ *  - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
+ *  - two non-zero entries in wnaf are separated by at least w-1 zeroes.
+ *  - the number of set values in wnaf is returned. This number is at most 256, and at most one more
+ *    than the number of bits in the (absolute value) of the input.
+ */
+static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
+    secp256k1_scalar s = *a;
+    int last_set_bit = -1;
+    int bit = 0;
+    int sign = 1;
+    int carry = 0;
+
+    VERIFY_CHECK(wnaf != NULL);
+    VERIFY_CHECK(0 <= len && len <= 256);
+    VERIFY_CHECK(a != NULL);
+    VERIFY_CHECK(2 <= w && w <= 31);
+
+    memset(wnaf, 0, len * sizeof(wnaf[0]));
+
+    if (secp256k1_scalar_get_bits(&s, 255, 1)) {
+        secp256k1_scalar_negate(&s, &s);
+        sign = -1;
+    }
+
+    while (bit < len) {
+        int now;
+        int word;
+        if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
+            bit++;
+            continue;
+        }
+
+        now = w;
+        if (now > len - bit) {
+            now = len - bit;
+        }
+
+        word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
+
+        carry = (word >> (w-1)) & 1;
+        word -= carry << w;
+
+        wnaf[bit] = sign * word;
+        last_set_bit = bit;
+
+        bit += now;
+    }
+#ifdef VERIFY
+    CHECK(carry == 0);
+    while (bit < 256) {
+        CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
+    } 
+#endif
+    return last_set_bit + 1;
+}
+
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_scalar na_1, na_lam;
+    /* Splitted G factors. */
+    secp256k1_scalar ng_1, ng_128;
+    int wnaf_na_1[130];
+    int wnaf_na_lam[130];
+    int bits_na_1;
+    int bits_na_lam;
+    int wnaf_ng_1[129];
+    int bits_ng_1;
+    int wnaf_ng_128[129];
+    int bits_ng_128;
+#else
+    int wnaf_na[256];
+    int bits_na;
+    int wnaf_ng[256];
+    int bits_ng;
+#endif
+    int i;
+    int bits;
+
+#ifdef USE_ENDOMORPHISM
+    /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&na_1, &na_lam, na);
+
+    /* build wnaf representation for na_1 and na_lam. */
+    bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   130, &na_1,   WINDOW_A);
+    bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
+    VERIFY_CHECK(bits_na_1 <= 130);
+    VERIFY_CHECK(bits_na_lam <= 130);
+    bits = bits_na_1;
+    if (bits_na_lam > bits) {
+        bits = bits_na_lam;
+    }
+#else
+    /* build wnaf representation for na. */
+    bits_na     = secp256k1_ecmult_wnaf(wnaf_na,     256, na,      WINDOW_A);
+    bits = bits_na;
+#endif
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     * The exception is the precomputed G table points, which are actually
+     * affine. Compared to the base used for other points, they have a Z ratio
+     * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+     * isomorphism to efficiently add with a known Z inverse.
+     */
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
+
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+
+    /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
+    secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
+
+    /* Build wnaf representation for ng_1 and ng_128 */
+    bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   129, &ng_1,   WINDOW_G);
+    bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
+    if (bits_ng_1 > bits) {
+        bits = bits_ng_1;
+    }
+    if (bits_ng_128 > bits) {
+        bits = bits_ng_128;
+    }
+#else
+    bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     256, ng,      WINDOW_G);
+    if (bits_ng > bits) {
+        bits = bits_ng;
+    }
+#endif
+
+    secp256k1_gej_set_infinity(r);
+
+    for (i = bits - 1; i >= 0; i--) {
+        int n;
+        secp256k1_gej_double_var(r, r, NULL);
+#ifdef USE_ENDOMORPHISM
+        if (i < bits_na_1 && (n = wnaf_na_1[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+        if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+#else
+        if (i < bits_na && (n = wnaf_na[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_ng && (n = wnaf_ng[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+#endif
+    }
+
+    if (!r->infinity) {
+        secp256k1_fe_mul(&r->z, &r->z, &Z);
+    }
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/field.h

@@ -31,86 +31,89 @@
 #endif
 
 /** Normalize a field element. */
-static void secp256k1_fe_normalize(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize(secp256k1_fe *r);
 
 /** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
 
 /** Normalize a field element, without constant-time guarantee. */
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
 
 /** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
  *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r);
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
 
 /** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
  *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r);
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
 
 /** Set a field element equal to a small integer. Resulting field element is normalized. */
-static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
 /** Verify whether a field element is zero. Requires the input to be normalized. */
-static int secp256k1_fe_is_zero(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 
 /** Check the "oddness" of a field element. Requires the input to be normalized. */
-static int secp256k1_fe_is_odd(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
 
 /** Compare two field elements. Requires magnitude-1 inputs. */
-static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
 /** Compare two field elements. Requires both inputs to be normalized */
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
-/** Set a field element equal to 32-byte big endian value. If succesful, the resulting field element is normalized. */
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a);
+/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
 
 /** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
  *  as an argument. The magnitude of the output is one higher. */
-static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m);
+static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
 
 /** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
  *  small integer. */
-static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
 
 /** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
-static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
  *  The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b);
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
 
 /** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
  *  The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Sets a field element to be the (modular) square root (if any exist) of another. Requires the
  *  input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be
  *  normalized). Return value indicates whether a square root was found. */
-static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
  *  at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
-static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
  *  at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
  *  outputs must not overlap in memory. */
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Convert a field element to the storage type. */
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t*);
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
 
 /** Convert a field element back from the storage type. */
-static void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t*);
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
 
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag);
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
 
 #endif

crypto/secp256k1/libsecp256k1/src/field_10x26.h

@@ -16,20 +16,20 @@ typedef struct {
     int magnitude;
     int normalized;
 #endif
-} secp256k1_fe_t;
+} secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
 #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
     (d0) & 0x3FFFFFFUL, \
-    ((d0) >> 26) | ((d1) & 0xFFFFFUL) << 6, \
-    ((d1) >> 20) | ((d2) & 0x3FFFUL) << 12, \
-    ((d2) >> 14) | ((d3) & 0xFFUL) << 18, \
-    ((d3) >> 8) | ((d4) & 0x3) << 24, \
-    ((d4) >> 2) & 0x3FFFFFFUL, \
-    ((d4) >> 28) | ((d5) & 0x3FFFFFUL) << 4, \
-    ((d5) >> 22) | ((d6) & 0xFFFF) << 10, \
-    ((d6) >> 16) | ((d7) & 0x3FF) << 16, \
-    ((d7) >> 10) \
+    (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
+    (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
+    (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
+    (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
+    (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
+    (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
+    (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
+    (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
+    (((uint32_t)d7) >> 10) \
 }
 
 #ifdef VERIFY
@@ -40,8 +40,8 @@ typedef struct {
 
 typedef struct {
     uint32_t n[8];
-} secp256k1_fe_storage_t;
+} secp256k1_fe_storage;
 
 #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
-
+#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
 #endif

crypto/secp256k1/libsecp256k1/src/field_10x26_impl.h

@@ -14,7 +14,7 @@
 #include "field.h"
 
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     const uint32_t *d = a->n;
     int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
     r &= (d[0] <= 0x3FFFFFFUL * m);
@@ -41,12 +41,12 @@ static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
     VERIFY_CHECK(r == 1);
 }
 #else
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     (void)a;
 }
 #endif
 
-static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -101,7 +101,7 @@ static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -132,7 +132,7 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -188,7 +188,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -217,7 +217,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
     uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
     uint32_t z0, z1;
     uint32_t x;
@@ -252,7 +252,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     t9 &= 0x03FFFFFUL;
     t1 += (x << 6);
 
-    t1 += (t0 >> 26); t0  = z0;
+    t1 += (t0 >> 26);
     t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
     t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
     t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
@@ -269,7 +269,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
 #ifdef VERIFY
@@ -279,7 +279,7 @@ SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
     const uint32_t *t = a->n;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -288,7 +288,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
     return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
@@ -296,7 +296,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     a->magnitude = 0;
@@ -307,7 +307,7 @@ SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -326,7 +326,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
     int i;
     r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
     r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
@@ -350,7 +350,7 @@ static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -368,7 +368,7 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
     }
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
@@ -390,7 +390,7 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp25
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -408,7 +408,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     secp256k1_fe_verify(a);
 #endif
@@ -1039,7 +1039,7 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t
 }
 
 
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b) {
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     VERIFY_CHECK(b->magnitude <= 8);
@@ -1055,7 +1055,7 @@ static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const s
 #endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     secp256k1_fe_verify(a);
@@ -1068,7 +1068,29 @@ static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint32_t mask0, mask1;
+    mask0 = flag + ~((uint32_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+    r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
+    r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
+    r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
+    r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
+    r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
+#ifdef VERIFY
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint32_t mask0, mask1;
     mask0 = flag + ~((uint32_t)0);
     mask1 = ~mask0;
@@ -1082,7 +1104,7 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r
     r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
 #endif
@@ -1096,7 +1118,7 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_f
     r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) {
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0x3FFFFFFUL;
     r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
     r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);

crypto/secp256k1/libsecp256k1/src/field_5x52.h

@@ -16,15 +16,15 @@ typedef struct {
     int magnitude;
     int normalized;
 #endif
-} secp256k1_fe_t;
+} secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
 #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
-    (d0) | ((uint64_t)(d1) & 0xFFFFFUL) << 32, \
-    ((d1) >> 20) | ((uint64_t)(d2)) << 12 | ((uint64_t)(d3) & 0xFFUL) << 44, \
-    ((d3) >> 8) | ((uint64_t)(d4) & 0xFFFFFFFUL) << 24, \
-    ((d4) >> 28) | ((uint64_t)(d5)) << 4 | ((uint64_t)(d6) & 0xFFFFUL) << 36, \
-    ((d6) >> 16) | ((uint64_t)(d7)) << 16 \
+    (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
+    ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
+    ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
+    ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
+    ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
 }
 
 #ifdef VERIFY
@@ -35,13 +35,13 @@ typedef struct {
 
 typedef struct {
     uint64_t n[4];
-} secp256k1_fe_storage_t;
+} secp256k1_fe_storage;
 
 #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
-    (d0) | ((uint64_t)(d1)) << 32, \
-    (d2) | ((uint64_t)(d3)) << 32, \
-    (d4) | ((uint64_t)(d5)) << 32, \
-    (d6) | ((uint64_t)(d7)) << 32 \
+    (d0) | (((uint64_t)(d1)) << 32), \
+    (d2) | (((uint64_t)(d3)) << 32), \
+    (d4) | (((uint64_t)(d5)) << 32), \
+    (d6) | (((uint64_t)(d7)) << 32) \
 }}
 
 #endif

crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h

@@ -31,7 +31,7 @@
  */
 
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     const uint64_t *d = a->n;
     int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
    /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
@@ -51,12 +51,12 @@ static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
     VERIFY_CHECK(r == 1);
 }
 #else
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     (void)a;
 }
 #endif
 
-static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -99,7 +99,7 @@ static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -123,7 +123,7 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -167,7 +167,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
@@ -190,7 +190,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
     uint64_t t0, t1, t2, t3, t4;
     uint64_t z0, z1;
     uint64_t x;
@@ -219,7 +219,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
 
     t4 &= 0x0FFFFFFFFFFFFULL;
 
-    t1 += (t0 >> 52); t0  = z0;
+    t1 += (t0 >> 52);
     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
@@ -231,7 +231,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
 #ifdef VERIFY
@@ -241,7 +241,7 @@ SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
     const uint64_t *t = a->n;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -250,7 +250,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
     return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
@@ -258,7 +258,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     a->magnitude = 0;
@@ -269,7 +269,7 @@ SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -288,7 +288,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
     int i;
     r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
     for (i=0; i<32; i++) {
@@ -311,7 +311,7 @@ static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -329,7 +329,7 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
     }
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
@@ -346,7 +346,7 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp25
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -359,7 +359,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     secp256k1_fe_verify(a);
 #endif
@@ -375,7 +375,7 @@ SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1
 #endif
 }
 
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b) {
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     VERIFY_CHECK(b->magnitude <= 8);
@@ -391,7 +391,7 @@ static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const s
 #endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     secp256k1_fe_verify(a);
@@ -404,7 +404,24 @@ static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint64_t mask0, mask1;
+    mask0 = flag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+#ifdef VERIFY
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint64_t mask0, mask1;
     mask0 = flag + ~((uint64_t)0);
     mask1 = ~mask0;
@@ -414,7 +431,7 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r
     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
 #endif
@@ -424,7 +441,7 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_f
     r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) {
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
     r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
     r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);

crypto/secp256k1/libsecp256k1/src/field_impl.h

@@ -21,15 +21,15 @@
 #error "Please select field implementation"
 #endif
 
-SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
-    secp256k1_fe_t na;
+SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
     secp256k1_fe_negate(&na, a, 1);
     secp256k1_fe_add(&na, b);
     return secp256k1_fe_normalizes_to_zero_var(&na);
 }
 
-static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
     int j;
 
     /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
@@ -117,8 +117,8 @@ static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
     return secp256k1_fe_equal_var(&t1, a);
 }
 
-static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
     int j;
 
     /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
@@ -207,11 +207,15 @@ static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
     secp256k1_fe_mul(r, a, &t1);
 }
 
-static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
 #if defined(USE_FIELD_INV_BUILTIN)
     secp256k1_fe_inv(r, a);
 #elif defined(USE_FIELD_INV_NUM)
-    secp256k1_num_t n, m;
+    secp256k1_num n, m;
+    static const secp256k1_fe negone = SECP256K1_FE_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
+    );
     /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
     static const unsigned char prime[32] = {
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
@@ -220,7 +224,7 @@ static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
         0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
     };
     unsigned char b[32];
-    secp256k1_fe_t c = *a;
+    secp256k1_fe c = *a;
     secp256k1_fe_normalize_var(&c);
     secp256k1_fe_get_b32(b, &c);
     secp256k1_num_set_bin(&n, b, 32);
@@ -228,13 +232,17 @@ static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
     secp256k1_num_mod_inverse(&n, &n, &m);
     secp256k1_num_get_bin(b, 32, &n);
     VERIFY_CHECK(secp256k1_fe_set_b32(r, b));
+    /* Verify the result is the (unique) valid inverse using non-GMP code. */
+    secp256k1_fe_mul(&c, &c, r);
+    secp256k1_fe_add(&c, &negone);
+    CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
 #else
 #error "Please select field inverse implementation"
 #endif
 }
 
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t u;
+static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe u;
     size_t i;
     if (len < 1) {
         return;
@@ -252,7 +260,7 @@ static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp25
     secp256k1_fe_inv_var(&u, &r[--i]);
 
     while (i > 0) {
-        int j = i--;
+        size_t j = i--;
         secp256k1_fe_mul(&r[j], &r[i], &u);
         secp256k1_fe_mul(&u, &u, &a[j]);
     }

crypto/secp256k1/libsecp256k1/src/gen_context.c

@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields           *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#define USE_BASIC_CONFIG 1
+
+#include "basic-config.h"
+#include "include/secp256k1.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_gen_impl.h"
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+int main(int argc, char **argv) {
+    secp256k1_ecmult_gen_context ctx;
+    int inner;
+    int outer;
+    FILE* fp;
+
+    (void)argc;
+    (void)argv;
+
+    fp = fopen("src/ecmult_static_context.h","w");
+    if (fp == NULL) {
+        fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n");
+        return -1;
+    }
+    
+    fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#include \"group.h\"\n");
+    fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
+    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = {\n");
+
+    secp256k1_ecmult_gen_context_init(&ctx);
+    secp256k1_ecmult_gen_context_build(&ctx, &default_error_callback);
+    for(outer = 0; outer != 64; outer++) {
+        fprintf(fp,"{\n");
+        for(inner = 0; inner != 16; inner++) {
+            fprintf(fp,"    SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
+            if (inner != 15) {
+                fprintf(fp,",\n");
+            } else {
+                fprintf(fp,"\n");
+            }
+        }
+        if (outer != 63) {
+            fprintf(fp,"},\n");
+        } else {
+            fprintf(fp,"}\n");
+        }
+    }
+    fprintf(fp,"};\n");
+    secp256k1_ecmult_gen_context_clear(&ctx);
+    
+    fprintf(fp, "#undef SC\n");
+    fprintf(fp, "#endif\n");
+    fclose(fp);
+    
+    return 0;
+}

crypto/secp256k1/libsecp256k1/src/group.h

@@ -0,0 +1,141 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_GROUP_
+#define _SECP256K1_GROUP_
+
+#include "num.h"
+#include "field.h"
+
+/** A group element of the secp256k1 curve, in affine coordinates. */
+typedef struct {
+    secp256k1_fe x;
+    secp256k1_fe y;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_ge;
+
+#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
+#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+/** A group element of the secp256k1 curve, in jacobian coordinates. */
+typedef struct {
+    secp256k1_fe x; /* actual X: x/z^2 */
+    secp256k1_fe y; /* actual Y: y/z^3 */
+    secp256k1_fe z;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_gej;
+
+#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
+#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+typedef struct {
+    secp256k1_fe_storage x;
+    secp256k1_fe_storage y;
+} secp256k1_ge_storage;
+
+#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
+
+#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
+
+/** Set a group element equal to the point at infinity */
+static void secp256k1_ge_set_infinity(secp256k1_ge *r);
+
+/** Set a group element equal to the point with given X and Y coordinates */
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
+ *  for Y. Return value indicates whether the result is valid. */
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
+
+/** Check whether a group element is valid (i.e., on the curve). */
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates */
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
+
+/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb);
+
+/** Set a batch of group elements equal to the inputs given in jacobian
+ *  coordinates (with known z-ratios). zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
+static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr);
+
+/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
+ *  the same global z "denominator". zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
+ *  coordinates of the result are stored in r, the common z coordinate is
+ *  stored in globalz. */
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
+
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej *r);
+
+/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
+static void secp256k1_gej_set_xy(secp256k1_gej *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
+
+/** Compare the X coordinate of a group element (jacobian). */
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
+ * a may not be zero. Constant time. */
+static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
+    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
+    guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
+
+#ifdef USE_ENDOMORPHISM
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
+#endif
+
+/** Clear a secp256k1_gej to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej *r);
+
+/** Clear a secp256k1_ge to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge *r);
+
+/** Convert a group element to the storage type. */
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
+
+/** Convert a group element back from the storage type. */
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
+
+/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
+
+#endif

