// #include #include #include #include #include typedef int32_t fe25519[10]; typedef struct { fe25519 X; fe25519 Y; fe25519 Z; } ge25519_p2; typedef struct { fe25519 X; fe25519 Y; fe25519 Z; fe25519 T; } ge25519_p3; typedef struct { fe25519 X; fe25519 Y; fe25519 Z; fe25519 T; } ge25519_p1p1; typedef struct { fe25519 yplusx; fe25519 yminusx; fe25519 xy2d; } ge25519_precomp; typedef struct { fe25519 YplusX; fe25519 YminusX; fe25519 Z; fe25519 T2d; } ge25519_cached; /* sqrt(-486664) */ /* sqrt(-1) */ static const fe25519 fe25519_sqrtm1 = { -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 }; /* sqrt(-486664) */ static const fe25519 ed25519_sqrtam2 = { -12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024 }; /* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ static const fe25519 ed25519_d = { -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 }; /* 2 * d = * 16295367250680780974490674513165176452449235426866156013048779062215315747161 */ static const fe25519 ed25519_d2 = { -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 }; /* A = 486662 */ #define ed25519_A_32 486662 static const fe25519 ed25519_A = { ed25519_A_32, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; /* sqrt(ad - 1) with a = -1 (mod p) */ static const fe25519 ed25519_sqrtadm1 = { 24849947, -153582, -23613485, 6347715, -21072328, -667138, -25271143, -15367704, -870347, 14525639 }; /* 1 / sqrt(a - d) */ static const fe25519 ed25519_invsqrtamd = { 6111485, 4156064, -27798727, 12243468, -25904040, 120897, 20826367, -7060776, 6093568, -1986012 }; /* 1 - d ^ 2 */ static const fe25519 ed25519_onemsqd = { 6275446, -16617371, -22938544, -3773710, 11667077, 7397348, -27922721, 1766195, -24433858, 672203 }; /* (d - 1) ^ 2 */ static const fe25519 ed25519_sqdmone = { 15551795, -11097455, -13425098, -10125071, -11896535, 10178284, -26634327, 4729244, -5282110, -10116402 }; void print_fe(const fe25519 f) { int i; for (i = 0; i < 10; i++) printf("%d -- %08x\n", i, f[i]); printf("_____________\n\n"); } void print_ge(const ge25519_p3* g) { int i; printf("\nge _____________\n"); for (i = 0; i < 10; i++) printf("X[%d]: %08x\n", i, g->X[i]); for (i = 0; i < 10; i++) printf("Y[%d]: %08x\n", i, g->Y[i]); for (i = 0; i < 10; i++) printf("Z[%d]: %08x\n", i, g->Z[i]); for (i = 0; i < 10; i++) printf("T[%d]: %08x\n", i, g->T[i]); } void print_ge2(const ge25519_p2* g) { int i; printf("\nge _____________\n"); for (i = 0; i < 10; i++) printf("X[%d]: %08x\n", i, g->X[i]); for (i = 0; i < 10; i++) printf("Y[%d]: %08x\n", i, g->Y[i]); for (i = 0; i < 10; i++) printf("Z[%d]: %08x\n", i, g->Z[i]); } void print_hex(const char *s) { while(*s) printf("%x", (unsigned int) *s++); printf("\n"); } char * bin2hex(char *const hex, const size_t hex_maxlen, const unsigned char *const bin, const size_t bin_len) { size_t i = (size_t) 0U; unsigned int x; int b; int c; while (i < bin_len) { c = bin[i] & 0xf; b = bin[i] >> 4; x = (unsigned char) (87U + c + (((c - 10U) >> 8) & ~38U)) << 8 | (unsigned char) (87U + b + (((b - 10U) >> 8) & ~38U)); hex[i * 2U] = (char) x; x >>= 8; hex[i * 2U + 1U] = (char) x; i++; } hex[i * 2U] = 0U; return hex; } int sodium_is_zero(const unsigned char *n, const size_t nlen) { size_t i; volatile unsigned char d = 0U; for (i = 0U; i < nlen; i++) { d |= n[i]; } return 1 & ((d - 1) >> 8); } static inline uint64_t load_3(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; return result; } static inline uint64_t load_4(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; result |= ((uint64_t) in[3]) << 24; // printf("%016llx\n", ((uint64_t) in[3]) << 24); // printf("%08llx\n", result); return result; } /* Ignores top bit of s. */ void fe25519_frombytes(fe25519 h, const unsigned char *s) { int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = (load_3(s + 29) & 8388607) << 2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; // printf("\nh0 _______________________________\n"); // printf("%08llx\n", h0 & 0xffff); // printf("%08llx\n", h0 >> 16); // printf("%08llx\n", h0); carry9 = (h9 + (int64_t)(1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); // printf("%08llx\n", h0 & 0xffff); // printf("%08llx\n", h0 >> 16); // printf("%08llx\n", h0); // printf("\nh2 _______________________________\n"); // printf("%08llx\n", h2 & 0xffff); // printf("%08llx\n", h2 >> 16); // printf("%08llx\n", h2); carry1 = (h1 + (int64_t)(1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); // printf("%08llx\n", h2 & 0xffff); // printf("%08llx\n", h2 >> 16); // printf("%08llx\n", h2); // printf("\nh4 _______________________________\n"); // printf("%08llx\n", h4 & 0xffff); // printf("%08llx\n", h4 >> 16); // printf("%08llx\n", h4); carry3 = (h3 + (int64_t)(1L << 24)) >> 25; h4 += carry3; // printf("%08llx\n", carry3); h3 -= carry3 * ((uint64_t) 1L << 25); // printf("%08llx\n", h4 & 0xffff); // printf("%08llx\n", h4 >> 16); // printf("%08llx\n", h4); // printf("\nh6 _______________________________\n"); // printf("%08llx\n", h6 & 0xffff); // printf("%08llx\n", h6 >> 16); // printf("%08llx\n", h6); carry5 = (h5 + (int64_t)(1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); // printf("%08llx\n", h6 & 0xffff); // printf("%08llx\n", h6 >> 16); // printf("%08llx\n", h6); // printf("\nh8 _______________________________\n"); // printf("%08llx\n", h8 & 0xffff); // printf("%08llx\n", h8 >> 16); // printf("%08llx\n", h8); carry7 = (h7 + (int64_t)(1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); // printf("%08llx\n", h8 & 0xffff); // printf("%08llx\n", h8 >> 16); // printf("%08llx\n", h8); // printf("h0 %08llx\n", h0); // printf("h1 %08llx\n", h1); // printf("h2 %08llx\n", h2); // printf("h3 %08llx\n", h3); // printf("h4 %08llx\n", h4); // printf("h5 %08llx\n", h5); // printf("h6 %08llx\n", h6); // printf("h7 %08llx\n", h7); // printf("h8 %08llx\n", h8); // printf("h9 %08llx\n", h9); // printf("carry5 %016llx\n", carry5); // printf("h6 %016llx\n", h6); // printf("h7 %016llx\n", h7); // printf("\nh1 _______________________________\n"); // printf("%08llx\n", h1 & 0xffff); // printf("%08llx\n", h1 >> 16); // printf("%08llx\n", h1); carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); // printf("%08llx\n", h1 & 0xffff); // printf("%08llx\n", h1 >> 16); // printf("%08llx\n", h1); // printf("\nh3 _______________________________\n"); // printf("%08llx\n", h3 & 0xffff); // printf("%08llx\n", h3 >> 16); // printf("%08llx\n", h3); carry2 = (h2 + (int64_t)(1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); // printf("%08llx\n", h3 & 0xffff); // printf("%08llx\n", h3 >> 16); // printf("%08llx\n", h3); // printf("\nh5 _______________________________\n"); // printf("%08llx\n", h5 & 0xffff); // printf("%08llx\n", h5 >> 16); // printf("%08llx\n", h5); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); // printf("%08llx\n", h5 & 0xffff); // printf("%08llx\n", h5 >> 16); // printf("%08llx\n", h5); // printf("\nh7 _______________________________\n"); // printf("%08llx\n", h7 & 0xffff); // printf("%08llx\n", h7 >> 16); // printf("%08llx\n", h7); carry6 = (h6 + (int64_t)(1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); // printf("%08llx\n", h7 & 0xffff); // printf("%08llx\n", h7 >> 16); // printf("%08llx\n", h7); // printf("\nh9 _______________________________\n"); // printf("%08llx\n", h9 & 0xffff); // printf("%08llx\n", h9 >> 