crypto/secp256k1/libsecp256k1/src/group_impl.h

@@ -0,0 +1,632 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_GROUP_IMPL_H_
+#define _SECP256K1_GROUP_IMPL_H_
+
+#include <string.h>
+
+#include "num.h"
+#include "field.h"
+#include "group.h"
+
+/** Generator for secp256k1, value 'g' defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ */
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
+    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
+    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
+    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
+);
+
+static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
+    secp256k1_fe zi2; 
+    secp256k1_fe zi3;
+    secp256k1_fe_sqr(&zi2, zi);
+    secp256k1_fe_mul(&zi3, &zi2, zi);
+    secp256k1_fe_mul(&r->x, &a->x, &zi2);
+    secp256k1_fe_mul(&r->y, &a->y, &zi3);
+    r->infinity = a->infinity;
+}
+
+static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
+    r->infinity = 1;
+}
+
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
+    r->infinity = 0;
+    r->x = *x;
+    r->y = *y;
+}
+
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
+    return a->infinity;
+}
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
+    *r = *a;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    secp256k1_fe_inv(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    if (a->infinity) {
+        return;
+    }
+    secp256k1_fe_inv_var(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb) {
+    secp256k1_fe *az;
+    secp256k1_fe *azi;
+    size_t i;
+    size_t count = 0;
+    az = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * len);
+    for (i = 0; i < len; i++) {
+        if (!a[i].infinity) {
+            az[count++] = a[i].z;
+        }
+    }
+
+    azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
+    secp256k1_fe_inv_all_var(count, azi, az);
+    free(az);
+
+    count = 0;
+    for (i = 0; i < len; i++) {
+        r[i].infinity = a[i].infinity;
+        if (!a[i].infinity) {
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &azi[count++]);
+        }
+    }
+    free(azi);
+}
+
+static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zi;
+
+    if (len > 0) {
+        /* Compute the inverse of the last z coordinate, and use it to compute the last affine output. */
+        secp256k1_fe_inv(&zi, &a[i].z);
+        secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+
+        /* Work out way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            secp256k1_fe_mul(&zi, &zi, &zr[i]);
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+        }
+    }
+}
+
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zs;
+
+    if (len > 0) {
+        /* The z of the final point gives us the "global Z" for the table. */
+        r[i].x = a[i].x;
+        r[i].y = a[i].y;
+        *globalz = a[i].z;
+        r[i].infinity = 0;
+        zs = zr[i];
+
+        /* Work our way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            if (i != len - 1) {
+                secp256k1_fe_mul(&zs, &zs, &zr[i]);
+            }
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
+        }
+    }
+}
+
+static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
+    r->infinity = 1;
+    secp256k1_fe_set_int(&r->x, 0);
+    secp256k1_fe_set_int(&r->y, 0);
+    secp256k1_fe_set_int(&r->z, 0);
+}
+
+static void secp256k1_gej_set_xy(secp256k1_gej *r, const secp256k1_fe *x, const secp256k1_fe *y) {
+    r->infinity = 0;
+    r->x = *x;
+    r->y = *y;
+    secp256k1_fe_set_int(&r->z, 1);
+}
+
+static void secp256k1_gej_clear(secp256k1_gej *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_clear(secp256k1_ge *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+}
+
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
+    secp256k1_fe x2, x3, c;
+    r->x = *x;
+    secp256k1_fe_sqr(&x2, x);
+    secp256k1_fe_mul(&x3, x, &x2);
+    r->infinity = 0;
+    secp256k1_fe_set_int(&c, 7);
+    secp256k1_fe_add(&c, &x3);
+    if (!secp256k1_fe_sqrt_var(&r->y, &c)) {
+        return 0;
+    }
+    secp256k1_fe_normalize_var(&r->y);
+    if (secp256k1_fe_is_odd(&r->y) != odd) {
+        secp256k1_fe_negate(&r->y, &r->y, 1);
+    }
+    return 1;
+}
+
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
+   r->infinity = a->infinity;
+   r->x = a->x;
+   r->y = a->y;
+   secp256k1_fe_set_int(&r->z, 1);
+}
+
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
+    secp256k1_fe r, r2;
+    VERIFY_CHECK(!a->infinity);
+    secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
+    r2 = a->x; secp256k1_fe_normalize_weak(&r2);
+    return secp256k1_fe_equal_var(&r, &r2);
+}
+
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
+    r->infinity = a->infinity;
+    r->x = a->x;
+    r->y = a->y;
+    r->z = a->z;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
+    return a->infinity;
+}
+
+static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
+    secp256k1_fe y2, x3, z2, z6;
+    if (a->infinity) {
+        return 0;
+    }
+    /** y^2 = x^3 + 7
+     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
+     *  Y^2 / Z^6 = X^3 / Z^6 + 7
+     *  Y^2 = X^3 + 7*Z^6
+     */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
+    secp256k1_fe_mul_int(&z6, 7);
+    secp256k1_fe_add(&x3, &z6);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
+    secp256k1_fe y2, x3, c;
+    if (a->infinity) {
+        return 0;
+    }
+    /* y^2 = x^3 + 7 */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_set_int(&c, 7);
+    secp256k1_fe_add(&x3, &c);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate */
+    secp256k1_fe t1,t2,t3,t4;
+    /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
+     *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
+     *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
+     */
+    r->infinity = a->infinity;
+    if (r->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        return;
+    }
+
+    if (rzr != NULL) {
+        *rzr = a->y;
+        secp256k1_fe_normalize_weak(rzr);
+        secp256k1_fe_mul_int(rzr, 2);
+    }
+
+    secp256k1_fe_mul(&r->z, &a->z, &a->y);
+    secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
+    secp256k1_fe_sqr(&t1, &a->x);
+    secp256k1_fe_mul_int(&t1, 3);         /* T1 = 3*X^2 (3) */
+    secp256k1_fe_sqr(&t2, &t1);           /* T2 = 9*X^4 (1) */
+    secp256k1_fe_sqr(&t3, &a->y);
+    secp256k1_fe_mul_int(&t3, 2);         /* T3 = 2*Y^2 (2) */
+    secp256k1_fe_sqr(&t4, &t3);
+    secp256k1_fe_mul_int(&t4, 2);         /* T4 = 8*Y^4 (2) */
+    secp256k1_fe_mul(&t3, &t3, &a->x);    /* T3 = 2*X*Y^2 (1) */
+    r->x = t3;
+    secp256k1_fe_mul_int(&r->x, 4);       /* X' = 8*X*Y^2 (4) */
+    secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
+    secp256k1_fe_add(&r->x, &t2);         /* X' = 9*X^4 - 8*X*Y^2 (6) */
+    secp256k1_fe_negate(&t2, &t2, 1);     /* T2 = -9*X^4 (2) */
+    secp256k1_fe_mul_int(&t3, 6);         /* T3 = 12*X*Y^2 (6) */
+    secp256k1_fe_add(&t3, &t2);           /* T3 = 12*X*Y^2 - 9*X^4 (8) */
+    secp256k1_fe_mul(&r->y, &t1, &t3);    /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
+    secp256k1_fe_negate(&t2, &t4, 2);     /* T2 = -8*Y^4 (3) */
+    secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
+}
+
+static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
+    secp256k1_gej_double_var(r, a, rzr);
+}
+
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
+    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        *r = *b;
+        return;
+    }
+
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+
+    r->infinity = 0;
+    secp256k1_fe_sqr(&z22, &b->z);
+    secp256k1_fe_sqr(&z12, &a->z);
+    secp256k1_fe_mul(&u1, &a->x, &z22);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    secp256k1_fe_mul(&h, &h, &b->z);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
+    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        secp256k1_gej_set_ge(r, b);
+        return;
+    }
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+    r->infinity = 0;
+
+    secp256k1_fe_sqr(&z12, &a->z);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
+    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
+    if (a->infinity) {
+        secp256k1_fe bzinv2, bzinv3;
+        r->infinity = b->infinity;
+        secp256k1_fe_sqr(&bzinv2, bzinv);
+        secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
+        secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
+        secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
+        secp256k1_fe_set_int(&r->z, 1);
+        return;
+    }
+    r->infinity = 0;
+
+    /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
+     *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
+     *  by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
+     *  This means that (rx,ry,rz) can be calculated as
+     *  (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
+     *  The variable az below holds the modified Z coordinate for a, which is used
+     *  for the computation of rx and ry, but not for rz.
+     */
+    secp256k1_fe_mul(&az, &a->z, bzinv);
+
+    secp256k1_fe_sqr(&z12, &az);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, NULL);
+        } else {
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
+    /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
+    static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
+    secp256k1_fe m_alt, rr_alt;
+    int infinity, degenerate;
+    VERIFY_CHECK(!b->infinity);
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+
+    /** In:
+     *    Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
+     *    In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
+     *  we find as solution for a unified addition/doubling formula:
+     *    lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
+     *    x3 = lambda^2 - (x1 + x2)
+     *    2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
+     *
+     *  Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
+     *    U1 = X1*Z2^2, U2 = X2*Z1^2
+     *    S1 = Y1*Z2^3, S2 = Y2*Z1^3
+     *    Z = Z1*Z2
+     *    T = U1+U2
+     *    M = S1+S2
+     *    Q = T*M^2
+     *    R = T^2-U1*U2
+     *    X3 = 4*(R^2-Q)
+     *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
+     *    Z3 = 2*M*Z
+     *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
+     *
+     *  This formula has the benefit of being the same for both addition
+     *  of distinct points and doubling. However, it breaks down in the
+     *  case that either point is infinity, or that y1 = -y2. We handle
+     *  these cases in the following ways:
+     *
+     *    - If b is infinity we simply bail by means of a VERIFY_CHECK.
+     *
+     *    - If a is infinity, we detect this, and at the end of the
+     *      computation replace the result (which will be meaningless,
+     *      but we compute to be constant-time) with b.x : b.y : 1.
+     *
+     *    - If a = -b, we have y1 = -y2, which is a degenerate case.
+     *      But here the answer is infinity, so we simply set the
+     *      infinity flag of the result, overriding the computed values
+     *      without even needing to cmov.
+     *
+     *    - If y1 = -y2 but x1 != x2, which does occur thanks to certain
+     *      properties of our curve (specifically, 1 has nontrivial cube
+     *      roots in our field, and the curve equation has no x coefficient)
+     *      then the answer is not infinity but also not given by the above
+     *      equation. In this case, we cmov in place an alternate expression
+     *      for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
+     *      expressions for lambda are defined, they are equal, and can be
+     *      obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
+     *      then substitution of x^3 + 7 for y^2 (using the curve equation).
+     *      For all pairs of nonzero points (a, b) at least one is defined,
+     *      so this covers everything.
+     */
+
+    secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
+    secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
+    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z1^2 (1) */
+    secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
+    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
+    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
+    secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
+    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 */
+    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (2) */
+    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (3) */
+    /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
+     *  case that Z = z1z2 = 0, and this is special-cased later on). */
+    degenerate = secp256k1_fe_normalizes_to_zero(&m) &
+                 secp256k1_fe_normalizes_to_zero(&rr);
+    /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
+     * This means either x1 == beta*x2 or beta*x1 == x2, where beta is
+     * a nontrivial cube root of one. In either case, an alternate
+     * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
+     * so we set R/M equal to this. */
+    rr_alt = s1;
+    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
+    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 */
+
+    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
+    secp256k1_fe_cmov(&m_alt, &m, !degenerate);
+    /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
+     * From here on out Ralt and Malt represent the numerator
+     * and denominator of lambda; R and M represent the explicit
+     * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
+    secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
+    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*Malt^2 (1) */
+    /* These two lines use the observation that either M == Malt or M == 0,
+     * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
+     * zero (which is "computed" by cmov). So the cost is one squaring
+     * versus two multiplications. */
+    secp256k1_fe_sqr(&n, &n);
+    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
+    secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
+    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Malt*Z (1) */
+    infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
+    secp256k1_fe_mul_int(&r->z, 2);                     /* r->z = Z3 = 2*Malt*Z (2) */
+    secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2-Q (3) */
+    secp256k1_fe_normalize_weak(&t);
+    r->x = t;                                           /* r->x = Ralt^2-Q (1) */
+    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*x3 (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = 2*x3 - Q: (4) */
+    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*x3 - Q) (1) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
+    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_mul_int(&r->x, 4);                     /* r->x = X3 = 4*(Ralt^2-Q) */
+    secp256k1_fe_mul_int(&r->y, 4);                     /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
+
+    /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
+    secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
+    secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
+    secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
+    r->infinity = infinity;
+}
+
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
+    /* Operations: 4 mul, 1 sqr */
+    secp256k1_fe zz;
+    VERIFY_CHECK(!secp256k1_fe_is_zero(s));
+    secp256k1_fe_sqr(&zz, s);
+    secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
+    secp256k1_fe_mul(&r->y, &r->y, &zz);
+    secp256k1_fe_mul(&r->y, &r->y, s);                  /* r->y *= s^3 */
+    secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
+}
+
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
+    secp256k1_fe x, y;
+    VERIFY_CHECK(!a->infinity);
+    x = a->x;
+    secp256k1_fe_normalize(&x);
+    y = a->y;
+    secp256k1_fe_normalize(&y);
+    secp256k1_fe_to_storage(&r->x, &x);
+    secp256k1_fe_to_storage(&r->y, &y);
+}
+
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
+    secp256k1_fe_from_storage(&r->x, &a->x);
+    secp256k1_fe_from_storage(&r->y, &a->y);
+    r->infinity = 0;
+}
+
+static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
+    secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
+    secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
+    static const secp256k1_fe beta = SECP256K1_FE_CONST(
+        0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
+        0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
+    );
+    *r = *a;
+    secp256k1_fe_mul(&r->x, &r->x, &beta);
+}
+#endif
+
+#endif

crypto/secp256k1/libsecp256k1/src/hash.h

@@ -34,7 +34,7 @@ typedef struct {
     int retry;
 } secp256k1_rfc6979_hmac_sha256_t;
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen);
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen);
 static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen);
 static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng);
 

crypto/secp256k1/libsecp256k1/src/hash_impl.h

@@ -202,7 +202,7 @@ static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsign
 }
 
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen) {
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen) {
     secp256k1_hmac_sha256_t hmac;
     static const unsigned char zero[1] = {0x00};
     static const unsigned char one[1] = {0x01};
@@ -215,11 +215,6 @@ static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha2
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
     secp256k1_hmac_sha256_write(&hmac, zero, 1);
     secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_write(&hmac, msg, msglen);
-    if (rnd && rndlen) {
-        /* RFC6979 3.6 "Additional data". */
-        secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
-    }
     secp256k1_hmac_sha256_finalize(&hmac, rng->k);
     secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
@@ -230,11 +225,6 @@ static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha2
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
     secp256k1_hmac_sha256_write(&hmac, one, 1);
     secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_write(&hmac, msg, msglen);
-    if (rnd && rndlen) {
-        /* RFC6979 3.6 "Additional data". */
-        secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
-    }
     secp256k1_hmac_sha256_finalize(&hmac, rng->k);
     secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);

crypto/secp256k1/libsecp256k1/src/modules/ecdh/Makefile.am.include

@@ -0,0 +1,9 @@
+include_HEADERS += include/secp256k1_ecdh.h
+noinst_HEADERS += src/modules/ecdh/main_impl.h
+noinst_HEADERS += src/modules/ecdh/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_ecdh
+bench_ecdh_SOURCES = src/bench_ecdh.c
+bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_ecdh_LDFLAGS = -static
+endif

crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h

@@ -0,0 +1,54 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_MAIN_
+#define _SECP256K1_MODULE_ECDH_MAIN_
+
+#include "include/secp256k1_ecdh.h"
+#include "ecmult_const_impl.h"
+
+int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const secp256k1_pubkey *point, const unsigned char *scalar) {
+    int ret = 0;
+    int overflow = 0;
+    secp256k1_gej res;
+    secp256k1_ge pt;
+    secp256k1_scalar s;
+    ARG_CHECK(result != NULL);
+    ARG_CHECK(point != NULL);
+    ARG_CHECK(scalar != NULL);
+    (void)ctx;
+
+    secp256k1_pubkey_load(ctx, &pt, point);
+    secp256k1_scalar_set_b32(&s, scalar, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&s)) {
+        ret = 0;
+    } else {
+        unsigned char x[32];
+        unsigned char y[1];
+        secp256k1_sha256_t sha;
+
+        secp256k1_ecmult_const(&res, &pt, &s);
+        secp256k1_ge_set_gej(&pt, &res);
+        /* Compute a hash of the point in compressed form
+         * Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not
+         * expect its output to be secret and has a timing sidechannel. */
+        secp256k1_fe_normalize(&pt.x);
+        secp256k1_fe_normalize(&pt.y);
+        secp256k1_fe_get_b32(x, &pt.x);
+        y[0] = 0x02 | secp256k1_fe_is_odd(&pt.y);
+
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, y, sizeof(y));
+        secp256k1_sha256_write(&sha, x, sizeof(x));
+        secp256k1_sha256_finalize(&sha, result);
+        ret = 1;
+    }
+
+    secp256k1_scalar_clear(&s);
+    return ret;
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h

@@ -0,0 +1,75 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_TESTS_
+#define _SECP256K1_MODULE_ECDH_TESTS_
+
+void test_ecdh_generator_basepoint(void) {
+    unsigned char s_one[32] = { 0 };
+    secp256k1_pubkey point[2];
+    int i;
+
+    s_one[31] = 1;
+    /* Check against pubkey creation when the basepoint is the generator */
+    for (i = 0; i < 100; ++i) {
+        secp256k1_sha256_t sha;
+        unsigned char s_b32[32];
+        unsigned char output_ecdh[32];
+        unsigned char output_ser[32];
+        unsigned char point_ser[33];
+        size_t point_ser_len = sizeof(point_ser);
+        secp256k1_scalar s;
+
+        random_scalar_order(&s);
+        secp256k1_scalar_get_b32(s_b32, &s);
+
+        /* compute using ECDH function */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[0], s_one) == 1);
+        CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32) == 1);
+        /* compute "explicitly" */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[1], s_b32) == 1);
+        CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
+        CHECK(point_ser_len == sizeof(point_ser));
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, point_ser, point_ser_len);
+        secp256k1_sha256_finalize(&sha, output_ser);
+        /* compare */
+        CHECK(memcmp(output_ecdh, output_ser, sizeof(output_ser)) == 0);
+    }
+}
+
+void test_bad_scalar(void) {
+    unsigned char s_zero[32] = { 0 };
+    unsigned char s_overflow[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+    };
+    unsigned char s_rand[32] = { 0 };
+    unsigned char output[32];
+    secp256k1_scalar rand;
+    secp256k1_pubkey point;
+
+    /* Create random point */
+    random_scalar_order(&rand);
+    secp256k1_scalar_get_b32(s_rand, &rand);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_rand) == 1);
+
+    /* Try to multiply it by bad values */
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_zero) == 0);
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 0);
+    /* ...and a good one */
+    s_overflow[31] -= 1;
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 1);
+}
+
+void run_ecdh_tests(void) {
+    test_ecdh_generator_basepoint();
+    test_bad_scalar();
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/recovery/Makefile.am.include

@@ -0,0 +1,9 @@
+include_HEADERS += include/secp256k1_recovery.h
+noinst_HEADERS += src/modules/recovery/main_impl.h
+noinst_HEADERS += src/modules/recovery/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_recover
+bench_recover_SOURCES = src/bench_recover.c
+bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_recover_LDFLAGS = -static
+endif

crypto/secp256k1/libsecp256k1/src/modules/recovery/main_impl.h

@@ -0,0 +1,156 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_MAIN_
+#define _SECP256K1_MODULE_RECOVERY_MAIN_
+
+#include "include/secp256k1_recovery.h"
+
+static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+    *recid = sig->data[64];
+}
+
+static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+    sig->data[64] = recid;
+}
+
+int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) {
+    secp256k1_scalar r, s;
+    int ret = 1;
+    int overflow = 0;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+    ARG_CHECK(recid >= 0 && recid <= 3);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid);
+    } else {
+        memset(sig, 0, sizeof(*sig));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) {
+    secp256k1_scalar r, s;
+    int recid;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin);
+    secp256k1_ecdsa_signature_save(sig, &r, &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int recid;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            unsigned char nonce32[32];
+            ret = noncefp(nonce32, seckey, msg32, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            memset(nonce32, 0, 32);
+            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    int recid;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
+    ARG_CHECK(recid >= 0 && recid < 4);
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
+        secp256k1_pubkey_save(pubkey, &q);
+        return 1;
+    } else {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/recovery/tests_impl.h

@@ -0,0 +1,249 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_TESTS_
+#define _SECP256K1_MODULE_RECOVERY_TESTS_
+
+void test_ecdsa_recovery_end_to_end(void) {
+    unsigned char extra[32] = {0x00};
+    unsigned char privkey[32];
+    unsigned char message[32];
+    secp256k1_ecdsa_signature signature[5];
+    secp256k1_ecdsa_recoverable_signature rsignature[5];
+    unsigned char sig[74];
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey recpubkey;
+    int recid = 0;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar msg, key;
+        random_scalar_order_test(&msg);
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_scalar_get_b32(message, &msg);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Serialize/parse compact and verify/recover. */
+    extra[0] = 0;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[4], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[1], message, privkey, NULL, extra) == 1);
+    extra[31] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[2], message, privkey, NULL, extra) == 1);
+    extra[31] = 0;
+    extra[0] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    memset(&rsignature[4], 0, sizeof(rsignature[4]));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    /* Parse compact (with recovery id) and recover. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1);
+    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    /* Serialize/destroy/parse signature and verify again. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    sig[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0);
+    /* Recover again */
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 ||
+          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+}
+
+/* Tests several edge cases. */
+void test_ecdsa_recovery_edge_cases(void) {
+    const unsigned char msg32[32] = {
+        'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
+        'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
+        'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
+        's', 's', 'a', 'g', 'e', '.', '.', '.'
+    };
+    const unsigned char sig64[64] = {
+        /* Generated by signing the above message with nonce 'This is the nonce we will use...'
+         * and secret key 0 (which is not valid), resulting in recid 0. */
+        0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
+        0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
+        0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
+        0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
+        0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
+        0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
+        0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
+        0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
+    };
+    secp256k1_pubkey pubkey;
+    /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
+    const unsigned char sigb64[64] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+    };
+    secp256k1_pubkey pubkeyb;
+    secp256k1_ecdsa_recoverable_signature rsig;
+    secp256k1_ecdsa_signature sig;
+    int recid;
+
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 0));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 1));
+    CHECK(secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 2));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 3));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+
+    for (recid = 0; recid < 4; recid++) {
+        int i;
+        int recid2;
+        /* (4,4) encoded in DER. */
+        unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
+        unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
+        unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
+        unsigned char sigbderalt1[39] = {
+            0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt2[39] = {
+            0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        unsigned char sigbderalt3[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt4[40] = {
+            0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        /* (order + r,4) encoded in DER. */
+        unsigned char sigbderlong[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
+            0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
+            0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
+        };
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        for (recid2 = 0; recid2 < 4; recid2++) {
+            secp256k1_pubkey pubkey2b;
+            CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid2) == 1);
+            CHECK(secp256k1_ecdsa_recover(ctx, &pubkey2b, &rsig, msg32) == 1);
+            /* Verifying with (order + r,4) should always fail. */
+            CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderlong, sizeof(sigbderlong)) == 0);
+        }
+        /* DER parsing tests. */
+        /* Zero length r/s. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0);
+        /* Leading zeros. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt1, sizeof(sigbderalt1)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt2, sizeof(sigbderalt2)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        sigbderalt3[4] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0);
+        sigbderalt4[7] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0);
+        /* Damage signature. */
+        sigbder[7]++;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        sigbder[7]--;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, 6) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder) - 1) == 0);
+        for(i = 0; i < 8; i++) {
+            int c;
+            unsigned char orig = sigbder[i];
+            /*Try every single-byte change.*/
+            for (c = 0; c < 256; c++) {
+                if (c == orig ) {
+                    continue;
+                }
+                sigbder[i] = c;
+                CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+            }
+            sigbder[i] = orig;
+        }
+    }
+
+    /* Test r/s equal to zero */
+    {
+        /* (1,1) encoded in DER. */
+        unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01};
+        unsigned char sigc64[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        secp256k1_pubkey pubkeyc;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyc, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 1);
+        sigcder[4] = 0;
+        sigc64[31] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+        sigcder[4] = 1;
+        sigcder[7] = 0;
+        sigc64[31] = 1;
+        sigc64[63] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+    }
+}
+
+void run_recovery_tests(void) {
+    int i;
+    for (i = 0; i < 64*count; i++) {
+        test_ecdsa_recovery_end_to_end();
+    }
+    test_ecdsa_recovery_edge_cases();
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/schnorr/Makefile.am.include

@@ -0,0 +1,11 @@
+include_HEADERS += include/secp256k1_schnorr.h
+noinst_HEADERS += src/modules/schnorr/main_impl.h
+noinst_HEADERS += src/modules/schnorr/schnorr.h
+noinst_HEADERS += src/modules/schnorr/schnorr_impl.h
+noinst_HEADERS += src/modules/schnorr/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_schnorr_verify
+bench_schnorr_verify_SOURCES = src/bench_schnorr_verify.c
+bench_schnorr_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_schnorr_verify_LDFLAGS = -static
+endif

crypto/secp256k1/libsecp256k1/src/modules/schnorr/main_impl.h

@@ -0,0 +1,164 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODULE_SCHNORR_MAIN
+#define SECP256K1_MODULE_SCHNORR_MAIN
+
+#include "include/secp256k1_schnorr.h"
+#include "modules/schnorr/schnorr_impl.h"
+
+static void secp256k1_schnorr_msghash_sha256(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
+    secp256k1_sha256_t sha;
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, r32, 32);
+    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_finalize(&sha, h32);
+}
+
+static const unsigned char secp256k1_schnorr_algo16[17] = "Schnorr+SHA256  ";
+
+int secp256k1_schnorr_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar sec, non;
+    int ret = 0;
+    int overflow = 0;
+    unsigned int count = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    while (1) {
+        unsigned char nonce32[32];
+        ret = noncefp(nonce32, msg32, seckey, secp256k1_schnorr_algo16, (void*)noncedata, count);
+        if (!ret) {
+            break;
+        }
+        secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+        memset(nonce32, 0, 32);
+        if (!secp256k1_scalar_is_zero(&non) && !overflow) {
+            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, NULL, secp256k1_schnorr_msghash_sha256, msg32)) {
+                break;
+            }
+        }
+        count++;
+    }
+    if (!ret) {
+        memset(sig64, 0, 64);
+    }
+    secp256k1_scalar_clear(&non);
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_schnorr_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_pubkey_load(ctx, &q, pubkey);
+    return secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32);
+}
+
+int secp256k1_schnorr_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *sig64, const unsigned char *msg32) {
+    secp256k1_ge q;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32)) {
+        secp256k1_pubkey_save(pubkey, &q);
+        return 1;
+    } else {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+}
+
+int secp256k1_schnorr_generate_nonce_pair(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, unsigned char *privnonce32, const unsigned char *sec32, const unsigned char *msg32, secp256k1_nonce_function noncefp, const void* noncedata) {
+    int count = 0;
+    int ret = 1;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+    secp256k1_scalar sec;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sec32 != NULL);
+    ARG_CHECK(pubnonce != NULL);
+    ARG_CHECK(privnonce32 != NULL);
+
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    do {
+        int overflow;
+        ret = noncefp(privnonce32, sec32, msg32, secp256k1_schnorr_algo16, (void*)noncedata, count++);
+        if (!ret) {
+            break;
+        }
+        secp256k1_scalar_set_b32(&sec, privnonce32, &overflow);
+        if (overflow || secp256k1_scalar_is_zero(&sec)) {
+            continue;
+        }
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sec);
+        secp256k1_ge_set_gej(&Q, &Qj);
+
+        secp256k1_pubkey_save(pubnonce, &Q);
+        break;
+    } while(1);
+
+    secp256k1_scalar_clear(&sec);
+    if (!ret) {
+        memset(pubnonce, 0, sizeof(*pubnonce));
+    }
+    return ret;
+}
+
+int secp256k1_schnorr_partial_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *sec32, const secp256k1_pubkey *pubnonce_others, const unsigned char *secnonce32) {
+    int overflow = 0;
+    secp256k1_scalar sec, non;
+    secp256k1_ge pubnon;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(sec32 != NULL);
+    ARG_CHECK(secnonce32 != NULL);
+    ARG_CHECK(pubnonce_others != NULL);
+
+    secp256k1_scalar_set_b32(&sec, sec32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&sec)) {
+        return -1;
+    }
+    secp256k1_scalar_set_b32(&non, secnonce32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&non)) {
+        return -1;
+    }
+    secp256k1_pubkey_load(ctx, &pubnon, pubnonce_others);
+    return secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, &pubnon, secp256k1_schnorr_msghash_sha256, msg32);
+}
+
+int secp256k1_schnorr_partial_combine(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char * const *sig64sin, int n) {
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(sig64sin != NULL);
+    return secp256k1_schnorr_sig_combine(sig64, n, sig64sin);
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/schnorr/schnorr.h

@@ -0,0 +1,20 @@
+/***********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ ***********************************************************************/
+
+#ifndef _SECP256K1_MODULE_SCHNORR_H_
+#define _SECP256K1_MODULE_SCHNORR_H_
+
+#include "scalar.h"
+#include "group.h"
+
+typedef void (*secp256k1_schnorr_msghash)(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32);
+
+static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_combine(unsigned char *sig64, int n, const unsigned char * const *sig64ins);
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/schnorr/schnorr_impl.h

@@ -0,0 +1,207 @@
+/***********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ ***********************************************************************/
+
+#ifndef _SECP256K1_SCHNORR_IMPL_H_
+#define _SECP256K1_SCHNORR_IMPL_H_
+
+#include <string.h>
+
+#include "schnorr.h"
+#include "num.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+/**
+ * Custom Schnorr-based signature scheme. They support multiparty signing, public key
+ * recovery and batch validation.
+ *
+ * Rationale for verifying R's y coordinate:
+ * In order to support batch validation and public key recovery, the full R point must
+ * be known to verifiers, rather than just its x coordinate. In order to not risk
+ * being more strict in batch validation than normal validation, validators must be
+ * required to reject signatures with incorrect y coordinate. This is only possible
+ * by including a (relatively slow) field inverse, or a field square root. However,
+ * batch validation offers potentially much higher benefits than this cost.
+ *
+ * Rationale for having an implicit y coordinate oddness:
+ * If we commit to having the full R point known to verifiers, there are two mechanism.
+ * Either include its oddness in the signature, or give it an implicit fixed value.
+ * As the R y coordinate can be flipped by a simple negation of the nonce, we choose the
+ * latter, as it comes with nearly zero impact on signing or validation performance, and
+ * saves a byte in the signature.
+ *
+ * Signing:
+ *   Inputs: 32-byte message m, 32-byte scalar key x (!=0), 32-byte scalar nonce k (!=0)
+ *
+ *   Compute point R = k * G. Reject nonce if R's y coordinate is odd (or negate nonce).
+ *   Compute 32-byte r, the serialization of R's x coordinate.
+ *   Compute scalar h = Hash(r || m). Reject nonce if h == 0 or h >= order.
+ *   Compute scalar s = k - h * x.
+ *   The signature is (r, s).
+ *
+ *
+ * Verification:
+ *   Inputs: 32-byte message m, public key point Q, signature: (32-byte r, scalar s)
+ *
+ *   Signature is invalid if s >= order.
+ *   Signature is invalid if r >= p.
+ *   Compute scalar h = Hash(r || m). Signature is invalid if h == 0 or h >= order.
+ *   Option 1 (faster for single verification):
+ *     Compute point R = h * Q + s * G. Signature is invalid if R is infinity or R's y coordinate is odd.
+ *     Signature is valid if the serialization of R's x coordinate equals r.
+ *   Option 2 (allows batch validation and pubkey recovery):
+ *     Decompress x coordinate r into point R, with odd y coordinate. Fail if R is not on the curve.
+ *     Signature is valid if R + h * Q + s * G == 0.
+ */
+
+static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Rj;
+    secp256k1_ge Ra;
+    unsigned char h32[32];
+    secp256k1_scalar h, s;
+    int overflow;
+    secp256k1_scalar n;
+
+    if (secp256k1_scalar_is_zero(key) || secp256k1_scalar_is_zero(nonce)) {
+        return 0;
+    }
+    n = *nonce;
+
+    secp256k1_ecmult_gen(ctx, &Rj, &n);
+    if (pubnonce != NULL) {
+        secp256k1_gej_add_ge(&Rj, &Rj, pubnonce);
+    }
+    secp256k1_ge_set_gej(&Ra, &Rj);
+    secp256k1_fe_normalize(&Ra.y);
+    if (secp256k1_fe_is_odd(&Ra.y)) {
+        /* R's y coordinate is odd, which is not allowed (see rationale above).
+           Force it to be even by negating the nonce. Note that this even works
+           for multiparty signing, as the R point is known to all participants,
+           which can all decide to flip the sign in unison, resulting in the
+           overall R point to be negated too. */
+        secp256k1_scalar_negate(&n, &n);
+    }
+    secp256k1_fe_normalize(&Ra.x);
+    secp256k1_fe_get_b32(sig64, &Ra.x);
+    hash(h32, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, h32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        secp256k1_scalar_clear(&n);
+        return 0;
+    }
+    secp256k1_scalar_mul(&s, &h, key);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_scalar_add(&s, &s, &n);
+    secp256k1_scalar_clear(&n);
+    secp256k1_scalar_get_b32(sig64 + 32, &s);
+    return 1;
+}
+
+static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Qj, Rj;
+    secp256k1_ge Ra;
+    secp256k1_fe Rx;
+    secp256k1_scalar h, s;
+    unsigned char hh[32];
+    int overflow;
+
+    if (secp256k1_ge_is_infinity(pubkey)) {
+        return 0;
+    }
+    hash(hh, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, hh, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        return 0;
+    }
+    overflow = 0;
+    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&Qj, pubkey);
+    secp256k1_ecmult(ctx, &Rj, &Qj, &h, &s);
+    if (secp256k1_gej_is_infinity(&Rj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej_var(&Ra, &Rj);
+    secp256k1_fe_normalize_var(&Ra.y);
+    if (secp256k1_fe_is_odd(&Ra.y)) {
+        return 0;
+    }
+    return secp256k1_fe_equal_var(&Rx, &Ra.x);
+}
+
+static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Qj, Rj;
+    secp256k1_ge Ra;
+    secp256k1_fe Rx;
+    secp256k1_scalar h, s;
+    unsigned char hh[32];
+    int overflow;
+
+    hash(hh, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, hh, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        return 0;
+    }
+    overflow = 0;
+    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
+        return 0;
+    }
+    if (!secp256k1_ge_set_xo_var(&Ra, &Rx, 0)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&Rj, &Ra);
+    secp256k1_scalar_inverse_var(&h, &h);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_scalar_mul(&s, &s, &h);
+    secp256k1_ecmult(ctx, &Qj, &Rj, &h, &s);
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(pubkey, &Qj);
+    return 1;
+}
+
+static int secp256k1_schnorr_sig_combine(unsigned char *sig64, int n, const unsigned char * const *sig64ins) {
+    secp256k1_scalar s = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    int i;
+    for (i = 0; i < n; i++) {
+        secp256k1_scalar si;
+        int overflow;
+        secp256k1_scalar_set_b32(&si, sig64ins[i] + 32, &overflow);
+        if (overflow) {
+            return -1;
+        }
+        if (i) {
+            if (memcmp(sig64ins[i - 1], sig64ins[i], 32) != 0) {
+                return -1;
+            }
+        }
+        secp256k1_scalar_add(&s, &s, &si);
+    }
+    if (secp256k1_scalar_is_zero(&s)) {
+        return 0;
+    }
+    memcpy(sig64, sig64ins[0], 32);
+    secp256k1_scalar_get_b32(sig64 + 32, &s);
+    secp256k1_scalar_clear(&s);
+    return 1;
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/modules/schnorr/tests_impl.h