16); // printf("%08llx\n", h9); carry8 = (h8 + (int64_t)(1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); // printf("%08llx\n", h9 & 0xffff); // printf("%08llx\n", h9 >> 16); // printf("%08llx\n", h9); h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } static void fe25519_sq2(fe25519 h, const fe25519 f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); carry1 = (h1 + (int64_t)(1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); carry5 = (h5 + (int64_t)(1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); carry2 = (h2 + (int64_t)(1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); carry6 = (h6 + (int64_t)(1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); carry3 = (h3 + (int64_t)(1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); carry7 = (h7 + (int64_t)(1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); carry8 = (h8 + (int64_t)(1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); carry9 = (h9 + (int64_t)(1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } /* Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). Proof: Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). Then 0> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ h0 += 19 * q; /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 * ((uint32_t) 1L << 26); carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 * ((uint32_t) 1L << 25); carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 * ((uint32_t) 1L << 26); carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 * ((uint32_t) 1L << 25); carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 * ((uint32_t) 1L << 26); carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 * ((uint32_t) 1L << 25); carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 * ((uint32_t) 1L << 26); carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 * ((uint32_t) 1L << 25); carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 * ((uint32_t) 1L << 26); carry9 = h9 >> 25; h9 -= carry9 * ((uint32_t) 1L << 25); h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. Have h0+...+2^230 h9 between 0 and 2^255-1; evidently 2^255 h10-2^255 q = 0. Goal: Output h0+...+2^230 h9. */ void fe25519_tobytes(unsigned char *s, const fe25519 h) { fe25519 t; fe25519_reduce(t, h); s[0] = t[0] >> 0; s[1] = t[0] >> 8; s[2] = t[0] >> 16; s[3] = (t[0] >> 24) | (t[1] * ((uint32_t) 1 << 2)); s[4] = t[1] >> 6; s[5] = t[1] >> 14; s[6] = (t[1] >> 22) | (t[2] * ((uint32_t) 1 << 3)); s[7] = t[2] >> 5; s[8] = t[2] >> 13; s[9] = (t[2] >> 21) | (t[3] * ((uint32_t) 1 << 5)); s[10] = t[3] >> 3; s[11] = t[3] >> 11; s[12] = (t[3] >> 19) | (t[4] * ((uint32_t) 1 << 6)); s[13] = t[4] >> 2; s[14] = t[4] >> 10; s[15] = t[4] >> 18; s[16] = t[5] >> 0; s[17] = t[5] >> 8; s[18] = t[5] >> 16; s[19] = (t[5] >> 24) | (t[6] * ((uint32_t) 1 << 1)); s[20] = t[6] >> 7; s[21] = t[6] >> 15; s[22] = (t[6] >> 23) | (t[7] * ((uint32_t) 1 << 3)); s[23] = t[7] >> 5; s[24] = t[7] >> 13; s[25] = (t[7] >> 21) | (t[8] * ((uint32_t) 1 << 4)); s[26] = t[8] >> 4; s[27] = t[8] >> 12; s[28] = (t[8] >> 20) | (t[9] * ((uint32_t) 1 << 6)); s[29] = t[9] >> 2; s[30] = t[9] >> 10; s[31] = t[9] >> 18; } /* h = 0 */ static inline void fe25519_0(fe25519 h) { memset(&h[0], 0, 10 * sizeof h[0]); } /* h = 1 */ static inline void fe25519_1(fe25519 h) { h[0] = 1; h[1] = 0; memset(&h[2], 0, 8 * sizeof h[0]); } /* h = f + g Can overlap h with f or g. * Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. * Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline void fe25519_add(fe25519 h, const fe25519 f, const fe25519 g) { int32_t h0 = f[0] + g[0]; int32_t h1 = f[1] + g[1]; int32_t h2 = f[2] + g[2]; int32_t h3 = f[3] + g[3]; int32_t h4 = f[4] + g[4]; int32_t h5 = f[5] + g[5]; int32_t h6 = f[6] + g[6]; int32_t h7 = f[7] + g[7]; int32_t h8 = f[8] + g[8]; int32_t h9 = f[9] + g[9]; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* h = f - g Can overlap h with f or g. * Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. * Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static void fe25519_sub(fe25519 h, const fe25519 f, const fe25519 g) { int32_t h0 = f[0] - g[0]; int32_t h1 = f[1] - g[1]; int32_t h2 = f[2] - g[2]; int32_t h3 = f[3] - g[3]; int32_t h4 = f[4] - g[4]; int32_t h5 = f[5] - g[5]; int32_t h6 = f[6] - g[6]; int32_t h7 = f[7] - g[7]; int32_t h8 = f[8] - g[8]; int32_t h9 = f[9] - g[9]; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* h = -f * Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. * Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ static inline void fe25519_neg(fe25519 h, const fe25519 f) { int32_t h0 = -f[0]; int32_t h1 = -f[1]; int32_t h2 = -f[2]; int32_t h3 = -f[3]; int32_t h4 = -f[4]; int32_t h5 = -f[5]; int32_t h6 = -f[6]; int32_t h7 = -f[7]; int32_t h8 = -f[8]; int32_t h9 = -f[9]; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. * Preconditions: b in {0,1}. */ static void fe25519_cmov(fe25519 f, const fe25519 g, unsigned int b) { uint32_t mask = (uint32_t) (-(int32_t) b); int32_t f0, f1, f2, f3, f4, f5, f6, f7, f8, f9; int32_t x0, x1, x2, x3, x4, x5, x6, x7, x8, x9; f0 = f[0]; f1 = f[1]; f2 = f[2]; f3 = f[3]; f4 = f[4]; f5 = f[5]; f6 = f[6]; f7 = f[7]; f8 = f[8]; f9 = f[9]; x0 = f0 ^ g[0]; x1 = f1 ^ g[1]; x2 = f2 ^ g[2]; x3 = f3 ^ g[3]; x4 = f4 ^ g[4]; x5 = f5 ^ g[5]; x6 = f6 ^ g[6]; x7 = f7 ^ g[7]; x8 = f8 ^ g[8]; x9 = f9 ^ g[9]; #ifdef HAVE_INLINE_ASM __asm__ __volatile__("" : "+r"(mask)); #endif x0 &= mask; x1 &= mask; x2 &= mask; x3 &= mask; x4 &= mask; x5 &= mask; x6 &= mask; x7 &= mask; x8 &= mask; x9 &= mask; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; } static void fe25519_cswap(fe25519 f, fe25519 g, unsigned int b) { uint32_t mask = (uint32_t) (-(int64_t) b); int32_t f0, f1, f2, f3, f4, f5, f6, f7, f8, f9; int32_t g0, g1, g2, g3, g4, g5, g6, g7, g8, g9; int32_t x0, x1, x2, x3, x4, x5, x6, x7, x8, x9; f0 = f[0]; f1 = f[1]; f2 = f[2]; f3 = f[3]; f4 = f[4]; f5 = f[5]; f6 = f[6]; f7 = f[7]; f8 = f[8]; f9 = f[9]; g0 = g[0]; g1 = g[1]; g2 = g[2]; g3 = g[3]; g4 = g[4]; g5 = g[5]; g6 = g[6]; g7 = g[7]; g8 = g[8]; g9 = g[9]; x0 = f0 ^ g0; x1 = f1 ^ g1; x2 = f2 ^ g2; x3 = f3 ^ g3; x4 = f4 ^ g4; x5 = f5 ^ g5; x6 = f6 ^ g6; x7 = f7 ^ g7; x8 = f8 ^ g8; x9 = f9 ^ g9; #ifdef HAVE_INLINE_ASM __asm__ __volatile__("" : "+r"(mask)); #endif x0 &= mask; x1 &= mask; x2 &= mask; x3 &= mask; x4 &= mask; x5 &= mask; x6 &= mask; x7 &= mask; x8 &= mask; x9 &= mask; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; g[0] = g0 ^ x0; g[1] = g1 ^ x1; g[2] = g2 ^ x2; g[3] = g3 ^ x3; g[4] = g4 ^ x4; g[5] = g5 ^ x5; g[6] = g6 ^ x6; g[7] = g7 ^ x7; g[8] = g8 ^ x8; g[9] = g9 ^ x9; } /* h = f */ static inline void fe25519_copy(fe25519 h, const fe25519 f) { memcpy(h, f, 10 * 4); } static inline void fe25519_cneg(fe25519 h, const fe25519 f, unsigned int b) { fe25519 negf; unsigned char res[32]; unsigned char hex[32]; fe25519_neg(negf, f); fe25519_copy(h, f); fe25519_cmov(h, negf, b); // printf("%s\n", hex); } /* return 1 if f is in {1,3,5,...,q-2} return 0 if f is in {0,2,4,...,q-1} Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline int fe25519_isnegative(const fe25519 f) { unsigned char s[32]; fe25519_tobytes(s, f); return s[0] & 1; } /* return 1 if f == 0 return 0 if f != 0 Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static inline int fe25519_iszero(const fe25519 