@@ -0,0 +1,175 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODULE_SCHNORR_TESTS
+#define SECP256K1_MODULE_SCHNORR_TESTS
+
+#include "include/secp256k1_schnorr.h"
+
+void test_schnorr_end_to_end(void) {
+    unsigned char privkey[32];
+    unsigned char message[32];
+    unsigned char schnorr_signature[64];
+    secp256k1_pubkey pubkey, recpubkey;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar key;
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_rand256_test(message);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Schnorr sign. */
+    CHECK(secp256k1_schnorr_sign(ctx, schnorr_signature, message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 1);
+    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) == 1);
+    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    /* Destroy signature and verify again. */
+    schnorr_signature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
+    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 0);
+    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) != 1 ||
+          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+}
+
+/** Horribly broken hash function. Do not use for anything but tests. */
+void test_schnorr_hash(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
+    int i;
+    for (i = 0; i < 32; i++) {
+        h32[i] = r32[i] ^ msg32[i];
+    }
+}
+
+void test_schnorr_sign_verify(void) {
+    unsigned char msg32[32];
+    unsigned char sig64[3][64];
+    secp256k1_gej pubkeyj[3];
+    secp256k1_ge pubkey[3];
+    secp256k1_scalar nonce[3], key[3];
+    int i = 0;
+    int k;
+
+    secp256k1_rand256_test(msg32);
+
+    for (k = 0; k < 3; k++) {
+        random_scalar_order_test(&key[k]);
+
+        do {
+            random_scalar_order_test(&nonce[k]);
+            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64[k], &key[k], &nonce[k], NULL, &test_schnorr_hash, msg32)) {
+                break;
+            }
+        } while(1);
+
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubkeyj[k], &key[k]);
+        secp256k1_ge_set_gej_var(&pubkey[k], &pubkeyj[k]);
+        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32));
+
+        for (i = 0; i < 4; i++) {
+            int pos = secp256k1_rand32() % 64;
+            int mod = 1 + (secp256k1_rand32() % 255);
+            sig64[k][pos] ^= mod;
+            CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32) == 0);
+            sig64[k][pos] ^= mod;
+        }
+    }
+}
+
+void test_schnorr_threshold(void) {
+    unsigned char msg[32];
+    unsigned char sec[5][32];
+    secp256k1_pubkey pub[5];
+    unsigned char nonce[5][32];
+    secp256k1_pubkey pubnonce[5];
+    unsigned char sig[5][64];
+    const unsigned char* sigs[5];
+    unsigned char allsig[64];
+    const secp256k1_pubkey* pubs[5];
+    secp256k1_pubkey allpub;
+    int n, i;
+    int damage;
+    int ret = 0;
+
+    damage = (secp256k1_rand32() % 2) ? (1 + (secp256k1_rand32() % 4)) : 0;
+    secp256k1_rand256_test(msg);
+    n = 2 + (secp256k1_rand32() % 4);
+    for (i = 0; i < n; i++) {
+        do {
+            secp256k1_rand256_test(sec[i]);
+        } while (!secp256k1_ec_seckey_verify(ctx, sec[i]));
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pub[i], sec[i]));
+        CHECK(secp256k1_schnorr_generate_nonce_pair(ctx, &pubnonce[i], nonce[i], msg, sec[i], NULL, NULL));
+        pubs[i] = &pub[i];
+    }
+    if (damage == 1) {
+        nonce[secp256k1_rand32() % n][secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
+    } else if (damage == 2) {
+        sec[secp256k1_rand32() % n][secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
+    }
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey allpubnonce;
+        const secp256k1_pubkey *pubnonces[4];
+        int j;
+        for (j = 0; j < i; j++) {
+            pubnonces[j] = &pubnonce[j];
+        }
+        for (j = i + 1; j < n; j++) {
+            pubnonces[j - 1] = &pubnonce[j];
+        }
+        CHECK(secp256k1_ec_pubkey_combine(ctx, &allpubnonce, pubnonces, n - 1));
+        ret |= (secp256k1_schnorr_partial_sign(ctx, sig[i], msg, sec[i], &allpubnonce, nonce[i]) != 1) * 1;
+        sigs[i] = sig[i];
+    }
+    if (damage == 3) {
+        sig[secp256k1_rand32() % n][secp256k1_rand32() % 64] ^= 1 + (secp256k1_rand32() % 255);
+    }
+    ret |= (secp256k1_ec_pubkey_combine(ctx, &allpub, pubs, n) != 1) * 2;
+    if ((ret & 1) == 0) {
+        ret |= (secp256k1_schnorr_partial_combine(ctx, allsig, sigs, n) != 1) * 4;
+    }
+    if (damage == 4) {
+        allsig[secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
+    }
+    if ((ret & 7) == 0) {
+        ret |= (secp256k1_schnorr_verify(ctx, allsig, msg, &allpub) != 1) * 8;
+    }
+    CHECK((ret == 0) == (damage == 0));
+}
+
+void test_schnorr_recovery(void) {
+    unsigned char msg32[32];
+    unsigned char sig64[64];
+    secp256k1_ge Q;
+
+    secp256k1_rand256_test(msg32);
+    secp256k1_rand256_test(sig64);
+    secp256k1_rand256_test(sig64 + 32);
+    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1) {
+        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1);
+    }
+}
+
+void run_schnorr_tests(void) {
+    int i;
+    for (i = 0; i < 32*count; i++) {
+        test_schnorr_end_to_end();
+    }
+    for (i = 0; i < 32 * count; i++) {
+         test_schnorr_sign_verify();
+    }
+    for (i = 0; i < 16 * count; i++) {
+         test_schnorr_recovery();
+    }
+    for (i = 0; i < 10 * count; i++) {
+         test_schnorr_threshold();
+    }
+}
+
+#endif

crypto/secp256k1/libsecp256k1/src/num.h

@@ -20,48 +20,48 @@
 #endif
 
 /** Copy a number. */
-static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a);
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
 
 /** Convert a number's absolute value to a binary big-endian string.
  *  There must be enough place. */
-static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a);
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a);
 
 /** Set a number to the value of a binary big-endian string. */
-static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen);
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen);
 
 /** Compute a modular inverse. The input must be less than the modulus. */
-static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m);
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
 
 /** Compare the absolute value of two numbers. */
-static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b);
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
 
 /** Test whether two number are equal (including sign). */
-static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b);
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
 
 /** Add two (signed) numbers. */
-static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Subtract two (signed) numbers. */
-static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Multiply two (signed) numbers. */
-static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
     even if r was negative. */
-static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m);
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
 
 /** Right-shift the passed number by bits bits. */
-static void secp256k1_num_shift(secp256k1_num_t *r, int bits);
+static void secp256k1_num_shift(secp256k1_num *r, int bits);
 
 /** Check whether a number is zero. */
-static int secp256k1_num_is_zero(const secp256k1_num_t *a);
+static int secp256k1_num_is_zero(const secp256k1_num *a);
 
 /** Check whether a number is strictly negative. */
-static int secp256k1_num_is_neg(const secp256k1_num_t *a);
+static int secp256k1_num_is_neg(const secp256k1_num *a);
 
 /** Change a number's sign. */
-static void secp256k1_num_negate(secp256k1_num_t *r);
+static void secp256k1_num_negate(secp256k1_num *r);
 
 #endif
 

crypto/secp256k1/libsecp256k1/src/num_gmp.h

@@ -15,6 +15,6 @@ typedef struct {
     mp_limb_t data[2*NUM_LIMBS];
     int neg;
     int limbs;
-} secp256k1_num_t;
+} secp256k1_num;
 
 #endif

crypto/secp256k1/libsecp256k1/src/num_gmp_impl.h

@@ -15,18 +15,18 @@
 #include "num.h"
 
 #ifdef VERIFY
-static void secp256k1_num_sanity(const secp256k1_num_t *a) {
+static void secp256k1_num_sanity(const secp256k1_num *a) {
     VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
 }
 #else
 #define secp256k1_num_sanity(a) do { } while(0)
 #endif
 
-static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
     *r = *a;
 }
 
-static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
     unsigned char tmp[65];
     int len = 0;
     int shift = 0;
@@ -42,7 +42,7 @@ static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const sec
     memset(tmp, 0, sizeof(tmp));
 }
 
-static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) {
     int len;
     VERIFY_CHECK(alen > 0);
     VERIFY_CHECK(alen <= 64);
@@ -59,7 +59,7 @@ static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, un
     }
 }
 
-static void secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
     r->limbs = a->limbs;
     if (c != 0) {
@@ -68,7 +68,7 @@ static void secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a,
     }
 }
 
-static void secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
     VERIFY_CHECK(c == 0);
     r->limbs = a->limbs;
@@ -77,7 +77,7 @@ static void secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a,
     }
 }
 
-static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
     secp256k1_num_sanity(r);
     secp256k1_num_sanity(m);
 
@@ -97,7 +97,7 @@ static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
     }
 }
 
-static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
     int i;
     mp_limb_t g[NUM_LIMBS+1];
     mp_limb_t u[NUM_LIMBS+1];
@@ -142,15 +142,15 @@ static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t
     memset(v, 0, sizeof(v));
 }
 
-static int secp256k1_num_is_zero(const secp256k1_num_t *a) {
+static int secp256k1_num_is_zero(const secp256k1_num *a) {
     return (a->limbs == 1 && a->data[0] == 0);
 }
 
-static int secp256k1_num_is_neg(const secp256k1_num_t *a) {
+static int secp256k1_num_is_neg(const secp256k1_num *a) {
     return (a->limbs > 1 || a->data[0] != 0) && a->neg;
 }
 
-static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
     if (a->limbs > b->limbs) {
         return 1;
     }
@@ -160,7 +160,7 @@ static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b)
     return mpn_cmp(a->data, b->data, a->limbs);
 }
 
-static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
     if (a->limbs > b->limbs) {
         return 0;
     }
@@ -173,7 +173,7 @@ static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b)
     return mpn_cmp(a->data, b->data, a->limbs) == 0;
 }
 
-static void secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, int bneg) {
+static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
     if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
         r->neg = a->neg;
         if (a->limbs >= b->limbs) {
@@ -192,19 +192,19 @@ static void secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, c
     }
 }
 
-static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
     secp256k1_num_subadd(r, a, b, 0);
 }
 
-static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
     secp256k1_num_subadd(r, a, b, 1);
 }
 
-static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t tmp[2*NUM_LIMBS+1];
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
@@ -231,13 +231,13 @@ static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, cons
     memset(tmp, 0, sizeof(tmp));
 }
 
-static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
-    int i;
+static void secp256k1_num_shift(secp256k1_num *r, int bits) {
     if (bits % GMP_NUMB_BITS) {
         /* Shift within limbs. */
         mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
     }
     if (bits >= GMP_NUMB_BITS) {
+        int i;
         /* Shift full limbs. */
         for (i = 0; i < r->limbs; i++) {
             int index = i + (bits / GMP_NUMB_BITS);
@@ -253,7 +253,7 @@ static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
     }
 }
 
-static void secp256k1_num_negate(secp256k1_num_t *r) {
+static void secp256k1_num_negate(secp256k1_num *r) {
     r->neg ^= 1;
 }
 

crypto/secp256k1/libsecp256k1/src/scalar.h

@@ -0,0 +1,104 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_
+#define _SECP256K1_SCALAR_
+
+#include "num.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(USE_SCALAR_4X64)
+#include "scalar_4x64.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+/** Clear a scalar to prevent the leak of sensitive data. */
+static void secp256k1_scalar_clear(secp256k1_scalar *r);
+
+/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
+static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Access bits from a scalar. Not constant time. */
+static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Set a scalar from a big endian byte array. */
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
+
+/** Set a scalar to an unsigned integer. */
+static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
+
+/** Convert a scalar to a byte array. */
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
+
+/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
+
+/** Multiply two scalars (modulo the group order). */
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Shift a scalar right by some amount strictly between 0 and 16, returning
+ *  the low bits that were shifted off */
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
+
+/** Compute the square of a scalar (modulo the group order). */
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order). */
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the complement of a scalar (modulo the group order). */
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Check whether a scalar equals zero. */
+static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
+
+/** Check whether a scalar equals one. */
+static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
+
+/** Check whether a scalar, considered as an nonnegative integer, is even. */
+static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
+
+/** Check whether a scalar is higher than the group order divided by 2. */
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
+
+/** Conditionally negate a number, in constant time.
+ * Returns -1 if the number was negated, 1 otherwise */
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
+
+#ifndef USE_NUM_NONE
+/** Convert a scalar to a number. */
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
+
+/** Get the order of the group as a number. */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r);
+#endif
+
+/** Compare two scalars. */
+static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+#ifdef USE_ENDOMORPHISM
+/** Find r1 and r2 such that r1+r2*2^128 = a. */
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+#endif
+
+/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
+
+#endif

crypto/secp256k1/libsecp256k1/src/scalar_4x64.h

@@ -12,7 +12,7 @@
 /** A scalar modulo the group order of the secp256k1 curve. */
 typedef struct {
     uint64_t d[4];
-} secp256k1_scalar_t;
+} secp256k1_scalar;
 
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
 

crypto/secp256k1/libsecp256k1/src/scalar_4x64_impl.h

@@ -24,26 +24,26 @@
 #define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
 #define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
 
-SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
     r->d[0] = 0;
     r->d[1] = 0;
     r->d[2] = 0;
     r->d[3] = 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
     r->d[0] = v;
     r->d[1] = 0;
     r->d[2] = 0;
     r->d[3] = 0;
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
     return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK(count < 32);
     VERIFY_CHECK(offset + count <= 256);
     if ((offset + count - 1) >> 6 == offset >> 6) {
@@ -54,7 +54,7 @@ SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256
     }
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
@@ -66,7 +66,7 @@ SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scal
     return yes;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsigned int overflow) {
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
     uint128_t t;
     VERIFY_CHECK(overflow <= 1);
     t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
@@ -80,7 +80,7 @@ SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsig
     return overflow;
 }
 
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     int overflow;
     uint128_t t = (uint128_t)a->d[0] + b->d[0];
     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
@@ -96,9 +96,10 @@ static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t
     return overflow;
 }
 
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     uint128_t t;
     VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
     t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
     t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
@@ -113,7 +114,7 @@ static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
 #endif
 }
 
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
     int over;
     r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
     r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
@@ -125,18 +126,18 @@ static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char
     }
 }
 
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
     bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
     bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
     bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
     bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
     return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
 }
 
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
     uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
     r->d[0] = t & nonzero; t >>= 64;
@@ -148,11 +149,11 @@ static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scala
     r->d[3] = t & nonzero;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
     return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
 }
 
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[3] < SECP256K1_N_H_3);
@@ -164,6 +165,22 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     return yes;
 }
 
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint64_t mask = !flag - 1;
+    uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
+    uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
 /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
 
 /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
@@ -250,7 +267,7 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     VERIFY_CHECK(c2 == 0); \
 }
 
-static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l) {
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
 #ifdef USE_ASM_X86_64
     /* Reduce 512 bits into 385. */
     uint64_t m0, m1, m2, m3, m4, m5, m6;
@@ -559,7 +576,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
 #ifdef USE_ASM_X86_64
     const uint64_t *pb = b->d;
     __asm__ __volatile__(
@@ -721,12 +738,12 @@ static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a,
     extract(l[5]);
     muladd_fast(a->d[3], b->d[3]);
     extract_fast(l[6]);
-    VERIFY_CHECK(c1 <= 0);
+    VERIFY_CHECK(c1 == 0);
     l[7] = c0;
 #endif
 }
 
-static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
 #ifdef USE_ASM_X86_64
     __asm__ __volatile__(
     /* Preload */
@@ -871,19 +888,31 @@ static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *a)
 #undef extract
 #undef extract_fast
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     uint64_t l[8];
     secp256k1_scalar_mul_512(l, a, b);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
+    r->d[3] = (r->d[3] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint64_t l[8];
     secp256k1_scalar_sqr_512(l, a);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
     r1->d[2] = 0;
@@ -894,11 +923,11 @@ static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_
     r2->d[3] = 0;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
     uint64_t l[8];
     unsigned int shiftlimbs;
     unsigned int shiftlow;
@@ -912,9 +941,7 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *
     r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
-    if ((l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1) {
-        secp256k1_scalar_add_bit(r, 0);
-    }
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
 }
 
 #endif

crypto/secp256k1/libsecp256k1/src/scalar_8x32.h

@@ -12,7 +12,7 @@
 /** A scalar modulo the group order of the secp256k1 curve. */
 typedef struct {
     uint32_t d[8];
-} secp256k1_scalar_t;
+} secp256k1_scalar;
 
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
 

crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h

@@ -34,7 +34,7 @@
 #define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
 #define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
 
-SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
     r->d[0] = 0;
     r->d[1] = 0;
     r->d[2] = 0;
@@ -45,7 +45,7 @@ SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
     r->d[7] = 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
     r->d[0] = v;
     r->d[1] = 0;
     r->d[2] = 0;
@@ -56,12 +56,12 @@ SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, uns
     r->d[7] = 0;
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
     return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK(count < 32);
     VERIFY_CHECK(offset + count <= 256);
     if ((offset + count - 1) >> 5 == offset >> 5) {
@@ -72,7 +72,7 @@ SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256
     }
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
@@ -90,7 +90,7 @@ SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scal
     return yes;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, uint32_t overflow) {
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
     uint64_t t;
     VERIFY_CHECK(overflow <= 1);
     t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
@@ -112,7 +112,7 @@ SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, uint3
     return overflow;
 }
 
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     int overflow;
     uint64_t t = (uint64_t)a->d[0] + b->d[0];
     r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
@@ -136,9 +136,10 @@ static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t
     return overflow;
 }
 
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     uint64_t t;
     VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
     t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
     r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
     t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
@@ -161,7 +162,7 @@ static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
 #endif
 }
 
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
     int over;
     r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
     r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
@@ -177,7 +178,7 @@ static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char
     }
 }
 
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
     bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
     bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
     bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
@@ -188,11 +189,11 @@ static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_
     bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
     return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
 }
 
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
     uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
     r->d[0] = t & nonzero; t >>= 32;
@@ -212,11 +213,11 @@ static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scala
     r->d[7] = t & nonzero;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
     return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
 }
 
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[7] < SECP256K1_N_H_7);
@@ -234,6 +235,31 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     return yes;
 }
 
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint32_t mask = !flag - 1;
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
+    uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
+    r->d[7] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+
 /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
 
 /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
@@ -320,7 +346,7 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     VERIFY_CHECK(c2 == 0); \
 }
 
-static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l) {
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
     uint64_t c;
     uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
     uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
@@ -462,7 +488,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
@@ -550,7 +576,7 @@ static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar_t *a, c
     l[15] = c0;
 }
 
-static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
@@ -618,20 +644,36 @@ static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar_t *a) {
 #undef extract
 #undef extract_fast
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     uint32_t l[16];
     secp256k1_scalar_mul_512(l, a, b);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
+    r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
+    r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
+    r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
+    r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
+    r->d[7] = (r->d[7] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint32_t l[16];
     secp256k1_scalar_sqr_512(l, a);
     secp256k1_scalar_reduce_512(r, l);
 }
 
 #ifdef USE_ENDOMORPHISM
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
     r1->d[2] = a->d[2];
@@ -651,11 +693,11 @@ static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_
 }
 #endif
 
-SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
     uint32_t l[16];
     unsigned int shiftlimbs;
     unsigned int shiftlow;
@@ -673,9 +715,7 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *
     r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
-    if ((l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1) {
-        secp256k1_scalar_add_bit(r, 0);
-    }
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
 }
 
 #endif

crypto/secp256k1/libsecp256k1/src/scalar_impl.h

@@ -25,14 +25,14 @@
 #endif
 
 #ifndef USE_NUM_NONE
-static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
     unsigned char c[32];
     secp256k1_scalar_get_b32(c, a);
     secp256k1_num_set_bin(r, c, 32);
 }
 
 /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
-static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
+static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
     static const unsigned char order[32] = {
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
@@ -43,11 +43,11 @@ static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
 }
 #endif
 
-static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
-    secp256k1_scalar_t *t;
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+    secp256k1_scalar *t;
     int i;
     /* First compute x ^ (2^N - 1) for some values of N. */
-    secp256k1_scalar_t x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
+    secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
 
     secp256k1_scalar_sqr(&x2,  x);
     secp256k1_scalar_mul(&x2, &x2,  x);
@@ -234,18 +234,27 @@ static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scal
     secp256k1_scalar_mul(r, t, &x6); /* 111111 */
 }
 
-static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    /* d[0] is present and is the lowest word for all representations */
+    return !(a->d[0] & 1);
+}
+
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
 #if defined(USE_SCALAR_INV_BUILTIN)
     secp256k1_scalar_inverse(r, x);
 #elif defined(USE_SCALAR_INV_NUM)
     unsigned char b[32];
-    secp256k1_num_t n, m;
-    secp256k1_scalar_get_b32(b, x);
+    secp256k1_num n, m;
+    secp256k1_scalar t = *x;
+    secp256k1_scalar_get_b32(b, &t);
     secp256k1_num_set_bin(&n, b, 32);
     secp256k1_scalar_order_get_num(&m);
     secp256k1_num_mod_inverse(&n, &n, &m);
     secp256k1_num_get_bin(b, 32, &n);
     secp256k1_scalar_set_b32(r, b, NULL);
+    /* Verify that the inverse was computed correctly, without GMP code. */
+    secp256k1_scalar_mul(&t, &t, r);
+    CHECK(secp256k1_scalar_is_one(&t));
 #else
 #error "Please select scalar inverse implementation"
 #endif
@@ -290,30 +299,31 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
  * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
  */
 
-static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
-    secp256k1_scalar_t c1, c2;
-    static const secp256k1_scalar_t minus_lambda = SECP256K1_SCALAR_CONST(
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    secp256k1_scalar c1, c2;
+    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
         0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
         0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
     );
-    static const secp256k1_scalar_t minus_b1 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
         0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
     );
-    static const secp256k1_scalar_t minus_b2 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
         0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
         0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
     );
-    static const secp256k1_scalar_t g1 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
         0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
     );
-    static const secp256k1_scalar_t g2 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
         0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
     );
     VERIFY_CHECK(r1 != a);
     VERIFY_CHECK(r2 != a);
+    /* these _var calls are constant time since the shift amount is constant */
     secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
     secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
     secp256k1_scalar_mul(&c1, &c1, &minus_b1);

crypto/secp256k1/libsecp256k1/src/secp256k1.c

@@ -0,0 +1,513 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#define SECP256K1_BUILD (1)
+
+#include "include/secp256k1.h"
+
+#include "util.h"
+#include "num_impl.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_impl.h"
+#include "ecmult_const_impl.h"
+#include "ecmult_gen_impl.h"
+#include "ecdsa_impl.h"
+#include "eckey_impl.h"
+#include "hash_impl.h"
+
+#define ARG_CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        secp256k1_callback_call(&ctx->illegal_callback, #cond); \
+        return 0; \
+    } \
+} while(0)
+
+static void default_illegal_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_illegal_callback = {
+    default_illegal_callback_fn,
+    NULL
+};
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+
+struct secp256k1_context_struct {
+    secp256k1_ecmult_context ecmult_ctx;
+    secp256k1_ecmult_gen_context ecmult_gen_ctx;
+    secp256k1_callback illegal_callback;
+    secp256k1_callback error_callback;
+};
+
+secp256k1_context* secp256k1_context_create(unsigned int flags) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = default_illegal_callback;
+    ret->error_callback = default_error_callback;
+
+    secp256k1_ecmult_context_init(&ret->ecmult_ctx);
+    secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
+
+    if (flags & SECP256K1_CONTEXT_SIGN) {
+        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback);
+    }
+    if (flags & SECP256K1_CONTEXT_VERIFY) {
+        secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback);
+    }
+
+    return ret;
+}
+
+secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = ctx->illegal_callback;
+    ret->error_callback = ctx->error_callback;
+    secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback);
+    secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback);
+    return ret;
+}
+
+void secp256k1_context_destroy(secp256k1_context* ctx) {
+    if (ctx != NULL) {
+        secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
+        secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
+
+        free(ctx);
+    }
+}
+
+void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_illegal_callback_fn;
+    }
+    ctx->illegal_callback.fn = fun;
+    ctx->illegal_callback.data = data;
+}
+
+void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_error_callback_fn;
+    }
+    ctx->error_callback.fn = fun;
+    ctx->error_callback.data = data;
+}
+
+static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        /* When the secp256k1_ge_storage type is exactly 64 byte, use its
+         * representation inside secp256k1_pubkey, as conversion is very fast.
+         * Note that secp256k1_pubkey_save must use the same representation. */
+        secp256k1_ge_storage s;
+        memcpy(&s, &pubkey->data[0], 64);
+        secp256k1_ge_from_storage(ge, &s);
+    } else {
+        /* Otherwise, fall back to 32-byte big endian for X and Y. */
+        secp256k1_fe x, y;
+        secp256k1_fe_set_b32(&x, pubkey->data);
+        secp256k1_fe_set_b32(&y, pubkey->data + 32);
+        secp256k1_ge_set_xy(ge, &x, &y);
+    }
+    ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
+    return 1;
+}
+
+static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        secp256k1_ge_storage s;
+        secp256k1_ge_to_storage(&s, ge);
+        memcpy(&pubkey->data[0], &s, 64);
+    } else {
+        VERIFY_CHECK(!secp256k1_ge_is_infinity(ge));
+        secp256k1_fe_normalize_var(&ge->x);
+        secp256k1_fe_normalize_var(&ge->y);
+        secp256k1_fe_get_b32(pubkey->data, &ge->x);
+        secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
+    }
+}
+
+int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) {
+    secp256k1_ge Q;
+
+    (void)ctx;
+    if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+    secp256k1_pubkey_save(pubkey, &Q);
+    secp256k1_ge_clear(&Q);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) {
+    secp256k1_ge Q;
+
+    (void)ctx;
+    return (secp256k1_pubkey_load(ctx, &Q, pubkey) &&
+            secp256k1_eckey_pubkey_serialize(&Q, output, outputlen, flags));
+}
+
+static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+}
+
+static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input != NULL);
+
+    if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+        return 1;
+    } else {
+        memset(sig, 0, sizeof(*sig));
+        return 0;
+    }
+}
+
+int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s);
+}
+
+int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return (secp256k1_pubkey_load(ctx, &q, pubkey) &&
+            secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
+}
+
+static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   unsigned char keydata[112];
+   int keylen = 64;
+   secp256k1_rfc6979_hmac_sha256_t rng;
+   unsigned int i;
+   /* We feed a byte array to the PRNG as input, consisting of:
+    * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
+    * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
+    * - optionally 16 extra bytes with the algorithm name (the extra data bytes
+    *   are set to zeroes when not present, while the algorithm name is).
+    */
+   memcpy(keydata, key32, 32);
+   memcpy(keydata + 32, msg32, 32);
+   if (data != NULL) {
+       memcpy(keydata + 64, data, 32);
+       keylen = 96;
+   }
+   if (algo16 != NULL) {
+       memset(keydata + keylen, 0, 96 - keylen);
+       memcpy(keydata + 96, algo16, 16);
+       keylen = 112;
+   }
+   secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, keylen);
+   memset(keydata, 0, sizeof(keydata));
+   for (i = 0; i <= counter; i++) {
+       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+   }
+   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+   return 1;
+}
+
+const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
+const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
+
+int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            unsigned char nonce32[32];
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            memset(nonce32, 0, 32);
+            if (!overflow && !secp256k1_scalar_is_zero(&non)) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_signature_save(signature, &r, &s);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) {
+    secp256k1_scalar sec;
+    int ret;
+    int overflow;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    (void)ctx;
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = !overflow && !secp256k1_scalar_is_zero(&sec);
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) {
+    secp256k1_gej pj;
+    secp256k1_ge p;
+    secp256k1_scalar sec;
+    int overflow;
+    int ret = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec));
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec);
+    secp256k1_ge_set_gej(&p, &pj);
+    secp256k1_pubkey_save(pubkey, &p);
+    secp256k1_scalar_clear(&sec);
+    if (!ret) {
+        memset(pubkey, 0, sizeof(*pubkey));
+    }
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar term;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+    (void)ctx;
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+
+    ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&term);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar term;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    if (!overflow && secp256k1_pubkey_load(ctx, &p, pubkey)) {
+        ret = secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term);
+        if (ret) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            memset(pubkey, 0, sizeof(*pubkey));
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar factor;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+    (void)ctx;
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&factor);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar factor;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    if (!overflow && secp256k1_pubkey_load(ctx, &p, pubkey)) {
+        ret = secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor);
+        if (ret) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            memset(pubkey, 0, sizeof(*pubkey));
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_ec_privkey_export(const secp256k1_context* ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *seckey, unsigned int flags) {
+    secp256k1_scalar key;
+    int ret = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(privkey != NULL);
+    ARG_CHECK(privkeylen != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+
+    secp256k1_scalar_set_b32(&key, seckey, NULL);
+    ret = secp256k1_eckey_privkey_serialize(&ctx->ecmult_gen_ctx, privkey, privkeylen, &key, flags);
+    secp256k1_scalar_clear(&key);
+    return ret;
+}
+
+int secp256k1_ec_privkey_import(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *privkey, size_t privkeylen) {
+    secp256k1_scalar key;
+    int ret = 0;
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(privkey != NULL);
+    (void)ctx;
+
+    ret = secp256k1_eckey_privkey_parse(&key, privkey, privkeylen);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &key);
+    }
+    secp256k1_scalar_clear(&key);
+    return ret;
+}
+
+int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, int n) {
+    int i;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+
+    ARG_CHECK(pubnonce != NULL);
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(pubnonces != NULL);
+
+    secp256k1_gej_set_infinity(&Qj);
+
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
+        secp256k1_gej_add_ge(&Qj, &Qj, &Q);
+    }
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        memset(pubnonce, 0, sizeof(*pubnonce));
+        return 0;
+    }
+    secp256k1_ge_set_gej(&Q, &Qj);
+    secp256k1_pubkey_save(pubnonce, &Q);
+    return 1;
+}
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+# include "modules/schnorr/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/main_impl.h"
+#endif

crypto/secp256k1/libsecp256k1/src/testrand_impl.h

@@ -18,7 +18,7 @@ static uint32_t secp256k1_test_rng_precomputed[8];
 static int secp256k1_test_rng_precomputed_used = 8;
 
 SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
-    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, (const unsigned char*)"TestRNG", 7, seed16, 16, NULL, 0);
+    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
 }
 
 SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {

crypto/secp256k1/libsecp256k1/src/util.h

@@ -15,6 +15,15 @@
 #include <stdint.h>
 #include <stdio.h>
 
+typedef struct {
+    void (*fn)(const char *text, void* data);
+    const void* data;
+} secp256k1_callback;
+
+static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
+    cb->fn(text, (void*)cb->data);
+}
+
 #ifdef DETERMINISTIC
 #define TEST_FAILURE(msg) do { \
     fprintf(stderr, "%s\n", msg); \
@@ -47,23 +56,20 @@
 } while(0)
 #endif
 
-/* Like assert(), but safe to use on expressions with side effects. */
-#ifndef NDEBUG
-#define DEBUG_CHECK CHECK
-#else
-#define DEBUG_CHECK(cond) do { (void)(cond); } while(0)
-#endif
-
-/* Like DEBUG_CHECK(), but when VERIFY is defined instead of NDEBUG not defined. */
+/* Like assert(), but when VERIFY is defined, and side-effect safe. */
 #ifdef VERIFY
 #define VERIFY_CHECK CHECK
+#define VERIFY_SETUP(stmt) do { stmt; } while(0)
 #else
 #define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
+#define VERIFY_SETUP(stmt)
 #endif
 
-static SECP256K1_INLINE void *checked_malloc(size_t size) {
+static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
     void *ret = malloc(size);
-    CHECK(ret != NULL);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
     return ret;
 }
 

crypto/secp256k1/secp256k1/.travis.yml

@@ -1,32 +0,0 @@
-language: c
-compiler:
-  - clang
-  - gcc
-install:
-  - sudo apt-get install -qq libssl-dev
-  - if [ "$BIGNUM" = "gmp" -o "$BIGNUM" = "auto" ]; then sudo apt-get install --no-install-recommends --no-upgrade -qq libgmp-dev; fi
-  - if [ -n "$EXTRAPACKAGES" ]; then sudo apt-get update && sudo apt-get install --no-install-recommends --no-upgrade $EXTRAPACKAGES; fi
-env:
-  global:
-    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  ASM=no  BUILD=check  EXTRAFLAGS= HOST= EXTRAPACKAGES=
-  matrix:
-    - SCALAR=32bit
-    - SCALAR=64bit
-    - FIELD=64bit
-    - FIELD=64bit     ENDOMORPHISM=yes
-    - FIELD=64bit                       ASM=x86_64
-    - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
-    - FIELD=32bit
-    - FIELD=32bit     ENDOMORPHISM=yes
-    - BIGNUM=no
-    - BIGNUM=no       ENDOMORPHISM=yes
-    - BUILD=distcheck
-    - EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
-    - HOST=i686-linux-gnu EXTRAPACKAGES="gcc-multilib"
-    - HOST=i686-linux-gnu EXTRAPACKAGES="gcc-multilib" ENDOMORPHISM=yes
-before_script: ./autogen.sh
-script:
- - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
- - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
- - ./configure --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
-os: linux

crypto/secp256k1/secp256k1/build-aux/m4/bitcoin_secp.m4

@@ -1,61 +0,0 @@
-dnl libsecp25k1 helper checks
-AC_DEFUN([SECP_INT128_CHECK],[
-has_int128=$ac_cv_type___int128
-])
-
-dnl 
-AC_DEFUN([SECP_64BIT_ASM_CHECK],[
-AC_MSG_CHECKING(for x86_64 assembly availability)
-AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
-  #include <stdint.h>]],[[
-  uint64_t a = 11, tmp;
-  __asm__ __volatile__("movq $0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
-  ]])],[has_64bit_asm=yes],[has_64bit_asm=no])
-AC_MSG_RESULT([$has_64bit_asm])
-])
-
-dnl
-AC_DEFUN([SECP_OPENSSL_CHECK],[
-if test x"$use_pkgconfig" = x"yes"; then
-    : #NOP
-  m4_ifdef([PKG_CHECK_MODULES],[
-    PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no])
-    if test x"$has_libcrypto" = x"yes"; then
-      TEMP_LIBS="$LIBS"
-      LIBS="$LIBS $CRYPTO_LIBS"
-      AC_CHECK_LIB(crypto, main,[AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])],[has_libcrypto=no])
-      LIBS="$TEMP_LIBS"
-    fi
-  ])
-else
-  AC_CHECK_HEADER(openssl/crypto.h,[AC_CHECK_LIB(crypto, main,[has_libcrypto=yes; CRYPTO_LIBS=-lcrypto; AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])]
-)])
-  LIBS=
-fi
-if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
-  AC_MSG_CHECKING(for EC functions in libcrypto)
-  AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
-    #include <openssl/ec.h>
-    #include <openssl/ecdsa.h>
-    #include <openssl/obj_mac.h>]],[[
-    EC_KEY *eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
-    ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
-    ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
-    EC_KEY_free(eckey);
-  ]])],[has_openssl_ec=yes],[has_openssl_ec=no])
-  AC_MSG_RESULT([$has_openssl_ec])
-fi
-])
-
-dnl
-AC_DEFUN([SECP_GMP_CHECK],[
-if test x"$has_gmp" != x"yes"; then
-  CPPFLAGS_TEMP="$CPPFLAGS"
-  CPPFLAGS="$GMP_CPPFLAGS $CPPFLAGS"
-  LIBS_TEMP="$LIBS"
-  LIBS="$GMP_LIBS $LIBS"
-  AC_CHECK_HEADER(gmp.h,[AC_CHECK_LIB(gmp, __gmpz_init,[has_gmp=yes; GMP_LIBS="$GMP_LIBS -lgmp"; AC_DEFINE(HAVE_LIBGMP,1,[Define this symbol if libgmp is installed])])])
-  CPPFLAGS="$CPPFLAGS_TEMP"
-  LIBS="$LIBS_TEMP"
-fi
-])

crypto/secp256k1/secp256k1/include/secp256k1.h

@@ -1,295 +0,0 @@
-#ifndef _SECP256K1_
-# define _SECP256K1_
-
-# ifdef __cplusplus
-extern "C" {
-# endif
-
-# if !defined(SECP256K1_GNUC_PREREQ)
-#  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
-#   define SECP256K1_GNUC_PREREQ(_maj,_min) \
- ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
-#  else
-#   define SECP256K1_GNUC_PREREQ(_maj,_min) 0
-#  endif
-# endif
-
-# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
-#  if SECP256K1_GNUC_PREREQ(2,7)
-#   define SECP256K1_INLINE __inline__
-#  elif (defined(_MSC_VER))
-#   define SECP256K1_INLINE __inline
-#  else
-#   define SECP256K1_INLINE
-#  endif
-# else
-#  define SECP256K1_INLINE inline
-# endif
-
-/**Warning attributes
-  * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
-  * some paranoid null checks. */
-# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
-#  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
-# else
-#  define SECP256K1_WARN_UNUSED_RESULT
-# endif
-# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
-#  define SECP256K1_ARG_NONNULL(_x)  __attribute__ ((__nonnull__(_x)))
-# else
-#  define SECP256K1_ARG_NONNULL(_x)
-# endif
-
-
-/** Flags to pass to secp256k1_start. */
-# define SECP256K1_START_VERIFY (1 << 0)
-# define SECP256K1_START_SIGN   (1 << 1)
-
-/** Initialize the library. This may take some time (10-100 ms).
- *  You need to call this before calling any other function.
- *  It cannot run in parallel with any other functions, but once
- *  secp256k1_start() returns, all other functions are thread-safe.
- */
-void secp256k1_start(unsigned int flags);
-
-/** Free all memory associated with this library. After this, no
- *  functions can be called anymore, except secp256k1_start()
- */
-void secp256k1_stop(void);
-
-/** Verify an ECDSA signature.
- *  Returns: 1: correct signature
- *           0: incorrect signature
- *          -1: invalid public key
- *          -2: invalid signature
- * In:       msg32:     the 32-byte message hash being verified (cannot be NULL)
- *           sig:       the signature being verified (cannot be NULL)
- *           siglen:    the length of the signature
- *           pubkey:    the public key to verify with (cannot be NULL)
- *           pubkeylen: the length of pubkey
- * Requires starting using SECP256K1_START_VERIFY.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
-  const unsigned char *msg32,
-  const unsigned char *sig,
-  int siglen,
-  const unsigned char *pubkey,
-  int pubkeylen
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
-
-/** A pointer to a function to deterministically generate a nonce.
- * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
- * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
- *          key32:     pointer to a 32-byte secret key (will not be NULL)
- *          attempt:   how many iterations we have tried to find a nonce.
- *                     This will almost always be 0, but different attempt values
- *                     are required to result in a different nonce.
- *          data:      Arbitrary data pointer that is passed through.
- * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
- * Except for test cases, this function should compute some cryptographic hash of
- * the message, the key and the attempt.
- */
-typedef int (*secp256k1_nonce_function_t)(
-  unsigned char *nonce32,
-  const unsigned char *msg32,
-  const unsigned char *key32,
-  unsigned int attempt,
-  const void *data
-);
-
-/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
- * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
- * extra entropy.
- */
-extern const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979;
-
-/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
-extern const secp256k1_nonce_function_t secp256k1_nonce_function_default;
-
-
-/** Create an ECDSA signature.
- *  Returns: 1: signature created
- *           0: the nonce generation function failed, the private key was invalid, or there is not
- *              enough space in the signature (as indicated by siglen).
- *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
- *           seckey: pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
- *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
- *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
- *  In/Out:  siglen: pointer to an int with the length of sig, which will be updated
- *                   to contain the actual signature length (<=72). If 0 is returned, this will be
- *                   set to zero.
- * Requires starting using SECP256K1_START_SIGN.
- *
- * The sig always has an s value in the lower half of the range (From 0x1
- * to 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
- * inclusive), unlike many other implementations.
- * With ECDSA a third-party can can forge a second distinct signature
- * of the same message given a single initial signature without knowing
- * the key by setting s to its additive inverse mod-order, 'flipping' the
- * sign of the random point R which is not included in the signature.
- * Since the forgery is of the same message this isn't universally
- * problematic, but in systems where message malleability or uniqueness
- * of signatures is important this can cause issues.  This forgery can be
- * blocked by all verifiers forcing signers to use a canonical form. The
- * lower-S form reduces the size of signatures slightly on average when
- * variable length encodings (such as DER) are used and is cheap to
- * verify, making it a good choice. Security of always using lower-S is
- * assured because anyone can trivially modify a signature after the
- * fact to enforce this property.  Adjusting it inside the signing
- * function avoids the need to re-serialize or have curve specific
- * constants outside of the library.  By always using a canonical form
- * even in applications where it isn't needed it becomes possible to
- * impose a requirement later if a need is discovered.
- * No other forms of ECDSA malleability are known and none seem likely,
- * but there is no formal proof that ECDSA, even with this additional
- * restriction, is free of other malleability.  Commonly used serialization
- * schemes will also accept various non-unique encodings, so care should
- * be taken when this property is required for an application.
- */
-int secp256k1_ecdsa_sign(
-  const unsigned char *msg32,
-  unsigned char *sig,
-  int *siglen,
-  const unsigned char *seckey,
-  secp256k1_nonce_function_t noncefp,
-  const void *ndata
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Create a compact ECDSA signature (64 byte + recovery id).
- *  Returns: 1: signature created
- *           0: the nonce generation function failed, or the secret key was invalid.
- *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
- *           seckey: pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
- *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
- *  Out:     sig:    pointer to a 64-byte array where the signature will be placed (cannot be NULL)
- *                   In case 0 is returned, the returned signature length will be zero.
- *           recid:  pointer to an int, which will be updated to contain the recovery id (can be NULL)
- * Requires starting using SECP256K1_START_SIGN.
- */
-int secp256k1_ecdsa_sign_compact(
-  const unsigned char *msg32,
-  unsigned char *sig64,
-  const unsigned char *seckey,
-  secp256k1_nonce_function_t noncefp,
-  const void *ndata,
-  int *recid
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
-
-/** Recover an ECDSA public key from a compact signature.
- *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
- *           0: otherwise.
- *  In:      msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
- *           sig64:      signature as 64 byte array (cannot be NULL)
- *           compressed: whether to recover a compressed or uncompressed pubkey
- *           recid:      the recovery id (0-3, as returned by ecdsa_sign_compact)
- *  Out:     pubkey:     pointer to a 33 or 65 byte array to put the pubkey (cannot be NULL)
- *           pubkeylen:  pointer to an int that will contain the pubkey length (cannot be NULL)
- * Requires starting using SECP256K1_START_VERIFY.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover_compact(
-  const unsigned char *msg32,
-  const unsigned char *sig64,
-  unsigned char *pubkey,
-  int *pubkeylen,
-  int compressed,
-  int recid
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Verify an ECDSA secret key.
- *  Returns: 1: secret key is valid
- *           0: secret key is invalid
- *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(const unsigned char *seckey) SECP256K1_ARG_NONNULL(1);
-
-/** Just validate a public key.
- *  Returns: 1: valid public key
- *           0: invalid public key
- *  In:      pubkey:    pointer to a 33-byte or 65-byte public key (cannot be NULL).
- *           pubkeylen: length of pubkey
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_verify(const unsigned char *pubkey, int pubkeylen) SECP256K1_ARG_NONNULL(1);
-
-/** Compute the public key for a secret key.
- *  In:     compressed: whether the computed public key should be compressed
- *          seckey:     pointer to a 32-byte private key (cannot be NULL)
- *  Out:    pubkey:     pointer to a 33-byte (if compressed) or 65-byte (if uncompressed)
- *                      area to store the public key (cannot be NULL)
- *          pubkeylen:  pointer to int that will be updated to contains the pubkey's
- *                      length (cannot be NULL)
- *  Returns: 1: secret was valid, public key stores
- *           0: secret was invalid, try again.
- * Requires starting using SECP256K1_START_SIGN.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
-  unsigned char *pubkey,
-  int *pubkeylen,
-  const unsigned char *seckey,
-  int compressed
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
-
-/** Decompress a public key.
- * In/Out: pubkey:    pointer to a 65-byte array to put the decompressed public key.
-                      It must contain a 33-byte or 65-byte public key already (cannot be NULL)
- *         pubkeylen: pointer to the size of the public key pointed to by pubkey (cannot be NULL)
-                      It will be updated to reflect the new size.
- * Returns: 0 if the passed public key was invalid, 1 otherwise. If 1 is returned, the
-            pubkey is replaced with its decompressed version.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_decompress(
-  unsigned char *pubkey,
-  int *pubkeylen
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
-
-/** Export a private key in DER format. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_export(
-  const unsigned char *seckey,
-  unsigned char *privkey,
-  int *privkeylen,
-  int compressed
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
-
-/** Import a private key in DER format. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_import(
-  unsigned char *seckey,
-  const unsigned char *privkey,
-  int privkeylen
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
-
-/** Tweak a private key by adding tweak to it. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
-  unsigned char *seckey,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
-
-/** Tweak a public key by adding tweak times the generator to it.
- * Requires starting with SECP256K1_START_VERIFY.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
-  unsigned char *pubkey,
-  int pubkeylen,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
-
-/** Tweak a private key by multiplying it with tweak. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
-  unsigned char *seckey,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
-
-/** Tweak a public key by multiplying it with tweak.
- * Requires starting with SECP256K1_START_VERIFY.
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
-  unsigned char *pubkey,
-  int pubkeylen,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
-
-# ifdef __cplusplus
-}
-# endif
-
-#endif

crypto/secp256k1/secp256k1/src/ecdsa.h

@@ -1,23 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_ECDSA_
-#define _SECP256K1_ECDSA_
-
-#include "scalar.h"
-#include "group.h"
-
-typedef struct {
-    secp256k1_scalar_t r, s;
-} secp256k1_ecdsa_sig_t;
-
-static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size);
-static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a);
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message);
-static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid);
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid);
-
-#endif

crypto/secp256k1/secp256k1/src/eckey.h

@@ -1,24 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_ECKEY_
-#define _SECP256K1_ECKEY_
-
-#include "group.h"
-#include "scalar.h"
-
-static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size);
-static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed);
-
-static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen);
-static int secp256k1_eckey_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed);
-
-static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
-
-#endif

crypto/secp256k1/secp256k1/src/ecmult.h

@@ -1,19 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_ECMULT_
-#define _SECP256K1_ECMULT_
-
-#include "num.h"
-#include "group.h"
-
-static void secp256k1_ecmult_start(void);
-static void secp256k1_ecmult_stop(void);
-
-/** Double multiply: R = na*A + ng*G */
-static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng);
-
-#endif

crypto/secp256k1/secp256k1/src/ecmult_gen_impl.h

@@ -1,128 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
-#define _SECP256K1_ECMULT_GEN_IMPL_H_
-
-#include "scalar.h"
-#include "group.h"
-#include "ecmult_gen.h"
-
-typedef struct {
-    /* For accelerating the computation of a*G:
-     * To harden against timing attacks, use the following mechanism:
-     * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
-     * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
-     *   * U_i = U * 2^i (for i=0..62)
-     *   * U_i = U * (1-2^63) (for i=63)
-     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
-     * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
-     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
-     * None of the resulting prec group elements have a known scalar, and neither do any of
-     * the intermediate sums while computing a*G.
-     */
-    secp256k1_ge_storage_t prec[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
-} secp256k1_ecmult_gen_consts_t;
-
-static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
-
-static void secp256k1_ecmult_gen_start(void) {
-    secp256k1_ge_t prec[1024];
-    secp256k1_gej_t gj;
-    secp256k1_gej_t nums_gej;
-    secp256k1_ecmult_gen_consts_t *ret;
-    int i, j;
-    if (secp256k1_ecmult_gen_consts != NULL) {
-        return;
-    }
-
-    /* Allocate the precomputation table. */
-    ret = (secp256k1_ecmult_gen_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_gen_consts_t));
-
-    /* get the generator */
-    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
-
-    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
-    {
-        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
-        secp256k1_fe_t nums_x;
-        secp256k1_ge_t nums_ge;
-        VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
-        VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
-        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
-        /* Add G to make the bits in x uniformly distributed. */
-        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g);
-    }
-
-    /* compute prec. */
-    {
-        secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
-        secp256k1_gej_t gbase;
-        secp256k1_gej_t numsbase;
-        gbase = gj; /* 16^j * G */
-        numsbase = nums_gej; /* 2^j * nums. */
-        for (j = 0; j < 64; j++) {
-            /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
-            precj[j*16] = numsbase;
-            for (i = 1; i < 16; i++) {
-                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
-            }
-            /* Multiply gbase by 16. */
-            for (i = 0; i < 4; i++) {
-                secp256k1_gej_double_var(&gbase, &gbase);
-            }
-            /* Multiply numbase by 2. */
-            secp256k1_gej_double_var(&numsbase, &numsbase);
-            if (j == 62) {
-                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
-                secp256k1_gej_neg(&numsbase, &numsbase);
-                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
-            }
-        }
-        secp256k1_ge_set_all_gej_var(1024, prec, precj);
-    }
-    for (j = 0; j < 64; j++) {
-        for (i = 0; i < 16; i++) {
-            secp256k1_ge_to_storage(&ret->prec[j][i], &prec[j*16 + i]);
-        }
-    }
-
-    /* Set the global pointer to the precomputation table. */
-    secp256k1_ecmult_gen_consts = ret;
-}
-
-static void secp256k1_ecmult_gen_stop(void) {
-    secp256k1_ecmult_gen_consts_t *c;
-    if (secp256k1_ecmult_gen_consts == NULL) {
-        return;
-    }
-
-    c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
-    secp256k1_ecmult_gen_consts = NULL;
-    free(c);
-}
-
-static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
-    const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
-    secp256k1_ge_t add;
-    secp256k1_ge_storage_t adds;
-    int bits;
-    int i, j;
-    secp256k1_gej_set_infinity(r);
-    add.infinity = 0;
-    for (j = 0; j < 64; j++) {
-        bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
-        for (i = 0; i < 16; i++) {
-            secp256k1_ge_storage_cmov(&adds, &c->prec[j][i], i == bits);
-        }
-        secp256k1_ge_from_storage(&add, &adds);
-        secp256k1_gej_add_ge(r, r, &add);
-    }
-    bits = 0;
-    secp256k1_ge_clear(&add);
-}
-
-#endif

crypto/secp256k1/secp256k1/src/ecmult_impl.h

@@ -1,302 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_ECMULT_IMPL_H_
-#define _SECP256K1_ECMULT_IMPL_H_
-
-#include "group.h"
-#include "scalar.h"
-#include "ecmult.h"
-
-/* optimal for 128-bit and 256-bit exponents. */
-#define WINDOW_A 5
-
-/** larger numbers may result in slightly better performance, at the cost of
-    exponentially larger precomputed tables. */
-#ifdef USE_ENDOMORPHISM
-/** Two tables for window size 15: 1.375 MiB. */
-#define WINDOW_G 15
-#else
-/** One table for window size 16: 1.375 MiB. */
-#define WINDOW_G 16
-#endif
-
-/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
- *  pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
- *  2^(w-2) entries.
- *
- *  There are two versions of this function:
- *  - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
- *    fast to precompute, but slower to use in later additions.
- *  - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
- *    (much) slower to precompute, but a bit faster to use in later additions.
- *  To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
- *  G is constant, so it only needs to be done once in advance.
- */
-static void secp256k1_ecmult_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
-    secp256k1_gej_t d;
-    int i;
-    pre[0] = *a;
-    secp256k1_gej_double_var(&d, &pre[0]);
-    for (i = 1; i < (1 << (w-2)); i++) {
-        secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]);
-    }
-}
-
-static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t *pre, const secp256k1_gej_t *a, int w) {
-    secp256k1_gej_t d;
-    int i;
-    const int table_size = 1 << (w-2);
-    secp256k1_gej_t *prej = (secp256k1_gej_t *)checked_malloc(sizeof(secp256k1_gej_t) * table_size);
-    secp256k1_ge_t *prea = (secp256k1_ge_t *)checked_malloc(sizeof(secp256k1_ge_t) * table_size);
-    prej[0] = *a;
-    secp256k1_gej_double_var(&d, a);
-    for (i = 1; i < table_size; i++) {
-        secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]);
-    }
-    secp256k1_ge_set_all_gej_var(table_size, prea, prej);
-    for (i = 0; i < table_size; i++) {
-        secp256k1_ge_to_storage(&pre[i], &prea[i]);
-    }
-    free(prej);
-    free(prea);
-}
-
-/** The number of entries a table with precomputed multiples needs to have. */
-#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
-
-/** The following two macro retrieves a particular odd multiple from a table
- *  of precomputed multiples. */
-#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) do { \
-    VERIFY_CHECK(((n) & 1) == 1); \
-    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
-    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
-    if ((n) > 0) { \
-        *(r) = (pre)[((n)-1)/2]; \
-    } else { \
-        secp256k1_gej_neg((r), &(pre)[(-(n)-1)/2]); \
-    } \
-} while(0)
-#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
-    VERIFY_CHECK(((n) & 1) == 1); \
-    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
-    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
-    if ((n) > 0) { \
-        secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
-    } else { \
-        secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
-        secp256k1_ge_neg((r), (r)); \
-    } \
-} while(0)
-
-typedef struct {
-    /* For accelerating the computation of a*P + b*G: */
-    secp256k1_ge_storage_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)];    /* odd multiples of the generator */
-#ifdef USE_ENDOMORPHISM
-    secp256k1_ge_storage_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of 2^128*generator */
-#endif
-} secp256k1_ecmult_consts_t;
-
-static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
-
-static void secp256k1_ecmult_start(void) {
-    secp256k1_gej_t gj;
-    secp256k1_ecmult_consts_t *ret;
-    if (secp256k1_ecmult_consts != NULL) {
-        return;
-    }
-
-    /* Allocate the precomputation table. */
-    ret = (secp256k1_ecmult_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_consts_t));
-
-    /* get the generator */
-    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
-
-
-    /* precompute the tables with odd multiples */
-    secp256k1_ecmult_table_precomp_ge_storage_var(ret->pre_g, &gj, WINDOW_G);
-
-#ifdef USE_ENDOMORPHISM
-    {
-        secp256k1_gej_t g_128j;
-        int i;
-        /* calculate 2^128*generator */
-        g_128j = gj;
-        for (i = 0; i < 128; i++) {
-            secp256k1_gej_double_var(&g_128j, &g_128j);
-        }
-        secp256k1_ecmult_table_precomp_ge_storage_var(ret->pre_g_128, &g_128j, WINDOW_G);
-    }
-#endif
-
-    /* Set the global pointer to the precomputation table. */
-    secp256k1_ecmult_consts = ret;
-}
-
-static void secp256k1_ecmult_stop(void) {
-    secp256k1_ecmult_consts_t *c;
-    if (secp256k1_ecmult_consts == NULL) {
-        return;
-    }
-
-    c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts;
-    secp256k1_ecmult_consts = NULL;
-    free(c);
-}
-
-/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
- *  with the following guarantees:
- *  - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
- *  - two non-zero entries in wnaf are separated by at least w-1 zeroes.
- *  - the number of set values in wnaf is returned. This number is at most 256, and at most one more
- *  - than the number of bits in the (absolute value) of the input.
- */
-static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_scalar_t *a, int w) {
-    secp256k1_scalar_t s = *a;
-    int set_bits = 0;
-    int bit = 0;
-    int sign = 1;
-
-    if (secp256k1_scalar_get_bits(&s, 255, 1)) {
-        secp256k1_scalar_negate(&s, &s);
-        sign = -1;
-    }
-
-    while (bit < 256) {
-        int now;
-        int word;
-        if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
-            bit++;
-            continue;
-        }
-        while (set_bits < bit) {
-            wnaf[set_bits++] = 0;
-        }
-        now = w;
-        if (bit + now > 256) {
-            now = 256 - bit;
-        }
-        word = secp256k1_scalar_get_bits_var(&s, bit, now);
-        if (word & (1 << (w-1))) {
-            secp256k1_scalar_add_bit(&s, bit + w);
-            wnaf[set_bits++] = sign * (word - (1 << w));
-        } else {
-            wnaf[set_bits++] = sign * word;
-        }
-        bit += now;
-    }
-    return set_bits;
-}
-
-static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
-    secp256k1_gej_t tmpj;
-    secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_ge_t tmpa;
-    const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
-#ifdef USE_ENDOMORPHISM
-    secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_scalar_t na_1, na_lam;
-    /* Splitted G factors. */
-    secp256k1_scalar_t ng_1, ng_128;
-    int wnaf_na_1[130];
-    int wnaf_na_lam[130];
-    int bits_na_1;
-    int bits_na_lam;
-    int wnaf_ng_1[129];
-    int bits_ng_1;
-    int wnaf_ng_128[129];
-    int bits_ng_128;
-#else
-    int wnaf_na[256];
-    int bits_na;
-    int wnaf_ng[257];
-    int bits_ng;
-#endif
-    int i;
-    int bits;
-
-#ifdef USE_ENDOMORPHISM
-    /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
-    secp256k1_scalar_split_lambda_var(&na_1, &na_lam, na);
-
-    /* build wnaf representation for na_1 and na_lam. */
-    bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   &na_1,   WINDOW_A);
-    bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
-    VERIFY_CHECK(bits_na_1 <= 130);
-    VERIFY_CHECK(bits_na_lam <= 130);
-    bits = bits_na_1;
-    if (bits_na_lam > bits) {
-        bits = bits_na_lam;
-    }
-#else
-    /* build wnaf representation for na. */
-    bits_na     = secp256k1_ecmult_wnaf(wnaf_na,     na,      WINDOW_A);
-    bits = bits_na;
-#endif
-
-    /* calculate odd multiples of a */
-    secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A);
-
-#ifdef USE_ENDOMORPHISM
-    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
-        secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]);
-    }
-
-    /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
-    secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
-
-    /* Build wnaf representation for ng_1 and ng_128 */
-    bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   &ng_1,   WINDOW_G);
-    bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
-    if (bits_ng_1 > bits) {
-        bits = bits_ng_1;
-    }
-    if (bits_ng_128 > bits) {
-        bits = bits_ng_128;
-    }
-#else
-    bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     ng,      WINDOW_G);
-    if (bits_ng > bits) {
-        bits = bits_ng;
-    }
-#endif
-
-    secp256k1_gej_set_infinity(r);
-
-    for (i = bits-1; i >= 0; i--) {
-        int n;
-        secp256k1_gej_double_var(r, r);
-#ifdef USE_ENDOMORPHISM
-        if (i < bits_na_1 && (n = wnaf_na_1[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
-        }
-        if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
-        }
-        if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
-        }
-        if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g_128, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
-        }
-#else
-        if (i < bits_na && (n = wnaf_na[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
-        }
-        if (i < bits_ng && (n = wnaf_ng[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
-        }
-#endif
-    }
-}
-
-#endif

crypto/secp256k1/secp256k1/src/group.h

@@ -1,118 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_GROUP_
-#define _SECP256K1_GROUP_
-
-#include "num.h"
-#include "field.h"
-
-/** A group element of the secp256k1 curve, in affine coordinates. */
-typedef struct {
-    secp256k1_fe_t x;
-    secp256k1_fe_t y;
-    int infinity; /* whether this represents the point at infinity */
-} secp256k1_ge_t;
-
-#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
-#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
-
-/** A group element of the secp256k1 curve, in jacobian coordinates. */
-typedef struct {
-    secp256k1_fe_t x; /* actual X: x/z^2 */
-    secp256k1_fe_t y; /* actual Y: y/z^3 */
-    secp256k1_fe_t z;
-    int infinity; /* whether this represents the point at infinity */
-} secp256k1_gej_t;
-
-#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
-#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
-
-typedef struct {
-    secp256k1_fe_storage_t x;
-    secp256k1_fe_storage_t y;
-} secp256k1_ge_storage_t;
-
-#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
-
-/** Set a group element equal to the point at infinity */
-static void secp256k1_ge_set_infinity(secp256k1_ge_t *r);
-
-/** Set a group element equal to the point with given X and Y coordinates */
-static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
-
-/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
- *  for Y. Return value indicates whether the result is valid. */
-static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd);
-
-/** Check whether a group element is the point at infinity. */
-static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
-
-/** Check whether a group element is valid (i.e., on the curve). */
-static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a);
-
-static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
-
-/** Set a group element equal to another which is given in jacobian coordinates */
-static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
-
-/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a);
-
-
-/** Set a group element (jacobian) equal to the point at infinity. */
-static void secp256k1_gej_set_infinity(secp256k1_gej_t *r);
-
-/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
-static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
-
-/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
-static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
-
-/** Compare the X coordinate of a group element (jacobian). */
-static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a);
-
-/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
-static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
-
-/** Check whether a group element is the point at infinity. */
-static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
-
-/** Set r equal to the double of a. */
-static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a);
-
-/** Set r equal to the sum of a and b. */
-static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
-
-/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
-static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
-
-/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
-    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
-    guarantee, and b is allowed to be infinity. */
-static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
-
-#ifdef USE_ENDOMORPHISM
-/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
-static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
-#endif
-
-/** Clear a secp256k1_gej_t to prevent leaking sensitive information. */
-static void secp256k1_gej_clear(secp256k1_gej_t *r);
-
-/** Clear a secp256k1_ge_t to prevent leaking sensitive information. */
-static void secp256k1_ge_clear(secp256k1_ge_t *r);
-
-/** Convert a group element to the storage type. */
-static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t*);
-
-/** Convert a group element back from the storage type. */
-static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t*);
-
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag);
-
-#endif

crypto/secp256k1/secp256k1/src/group_impl.h

@@ -1,434 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_GROUP_IMPL_H_
-#define _SECP256K1_GROUP_IMPL_H_
-
-#include <string.h>
-
-#include "num.h"
-#include "field.h"
-#include "group.h"
-
-/** Generator for secp256k1, value 'g' defined in
- *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
- */
-static const secp256k1_ge_t secp256k1_ge_const_g = SECP256K1_GE_CONST(
-    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
-    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
-    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
-    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
-);
-
-static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
-    r->infinity = 1;
-}
-
-static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
-    r->infinity = 0;
-    r->x = *x;
-    r->y = *y;
-}
-
-static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
-    return a->infinity;
-}
-
-static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
-    *r = *a;
-    secp256k1_fe_normalize_weak(&r->y);
-    secp256k1_fe_negate(&r->y, &r->y, 1);
-}
-
-static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
-    secp256k1_fe_t z2, z3;
-    r->infinity = a->infinity;
-    secp256k1_fe_inv(&a->z, &a->z);
-    secp256k1_fe_sqr(&z2, &a->z);
-    secp256k1_fe_mul(&z3, &a->z, &z2);
-    secp256k1_fe_mul(&a->x, &a->x, &z2);
-    secp256k1_fe_mul(&a->y, &a->y, &z3);
-    secp256k1_fe_set_int(&a->z, 1);
-    r->x = a->x;
-    r->y = a->y;
-}
-
-static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
-    secp256k1_fe_t z2, z3;
-    r->infinity = a->infinity;
-    if (a->infinity) {
-        return;
-    }
-    secp256k1_fe_inv_var(&a->z, &a->z);
-    secp256k1_fe_sqr(&z2, &a->z);
-    secp256k1_fe_mul(&z3, &a->z, &z2);
-    secp256k1_fe_mul(&a->x, &a->x, &z2);
-    secp256k1_fe_mul(&a->y, &a->y, &z3);
-    secp256k1_fe_set_int(&a->z, 1);
-    r->x = a->x;
-    r->y = a->y;
-}
-
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a) {
-    secp256k1_fe_t *az;
-    secp256k1_fe_t *azi;
-    size_t i;
-    size_t count = 0;
-    az = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * len);
-    for (i = 0; i < len; i++) {
-        if (!a[i].infinity) {
-            az[count++] = a[i].z;
-        }
-    }
-
-    azi = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * count);
-    secp256k1_fe_inv_all_var(count, azi, az);
-    free(az);
-
-    count = 0;
-    for (i = 0; i < len; i++) {
-        r[i].infinity = a[i].infinity;
-        if (!a[i].infinity) {
-            secp256k1_fe_t zi2, zi3;
-            secp256k1_fe_t *zi = &azi[count++];
-            secp256k1_fe_sqr(&zi2, zi);
-            secp256k1_fe_mul(&zi3, &zi2, zi);
-            secp256k1_fe_mul(&r[i].x, &a[i].x, &zi2);
-            secp256k1_fe_mul(&r[i].y, &a[i].y, &zi3);
-        }
-    }
-    free(azi);
-}
-
-static void secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
-    r->infinity = 1;
-    secp256k1_fe_set_int(&r->x, 0);
-    secp256k1_fe_set_int(&r->y, 0);
-    secp256k1_fe_set_int(&r->z, 0);
-}
-
-static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
-    r->infinity = 0;
-    r->x = *x;
-    r->y = *y;
-    secp256k1_fe_set_int(&r->z, 1);
-}
-
-static void secp256k1_gej_clear(secp256k1_gej_t *r) {
-    r->infinity = 0;
-    secp256k1_fe_clear(&r->x);
-    secp256k1_fe_clear(&r->y);
-    secp256k1_fe_clear(&r->z);
-}
-
-static void secp256k1_ge_clear(secp256k1_ge_t *r) {
-    r->infinity = 0;
-    secp256k1_fe_clear(&r->x);
-    secp256k1_fe_clear(&r->y);
-}
-
-static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
-    secp256k1_fe_t x2, x3, c;
-    r->x = *x;
-    secp256k1_fe_sqr(&x2, x);
-    secp256k1_fe_mul(&x3, x, &x2);
-    r->infinity = 0;
-    secp256k1_fe_set_int(&c, 7);
-    secp256k1_fe_add(&c, &x3);
-    if (!secp256k1_fe_sqrt_var(&r->y, &c)) {
-        return 0;
-    }
-    secp256k1_fe_normalize_var(&r->y);
-    if (secp256k1_fe_is_odd(&r->y) != odd) {
-        secp256k1_fe_negate(&r->y, &r->y, 1);
-    }
-    return 1;
-}
-
-static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
-   r->infinity = a->infinity;
-   r->x = a->x;
-   r->y = a->y;
-   secp256k1_fe_set_int(&r->z, 1);
-}
-
-static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a) {
-    secp256k1_fe_t r, r2;
-    VERIFY_CHECK(!a->infinity);
-    secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
-    r2 = a->x; secp256k1_fe_normalize_weak(&r2);
-    return secp256k1_fe_equal_var(&r, &r2);
-}
-
-static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
-    r->infinity = a->infinity;
-    r->x = a->x;
-    r->y = a->y;
-    r->z = a->z;
-    secp256k1_fe_normalize_weak(&r->y);
-    secp256k1_fe_negate(&r->y, &r->y, 1);
-}
-
-static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
-    return a->infinity;
-}
-
-static int secp256k1_gej_is_valid_var(const secp256k1_gej_t *a) {
-    secp256k1_fe_t y2, x3, z2, z6;
-    if (a->infinity) {
-        return 0;
-    }
-    /** y^2 = x^3 + 7
-     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
-     *  Y^2 / Z^6 = X^3 / Z^6 + 7
-     *  Y^2 = X^3 + 7*Z^6
-     */
-    secp256k1_fe_sqr(&y2, &a->y);
-    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
-    secp256k1_fe_sqr(&z2, &a->z);
-    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
-    secp256k1_fe_mul_int(&z6, 7);
-    secp256k1_fe_add(&x3, &z6);
-    secp256k1_fe_normalize_weak(&x3);
-    return secp256k1_fe_equal_var(&y2, &x3);
-}
-
-static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a) {
-    secp256k1_fe_t y2, x3, c;
-    if (a->infinity) {
-        return 0;
-    }
-    /* y^2 = x^3 + 7 */
-    secp256k1_fe_sqr(&y2, &a->y);
-    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
-    secp256k1_fe_set_int(&c, 7);
-    secp256k1_fe_add(&x3, &c);
-    secp256k1_fe_normalize_weak(&x3);
-    return secp256k1_fe_equal_var(&y2, &x3);
-}
-
-static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
-    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t t1,t2,t3,t4;
-    /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
-     *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
-     *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
-     */
-    r->infinity = a->infinity;
-    if (r->infinity) {
-        return;
-    }
-
-    secp256k1_fe_mul(&r->z, &a->z, &a->y);
-    secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
-    secp256k1_fe_sqr(&t1, &a->x);
-    secp256k1_fe_mul_int(&t1, 3);         /* T1 = 3*X^2 (3) */
-    secp256k1_fe_sqr(&t2, &t1);           /* T2 = 9*X^4 (1) */
-    secp256k1_fe_sqr(&t3, &a->y);
-    secp256k1_fe_mul_int(&t3, 2);         /* T3 = 2*Y^2 (2) */
-    secp256k1_fe_sqr(&t4, &t3);
-    secp256k1_fe_mul_int(&t4, 2);         /* T4 = 8*Y^4 (2) */
-    secp256k1_fe_mul(&t3, &t3, &a->x);    /* T3 = 2*X*Y^2 (1) */
-    r->x = t3;
-    secp256k1_fe_mul_int(&r->x, 4);       /* X' = 8*X*Y^2 (4) */
-    secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
-    secp256k1_fe_add(&r->x, &t2);         /* X' = 9*X^4 - 8*X*Y^2 (6) */
-    secp256k1_fe_negate(&t2, &t2, 1);     /* T2 = -9*X^4 (2) */
-    secp256k1_fe_mul_int(&t3, 6);         /* T3 = 12*X*Y^2 (6) */
-    secp256k1_fe_add(&t3, &t2);           /* T3 = 12*X*Y^2 - 9*X^4 (8) */
-    secp256k1_fe_mul(&r->y, &t1, &t3);    /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
-    secp256k1_fe_negate(&t2, &t4, 2);     /* T2 = -8*Y^4 (3) */
-    secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
-}
-
-static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
-    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
-    if (a->infinity) {
-        *r = *b;
-        return;
-    }
-    if (b->infinity) {
-        *r = *a;
-        return;
-    }
-    r->infinity = 0;
-    secp256k1_fe_sqr(&z22, &b->z);
-    secp256k1_fe_sqr(&z12, &a->z);
-    secp256k1_fe_mul(&u1, &a->x, &z22);
-    secp256k1_fe_mul(&u2, &b->x, &z12);
-    secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
-    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
-    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
-    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
-        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
-            secp256k1_gej_double_var(r, a);
-        } else {
-            r->infinity = 1;
-        }
-        return;
-    }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
-    secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
-    secp256k1_fe_add(&r->y, &h3);
-}
-
-static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
-    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
-    if (a->infinity) {
-        r->infinity = b->infinity;
-        r->x = b->x;
-        r->y = b->y;
-        secp256k1_fe_set_int(&r->z, 1);
-        return;
-    }
-    if (b->infinity) {
-        *r = *a;
-        return;
-    }
-    r->infinity = 0;
-    secp256k1_fe_sqr(&z12, &a->z);
-    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
-    secp256k1_fe_mul(&u2, &b->x, &z12);
-    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
-    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
-    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
-    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
-        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
-            secp256k1_gej_double_var(r, a);
-        } else {
-            r->infinity = 1;
-        }
-        return;
-    }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
-    secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
-    secp256k1_fe_add(&r->y, &h3);
-}
-
-static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
-    /* Operations: 7 mul, 5 sqr, 5 normalize, 19 mul_int/add/negate */
-    secp256k1_fe_t zz, u1, u2, s1, s2, z, t, m, n, q, rr;
-    int infinity;
-    VERIFY_CHECK(!b->infinity);
-    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
-
-    /** In:
-     *    Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
-     *    In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
-     *  we find as solution for a unified addition/doubling formula:
-     *    lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
-     *    x3 = lambda^2 - (x1 + x2)
-     *    2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
-     *
-     *  Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
-     *    U1 = X1*Z2^2, U2 = X2*Z1^2
-     *    S1 = Y1*Z2^3, S2 = Y2*Z1^3
-     *    Z = Z1*Z2
-     *    T = U1+U2
-     *    M = S1+S2
-     *    Q = T*M^2
-     *    R = T^2-U1*U2
-     *    X3 = 4*(R^2-Q)
-     *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
-     *    Z3 = 2*M*Z
-     *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
-     */
-
-    secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
-    u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
-    secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
-    s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
-    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z2^2 (1) */
-    secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
-    z = a->z;                                           /* z = Z = Z1*Z2 (8) */
-    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
-    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
-    secp256k1_fe_sqr(&n, &m);                           /* n = M^2 (1) */
-    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*M^2 (1) */
-    secp256k1_fe_sqr(&n, &n);                           /* n = M^4 (1) */
-    secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
-    secp256k1_fe_mul(&t, &u1, &u2); secp256k1_fe_negate(&t, &t, 1); /* t = -U1*U2 (2) */
-    secp256k1_fe_add(&rr, &t);                                      /* rr = R = T^2-U1*U2 (3) */
-    secp256k1_fe_sqr(&t, &rr);                                      /* t = R^2 (1) */
-    secp256k1_fe_mul(&r->z, &m, &z);                                /* r->z = M*Z (1) */
-    infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
-    secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); /* r->z = Z3 = 2*M*Z (2) */
-    r->x = t;                                           /* r->x = R^2 (1) */
-    secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
-    secp256k1_fe_add(&r->x, &q);                        /* r->x = R^2-Q (3) */
-    secp256k1_fe_normalize(&r->x);
-    secp256k1_fe_mul_int(&q, 3);                        /* q = -3*Q (6) */
-    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*R^2 (2) */
-    secp256k1_fe_add(&t, &q);                           /* t = 2*R^2-3*Q (8) */
-    secp256k1_fe_mul(&t, &t, &rr);                      /* t = R*(2*R^2-3*Q) (1) */
-    secp256k1_fe_add(&t, &n);                           /* t = R*(2*R^2-3*Q)+M^4 (2) */
-    secp256k1_fe_negate(&r->y, &t, 2);                  /* r->y = R*(3*Q-2*R^2)-M^4 (3) */
-    secp256k1_fe_normalize_weak(&r->y);
-    secp256k1_fe_mul_int(&r->x, 4 * (1 - a->infinity)); /* r->x = X3 = 4*(R^2-Q) */
-    secp256k1_fe_mul_int(&r->y, 4 * (1 - a->infinity)); /* r->y = Y3 = 4*R*(3*Q-2*R^2)-4*M^4 (4) */
-
-    /** In case a->infinity == 1, the above code results in r->x, r->y, and r->z all equal to 0.
-     *  Add b->x to x, b->y to y, and 1 to z in that case.
-     */
-    t = b->x; secp256k1_fe_mul_int(&t, a->infinity);
-    secp256k1_fe_add(&r->x, &t);
-    t = b->y; secp256k1_fe_mul_int(&t, a->infinity);
-    secp256k1_fe_add(&r->y, &t);
-    secp256k1_fe_set_int(&t, a->infinity);
-    secp256k1_fe_add(&r->z, &t);
-    r->infinity = infinity;
-}
-
-static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t *a) {
-    secp256k1_fe_t x, y;
-    VERIFY_CHECK(!a->infinity);
-    x = a->x;
-    secp256k1_fe_normalize(&x);
-    y = a->y;
-    secp256k1_fe_normalize(&y);
-    secp256k1_fe_to_storage(&r->x, &x);
-    secp256k1_fe_to_storage(&r->y, &y);
-}
-
-static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t *a) {
-    secp256k1_fe_from_storage(&r->x, &a->x);
-    secp256k1_fe_from_storage(&r->y, &a->y);
-    r->infinity = 0;
-}
-
-static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag) {
-    secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
-    secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
-}
-
-#ifdef USE_ENDOMORPHISM
-static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
-    static const secp256k1_fe_t beta = SECP256K1_FE_CONST(
-        0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
-        0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
-    );
-    *r = *a;
-    secp256k1_fe_mul(&r->x, &r->x, &beta);
-}
-#endif
-
-#endif

crypto/secp256k1/secp256k1/src/scalar.h

@@ -1,93 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                   *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef _SECP256K1_SCALAR_
-#define _SECP256K1_SCALAR_
-
-#include "num.h"
-
-#if defined HAVE_CONFIG_H
-#include "libsecp256k1-config.h"
-#endif
-
-#if defined(USE_SCALAR_4X64)
-#include "scalar_4x64.h"
-#elif defined(USE_SCALAR_8X32)
-#include "scalar_8x32.h"
-#else
-#error "Please select scalar implementation"
-#endif
-
-/** Clear a scalar to prevent the leak of sensitive data. */
-static void secp256k1_scalar_clear(secp256k1_scalar_t *r);
-
-/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
-static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
-
-/** Access bits from a scalar. Not constant time. */
-static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
-
-/** Set a scalar from a big endian byte array. */
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *bin, int *overflow);
-
-/** Set a scalar to an unsigned integer. */
-static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v);
-
-/** Convert a scalar to a byte array. */
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a);
-
-/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
-
-/** Add a power of two to a scalar. The result is not allowed to overflow. */
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit);
-
-/** Multiply two scalars (modulo the group order). */
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
-
-/** Compute the square of a scalar (modulo the group order). */
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
-
-/** Compute the inverse of a scalar (modulo the group order). */
-static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
-
-/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
-static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
-
-/** Compute the complement of a scalar (modulo the group order). */
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
-
-/** Check whether a scalar equals zero. */
-static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a);
-
-/** Check whether a scalar equals one. */
-static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a);
-
-/** Check whether a scalar is higher than the group order divided by 2. */
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a);
-
-#ifndef USE_NUM_NONE
-/** Convert a scalar to a number. */
-static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a);
-
-/** Get the order of the group as a number. */
-static void secp256k1_scalar_order_get_num(secp256k1_num_t *r);
-#endif
-
-/** Compare two scalars. */
-static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
-
-#ifdef USE_ENDOMORPHISM
-/** Find r1 and r2 such that r1+r2*2^128 = a. */
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
-/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
-static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
-#endif
-
-/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
-static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift);
-
-#endif

crypto/secp256k1/secp256k1/src/secp256k1.c

@@ -1,372 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#define SECP256K1_BUILD (1)
-
-#include "include/secp256k1.h"
-
-#include "util.h"
-#include "num_impl.h"
-#include "field_impl.h"
-#include "scalar_impl.h"
-#include "group_impl.h"
-#include "ecmult_impl.h"
-#include "ecmult_gen_impl.h"
-#include "ecdsa_impl.h"
-#include "eckey_impl.h"
-#include "hash_impl.h"
-
-void secp256k1_start(unsigned int flags) {
-    if (flags & SECP256K1_START_SIGN) {
-        secp256k1_ecmult_gen_start();
-    }
-    if (flags & SECP256K1_START_VERIFY) {
-        secp256k1_ecmult_start();
-    }
-}
-
-void secp256k1_stop(void) {
-    secp256k1_ecmult_stop();
-    secp256k1_ecmult_gen_stop();
-}
-
-int secp256k1_ecdsa_verify(const unsigned char *msg32, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
-    secp256k1_ge_t q;
-    secp256k1_ecdsa_sig_t s;
-    secp256k1_scalar_t m;
-    int ret = -3;
-    DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-
-    secp256k1_scalar_set_b32(&m, msg32, NULL);
-
-    if (secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen)) {
-        if (secp256k1_ecdsa_sig_parse(&s, sig, siglen)) {
-            if (secp256k1_ecdsa_sig_verify(&s, &q, &m)) {
-                /* success is 1, all other values are fail */
-                ret = 1;
-            } else {
-                ret = 0;
-            }
-        } else {
-            ret = -2;
-        }
-    } else {
-        ret = -1;
-    }
-
-    return ret;
-}
-
-static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
-   secp256k1_rfc6979_hmac_sha256_t rng;
-   unsigned int i;
-   secp256k1_rfc6979_hmac_sha256_initialize(&rng, key32, 32, msg32, 32, (const unsigned char*)data, data != NULL ? 32 : 0);
-   for (i = 0; i <= counter; i++) {
-       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
-   }
-   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
-   return 1;
-}
-
-const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
-const secp256k1_nonce_function_t secp256k1_nonce_function_default = nonce_function_rfc6979;
-
-int secp256k1_ecdsa_sign(const unsigned char *msg32, unsigned char *signature, int *signaturelen, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata) {
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t sec, non, msg;
-    int ret = 0;
-    int overflow = 0;
-    unsigned int count = 0;
-    DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(signature != NULL);
-    DEBUG_CHECK(signaturelen != NULL);
-    DEBUG_CHECK(seckey != NULL);
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
-    }
-
-    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    /* Fail if the secret key is invalid. */
-    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
-        secp256k1_scalar_set_b32(&msg, msg32, NULL);
-        while (1) {
-            unsigned char nonce32[32];
-            ret = noncefp(nonce32, msg32, seckey, count, noncedata);
-            if (!ret) {
-                break;
-            }
-            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-            memset(nonce32, 0, 32);
-            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
-                if (secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, NULL)) {
-                    break;
-                }
-            }
-            count++;
-        }
-        if (ret) {
-            ret = secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig);
-        }
-        secp256k1_scalar_clear(&msg);
-        secp256k1_scalar_clear(&non);
-        secp256k1_scalar_clear(&sec);
-    }
-    if (!ret) {
-        *signaturelen = 0;
-    }
-    return ret;
-}
-
-int secp256k1_ecdsa_sign_compact(const unsigned char *msg32, unsigned char *sig64, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata, int *recid) {
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t sec, non, msg;
-    int ret = 0;
-    int overflow = 0;
-    unsigned int count = 0;
-    DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig64 != NULL);
-    DEBUG_CHECK(seckey != NULL);
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
-    }
-
-    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    /* Fail if the secret key is invalid. */
-    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
-        secp256k1_scalar_set_b32(&msg, msg32, NULL);
-        while (1) {
-            unsigned char nonce32[32];
-            ret = noncefp(nonce32, msg32, seckey, count, noncedata);
-            if (!ret) {
-                break;
-            }
-            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-            memset(nonce32, 0, 32);
-            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
-                if (secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, recid)) {
-                    break;
-                }
-            }
-            count++;
-        }
-        if (ret) {
-            secp256k1_scalar_get_b32(sig64, &sig.r);
-            secp256k1_scalar_get_b32(sig64 + 32, &sig.s);
-        }
-        secp256k1_scalar_clear(&msg);
-        secp256k1_scalar_clear(&non);
-        secp256k1_scalar_clear(&sec);
-    }
-    if (!ret) {
-        memset(sig64, 0, 64);
-    }
-    return ret;
-}
-
-int secp256k1_ecdsa_recover_compact(const unsigned char *msg32, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
-    secp256k1_ge_t q;
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t m;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig64 != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-    DEBUG_CHECK(recid >= 0 && recid <= 3);
-
-    secp256k1_scalar_set_b32(&sig.r, sig64, &overflow);
-    if (!overflow) {
-        secp256k1_scalar_set_b32(&sig.s, sig64 + 32, &overflow);
-        if (!overflow) {
-            secp256k1_scalar_set_b32(&m, msg32, NULL);
-
-            if (secp256k1_ecdsa_sig_recover(&sig, &q, &m, recid)) {
-                ret = secp256k1_eckey_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
-            }
-        }
-    }
-    return ret;
-}
-
-int secp256k1_ec_seckey_verify(const unsigned char *seckey) {
-    secp256k1_scalar_t sec;
-    int ret;
-    int overflow;
-    DEBUG_CHECK(seckey != NULL);
-
-    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    ret = !secp256k1_scalar_is_zero(&sec) && !overflow;
-    secp256k1_scalar_clear(&sec);
-    return ret;
-}
-
-int secp256k1_ec_pubkey_verify(const unsigned char *pubkey, int pubkeylen) {
-    secp256k1_ge_t q;
-    DEBUG_CHECK(pubkey != NULL);
-
-    return secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen);
-}
-
-int secp256k1_ec_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed) {
-    secp256k1_gej_t pj;
-    secp256k1_ge_t p;
-    secp256k1_scalar_t sec;
-    int overflow;
-    int ret = 0;
-    DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-    DEBUG_CHECK(seckey != NULL);
-
-    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    if (!overflow) {
-        secp256k1_ecmult_gen(&pj, &sec);
-        secp256k1_scalar_clear(&sec);
-        secp256k1_ge_set_gej(&p, &pj);
-        ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, compressed);
-    }
-    if (!ret) {
-        *pubkeylen = 0;
-    }
-    return ret;
-}
-
-int secp256k1_ec_pubkey_decompress(unsigned char *pubkey, int *pubkeylen) {
-    secp256k1_ge_t p;
-    int ret = 0;
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-
-    if (secp256k1_eckey_pubkey_parse(&p, pubkey, *pubkeylen)) {
-        ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, 0);
-    }
-    return ret;
-}
-
-int secp256k1_ec_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
-    secp256k1_scalar_t term;
-    secp256k1_scalar_t sec;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(tweak != NULL);
-
-    secp256k1_scalar_set_b32(&term, tweak, &overflow);
-    secp256k1_scalar_set_b32(&sec, seckey, NULL);
-
-    ret = secp256k1_eckey_privkey_tweak_add(&sec, &term) && !overflow;
-    if (ret) {
-        secp256k1_scalar_get_b32(seckey, &sec);
-    }
-
-    secp256k1_scalar_clear(&sec);
-    secp256k1_scalar_clear(&term);
-    return ret;
-}
-
-int secp256k1_ec_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
-    secp256k1_ge_t p;
-    secp256k1_scalar_t term;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(tweak != NULL);
-
-    secp256k1_scalar_set_b32(&term, tweak, &overflow);
-    if (!overflow) {
-        ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
-        if (ret) {
-            ret = secp256k1_eckey_pubkey_tweak_add(&p, &term);
-        }
-        if (ret) {
-            int oldlen = pubkeylen;
-            ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
-            VERIFY_CHECK(pubkeylen == oldlen);
-        }
-    }
-
-    return ret;
-}
-
-int secp256k1_ec_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak) {
-    secp256k1_scalar_t factor;
-    secp256k1_scalar_t sec;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(tweak != NULL);
-
-    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
-    secp256k1_scalar_set_b32(&sec, seckey, NULL);
-    ret = secp256k1_eckey_privkey_tweak_mul(&sec, &factor) && !overflow;
-    if (ret) {
-        secp256k1_scalar_get_b32(seckey, &sec);
-    }
-
-    secp256k1_scalar_clear(&sec);
-    secp256k1_scalar_clear(&factor);
-    return ret;
-}
-
-int secp256k1_ec_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
-    secp256k1_ge_t p;
-    secp256k1_scalar_t factor;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(tweak != NULL);
-
-    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
-    if (!overflow) {
-        ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
-        if (ret) {
-            ret = secp256k1_eckey_pubkey_tweak_mul(&p, &factor);
-        }
-        if (ret) {
-            int oldlen = pubkeylen;
-            ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
-            VERIFY_CHECK(pubkeylen == oldlen);
-        }
-    }
-
-    return ret;
-}
-
-int secp256k1_ec_privkey_export(const unsigned char *seckey, unsigned char *privkey, int *privkeylen, int compressed) {
-    secp256k1_scalar_t key;
-    int ret = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(privkey != NULL);
-    DEBUG_CHECK(privkeylen != NULL);
-
-    secp256k1_scalar_set_b32(&key, seckey, NULL);
-    ret = secp256k1_eckey_privkey_serialize(privkey, privkeylen, &key, compressed);
-    secp256k1_scalar_clear(&key);
-    return ret;
-}
-
-int secp256k1_ec_privkey_import(unsigned char *seckey, const unsigned char *privkey, int privkeylen) {
-    secp256k1_scalar_t key;
-    int ret = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(privkey != NULL);
-
-    ret = secp256k1_eckey_privkey_parse(&key, privkey, privkeylen);
-    if (ret) {
-        secp256k1_scalar_get_b32(seckey, &key);
-    }
-    secp256k1_scalar_clear(&key);
-    return ret;
-}