f) { unsigned char s[32]; fe25519_tobytes(s, f); return sodium_is_zero(s, 32); } void sc25519_mul(unsigned char s[32], const unsigned char a[32], const unsigned char b[32]) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t s0; int64_t s1; int64_t s2; int64_t s3; int64_t s4; int64_t s5; int64_t s6; int64_t s7; int64_t s8; int64_t s9; int64_t s10; int64_t s11; int64_t s12; int64_t s13; int64_t s14; int64_t s15; int64_t s16; int64_t s17; int64_t s18; int64_t s19; int64_t s20; int64_t s21; int64_t s22; int64_t s23; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; int64_t carry17; int64_t carry18; int64_t carry19; int64_t carry20; int64_t carry21; int64_t carry22; s0 = a0 * b0; s1 = a0 * b1 + a1 * b0; s2 = a0 * b2 + a1 * b1 + a2 * b0; s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; s20 = a9 * b11 + a10 * b10 + a11 * b9; s21 = a10 * b11 + a11 * b10; s22 = a11 * b11; s23 = 0; carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); carry18 = (s18 + (int64_t) (1L << 20)) >> 21; s19 += carry18; s18 -= carry18 * ((uint64_t) 1L << 21); carry20 = (s20 + (int64_t) (1L << 20)) >> 21; s21 += carry20; s20 -= carry20 * ((uint64_t) 1L << 21); carry22 = (s22 + (int64_t) (1L << 20)) >> 21; s23 += carry22; s22 -= carry22 * ((uint64_t) 1L << 21); carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); carry17 = (s17 + (int64_t) (1L << 20)) >> 21; s18 += carry17; s17 -= carry17 * ((uint64_t) 1L << 21); carry19 = (s19 + (int64_t) (1L << 20)) >> 21; s20 += carry19; s19 -= carry19 * ((uint64_t) 1L << 21); carry21 = (s21 + (int64_t) (1L << 20)) >> 21; s22 += carry21; s21 -= carry21 * ((uint64_t) 1L << 21); s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } void sc25519_sq(unsigned char *s, const unsigned char *a) { sc25519_mul(s, a, a); } void sc25519_sqmul(unsigned char s[32], const int n, const unsigned char a[32]) { int i; for (i = 0; i < n; i++) { sc25519_sq(s, s); } sc25519_mul(s, s, a); } void sc25519_muladd(unsigned char s[32], const unsigned char a[32], const unsigned char b[32], const unsigned char c[32]) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t c0 = 2097151 & load_3(c); int64_t c1 = 2097151 & (load_4(c + 2) >> 5); int64_t c2 = 2097151 & (load_3(c + 5) >> 2); int64_t c3 = 2097151 & (load_4(c + 7) >> 7); int64_t c4 = 2097151 & (load_4(c + 10) >> 4); int64_t c5 = 2097151 & (load_3(c + 13) >> 1); int64_t c6 = 2097151 & (load_4(c + 15) >> 6); int64_t c7 = 2097151 & (load_3(c + 18) >> 3); int64_t c8 = 2097151 & load_3(c + 21); int64_t c9 = 2097151 & (load_4(c + 23) >> 5); int64_t c10 = 2097151 & (load_3(c + 26) >> 2); int64_t c11 = (load_4(c + 28) >> 7); int64_t s0; int64_t s1; int64_t s2; int64_t s3; int64_t s4; int64_t s5; int64_t s6; int64_t s7; int64_t s8; int64_t s9; int64_t s10; int64_t s11; int64_t s12; int64_t s13; int64_t s14; int64_t s15; int64_t s16; int64_t s17; int64_t s18; int64_t s19; int64_t s20; int64_t s21; int64_t s22; int64_t s23; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; int64_t carry17; int64_t carry18; int64_t carry19; int64_t carry20; int64_t carry21; int64_t carry22; s0 = c0 + a0 * b0; s1 = c1 + a0 * b1 + a1 * b0; s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; s20 = a9 * b11 + a10 * b10 + a11 * b9; s21 = a10 * b11 + a11 * b10; s22 = a11 * b11; s23 = 0; carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); carry18 = (s18 + (int64_t) (1L << 20)) >> 21; s19 += carry18; s18 -= carry18 * ((uint64_t) 1L << 21); carry20 = (s20 + (int64_t) (1L << 20)) >> 21; s21 += carry20; s20 -= carry20 * ((uint64_t) 1L << 21); carry22 = (s22 + (int64_t) (1L << 20)) >> 21; s23 += carry22; s22 -= carry22 * ((uint64_t) 1L << 21); carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); carry17 = (s17 + (int64_t) (1L << 20)) >> 21; s18 += carry17; s17 -= carry17 * ((uint64_t) 1L << 21); carry19 = (s19 + (int64_t) (1L << 20)) >> 21; s20 += carry19; s19 -= carry19 * ((uint64_t) 1L << 21); carry21 = (s21 + (int64_t) (1L << 20)) >> 21; s22 += carry21; s21 -= carry21 * ((uint64_t) 1L << 21); s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } static void fe25519_mul(fe25519 h, const fe25519 f, const fe25519 g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ int32_t g3_19 = 19 * g3; int32_t g4_19 = 19 * g4; int32_t g5_19 = 19 * g5; int32_t g6_19 = 19 * g6; int32_t g7_19 = 19 * g7; int32_t g8_19 = 19 * g8; int32_t g9_19 = 19 * g9; int32_t f1_2 = 2 * f1; int32_t f3_2 = 2 * f3; int32_t f5_2 = 2 * f5; int32_t f7_2 = 2 * f7; int32_t f9_2 = 2 * f9; // printf("%016llx\n", (int64_t) 0); // printf("%016llx\n", (int64_t) f0 ); // printf("%016llx\n", (int64_t) f1 ); // printf("%016llx\n", (int64_t) f2 ); // printf("%016llx\n", (int64_t) f3 ); // printf("%016llx\n", (int64_t) f4 ); // printf("%016llx\n", (int64_t) f5 ); // printf("%016llx\n", (int64_t) f6 ); // printf("%016llx\n", (int64_t) f7 ); // printf("%016llx\n", (int64_t) f8 ); // printf("%016llx\n", (int64_t) f9 ); // printf("%016llx\n", (int64_t) g0 ); // printf("%016llx\n", (int64_t) g1 ); // printf("%016llx\n", (int64_t) g2 ); // printf("%016llx\n", (int64_t) g3 ); // printf("%016llx\n", (int64_t) g4 ); // printf("%016llx\n", (int64_t) g5 ); // printf("%016llx\n", (int64_t) g6 ); // printf("%016llx\n", (int64_t) g7 ); // printf("%016llx\n", (int64_t) g8 ); // printf("%016llx\n", (int64_t) g9 ); // printf("%016llx\n", (int64_t) g1_19); // printf("%016llx\n", (int64_t) g2_19); // printf("%016llx\n", (int64_t) g3_19); // printf("%016llx\n", (int64_t) g4_19); // printf("%016llx\n", (int64_t) g5_19); // printf("%016llx\n", (int64_t) g6_19); // printf("%016llx\n", (int64_t) g7_19); // printf("%016llx\n", (int64_t) g8_19); // printf("%016llx\n", (int64_t) g9_19); // printf("%016llx\n", (int64_t) f1_2 ); // printf("%016llx\n", (int64_t) f3_2 ); // printf("%016llx\n", (int64_t) f5_2 ); // printf("%016llx\n", (int64_t) f7_2 ); // printf("%016llx\n", (int64_t) f9_2 ); int64_t f0g0 = f0 * (int64_t) g0; int64_t f0g1 = f0 * (int64_t) g1; int64_t f0g2 = f0 * (int64_t) g2; int64_t f0g3 = f0 * (int64_t) g3; int64_t f0g4 = f0 * (int64_t) g4; int64_t f0g5 = f0 * (int64_t) g5; int64_t f0g6 = f0 * (int64_t) g6; int64_t f0g7 = f0 * (int64_t) g7; int64_t f0g8 = f0 * (int64_t) g8; int64_t f0g9 = f0 * (int64_t) g9; int64_t f1g0 = f1 * (int64_t) g0; int64_t f1g1_2 = f1_2 * (int64_t) g1; int64_t f1g2 = f1 * (int64_t) g2; int64_t f1g3_2 = f1_2 * (int64_t) g3; int64_t f1g4 = f1 * (int64_t) g4; int64_t f1g5_2 = f1_2 * (int64_t) g5; int64_t f1g6 = f1 * (int64_t) g6; int64_t f1g7_2 = f1_2 * (int64_t) g7; int64_t f1g8 = f1 * (int64_t) g8; int64_t f1g9_38 = f1_2 * (int64_t) g9_19; int64_t f2g0 = f2 * (int64_t) g0; int64_t f2g1 = f2 * (int64_t) g1; int64_t f2g2 = f2 * (int64_t) g2; int64_t f2g3 = f2 * (int64_t) g3; int64_t f2g4 = f2 * (int64_t) g4; int64_t f2g5 = f2 * (int64_t) g5; int64_t f2g6 = f2 * (int64_t) g6; int64_t f2g7 = f2 * (int64_t) g7; int64_t f2g8_19 = f2 * (int64_t) g8_19; int64_t f2g9_19 = f2 * (int64_t) g9_19; int64_t f3g0 = f3 * (int64_t) g0; int64_t f3g1_2 = f3_2 * (int64_t) g1; int64_t f3g2 = f3 * (int64_t) g2; int64_t f3g3_2 = f3_2 * (int64_t) g3; int64_t f3g4 = f3 * (int64_t) g4; int64_t f3g5_2 = f3_2 * (int64_t) g5; int64_t f3g6 = f3 * (int64_t) g6; int64_t f3g7_38 = f3_2 * (int64_t) g7_19; int64_t f3g8_19 = f3 * (int64_t) g8_19; int64_t f3g9_38 = f3_2 * (int64_t) g9_19; int64_t f4g0 = f4 * (int64_t) g0; int64_t f4g1 = f4 * (int64_t) g1; int64_t f4g2 = f4 * (int64_t) g2; int64_t f4g3 = f4 * (int64_t) g3; int64_t f4g4 = f4 * (int64_t) g4; int64_t f4g5 = f4 * (int64_t) g5; int64_t f4g6_19 = f4 * (int64_t) g6_19; int64_t f4g7_19 = f4 * (int64_t) g7_19; int64_t f4g8_19 = f4 * (int64_t) g8_19; int64_t f4g9_19 = f4 * (int64_t) g9_19; int64_t f5g0 = f5 * (int64_t) g0; int64_t f5g1_2 = f5_2 * (int64_t) g1; int64_t f5g2 = f5 * (int64_t) g2; int64_t f5g3_2 = f5_2 * (int64_t) g3; int64_t f5g4 = f5 * (int64_t) g4; int64_t f5g5_38 = f5_2 * (int64_t) g5_19; int64_t f5g6_19 = f5 * (int64_t) g6_19; int64_t f5g7_38 = f5_2 * (int64_t) g7_19; int64_t f5g8_19 = f5 * (int64_t) g8_19; int64_t f5g9_38 = f5_2 * (int64_t) g9_19; int64_t f6g0 = f6 * (int64_t) g0; int64_t f6g1 = f6 * (int64_t) g1; int64_t f6g2 = f6 * (int64_t) g2; int64_t f6g3 = f6 * (int64_t) g3; int64_t f6g4_19 = f6 * (int64_t) g4_19; int64_t f6g5_19 = f6 * (int64_t) g5_19; int64_t f6g6_19 = f6 * (int64_t) g6_19; int64_t f6g7_19 = f6 * (int64_t) g7_19; int64_t f6g8_19 = f6 * (int64_t) g8_19; int64_t f6g9_19 = f6 * (int64_t) g9_19; int64_t f7g0 = f7 * (int64_t) g0; int64_t f7g1_2 = f7_2 * (int64_t) g1; int64_t f7g2 = f7 * (int64_t) g2; int64_t f7g3_38 = f7_2 * (int64_t) g3_19; int64_t f7g4_19 = f7 * (int64_t) g4_19; int64_t f7g5_38 = f7_2 * (int64_t) g5_19; int64_t f7g6_19 = f7 * (int64_t) g6_19; int64_t f7g7_38 = f7_2 * (int64_t) g7_19; int64_t f7g8_19 = f7 * (int64_t) g8_19; int64_t f7g9_38 = f7_2 * (int64_t) g9_19; int64_t f8g0 = f8 * (int64_t) g0; int64_t f8g1 = f8 * (int64_t) g1; int64_t f8g2_19 = f8 * (int64_t) g2_19; int64_t f8g3_19 = f8 * (int64_t) g3_19; int64_t f8g4_19 = f8 * (int64_t) g4_19; int64_t f8g5_19 = f8 * (int64_t) g5_19; int64_t f8g6_19 = f8 * (int64_t) g6_19; int64_t f8g7_19 = f8 * (int64_t) g7_19; int64_t f8g8_19 = f8 * (int64_t) g8_19; int64_t f8g9_19 = f8 * (int64_t) g9_19; int64_t f9g0 = f9 * (int64_t) g0; int64_t f9g1_38 = f9_2 * (int64_t) g1_19; int64_t f9g2_19 = f9 * (int64_t) g2_19; int64_t f9g3_38 = f9_2 * (int64_t) g3_19; int64_t f9g4_19 = f9 * (int64_t) g4_19; int64_t f9g5_38 = f9_2 * (int64_t) g5_19; int64_t f9g6_19 = f9 * (int64_t) g6_19; int64_t f9g7_38 = f9_2 * (int64_t) g7_19; int64_t f9g8_19 = f9 * (int64_t) g8_19; int64_t f9g9_38 = f9_2 * (int64_t) g9_19; // printf("%016llx\n", (0x100000000 - 0xff8145bell) * (0x100000000 - 0xff8145bell)); // printf("%016llx\n", (int64_t) (-1 * (int64_t) g0)); // printf("%016llx\n", (int64_t) (-1 * (int64_t) g0)); // printf("%016llx\n", f0g0 ); // printf("%016llx\n", f0g1 ); // printf("%016llx\n", f0g2 ); // printf("%016llx\n", f0g3 ); // printf("%016llx\n", f0g4 ); // printf("%016llx\n", f0g5 ); // printf("%016llx\n", f0g6 ); // printf("%016llx\n", f0g7 ); // printf("%016llx\n", f0g8 ); // printf("%016llx\n", f0g9 ); // printf("%016llx\n", f1g0 ); // printf("%016llx\n", f1g1_2 ); // printf("%016llx\n", f1g2 ); // printf("%016llx\n", f1g3_2 ); // printf("%016llx\n", f1g4 ); // printf("%016llx\n", f1g5_2 ); // printf("%016llx\n", f1g6 ); // printf("%016llx\n", f1g7_2 ); // printf("%016llx\n", f1g8 ); // printf("%016llx\n", f1g9_38); // printf("%016llx\n", f2g0 ); // printf("%016llx\n", f2g1 ); // printf("%016llx\n", f2g2 ); // printf("%016llx\n", f2g3 ); // printf("%016llx\n", f2g4 ); // printf("%016llx\n", f2g5 ); // printf("%016llx\n", f2g6 ); // printf("%016llx\n", f2g7 ); // printf("%016llx\n", f2g8_19); // printf("%016llx\n", f2g9_19); // printf("%016llx\n", f3g0 ); // printf("%016llx\n", f3g1_2 ); // printf("%016llx\n", f3g2 ); // printf("%016llx\n", f3g3_2 ); // printf("%016llx\n", f3g4 ); // printf("%016llx\n", f3g5_2 ); // printf("%016llx\n", f3g6 ); // printf("%016llx\n", f3g7_38); // printf("%016llx\n", f3g8_19); // printf("%016llx\n", f3g9_38); // printf("%016llx\n", f4g0 ); // printf("%016llx\n", f4g1 ); // printf("%016llx\n", f4g2 ); // printf("%016llx\n", f4g3 ); // printf("%016llx\n", f4g4 ); // printf("%016llx\n", f4g5 ); // printf("%016llx\n", f4g6_19); // printf("%016llx\n", f4g7_19); // printf("%016llx\n", f4g8_19); // printf("%016llx\n", f4g9_19); // printf("%016llx\n", f5g0 ); // printf("%016llx\n", f5g1_2 ); // printf("%016llx\n", f5g2 ); // printf("%016llx\n", f5g3_2 ); // printf("%016llx\n", f5g4 ); // printf("%016llx\n", f5g5_38); // printf("%016llx\n", f5g6_19); // printf("%016llx\n", f5g7_38); // printf("%016llx\n", f5g8_19); // printf("%016llx\n", f5g9_38); // printf("%016llx\n", f6g0 ); // printf("%016llx\n", f6g1 ); // printf("%016llx\n", f6g2 ); // printf("%016llx\n", f6g3 ); // printf("%016llx\n", f6g4_19); // printf("%016llx\n", f6g5_19); // printf("%016llx\n", f6g6_19); // printf("%016llx\n", f6g7_19); // printf("%016llx\n", f6g8_19); // printf("%016llx\n", f6g9_19); // printf("%016llx\n", f7g0 ); // printf("%016llx\n", f7g1_2 ); // printf("%016llx\n", f7g2 ); // printf("%016llx\n", f7g3_38); // printf("%016llx\n", f7g4_19); // printf("%016llx\n", f7g5_38); // printf("%016llx\n", f7g6_19); // printf("%016llx\n", f7g7_38); // printf("%016llx\n", f7g8_19); // printf("%016llx\n", f7g9_38); // printf("%016llx\n", f8g0 ); // printf("%016llx\n", f8g1 ); // printf("%016llx\n", f8g2_19); // printf("%016llx\n", f8g3_19); // printf("%016llx\n", f8g4_19); // printf("%016llx\n", f8g5_19); // printf("%016llx\n", f8g6_19); // printf("%016llx\n", f8g7_19); // printf("%016llx\n", f8g8_19); // printf("%016llx\n", f8g9_19); // printf("%016llx\n", f9g0 ); // printf("%016llx\n", f9g1_38); // printf("%016llx\n", f9g2_19); // printf("%016llx\n", f9g3_38); // printf("%016llx\n", f9g4_19); // printf("%016llx\n", f9g5_38); // printf("%016llx\n", f9g6_19); // printf("%016llx\n", f9g7_38); // printf("%016llx\n", f9g8_19); // printf("%016llx\n", f9g9_38); int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); /* |h0| <= 2^25 */ /* |h4| <= 2^25 */ /* |h1| <= 1.71*2^59 */ /* |h5| <= 1.71*2^59 */ carry1 = (h1 + (int64_t)(1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); carry5 = (h5 + (int64_t)(1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); /* |h1| <= 2^24; from now on fits into int32 */ /* |h5| <= 2^24; from now on fits into int32 */ /* |h2| <= 1.41*2^60 */ /* |h6| <= 1.41*2^60 */ carry2 = (h2 + (int64_t)(1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); carry6 = (h6 + (int64_t)(1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); /* |h2| <= 2^25; from now on fits into int32 unchanged */ /* |h6| <= 2^25; from now on fits into int32 unchanged */ /* |h3| <= 1.71*2^59 */ /* |h7| <= 1.71*2^59 */ carry3 = (h3 + (int64_t)(1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); carry7 = (h7 + (int64_t)(1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); /* |h3| <= 2^24; from now on fits into int32 unchanged */ /* |h7| <= 2^24; from now on fits into int32 unchanged */ /* |h4| <= 1.72*2^34 */ /* |h8| <= 1.41*2^60 */ carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); carry8 = (h8 + (int64_t)(1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); /* |h4| <= 2^25; from now on fits into int32 unchanged */ /* |h8| <= 2^25; from now on fits into int32 unchanged */ /* |h5| <= 1.01*2^24 */ /* |h9| <= 1.71*2^59 */ carry9 = (h9 + (int64_t)(1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); /* |h9| <= 2^24; from now on fits into int32 unchanged */ /* |h0| <= 1.1*2^39 */ carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; // printf("%x\n", f0); // printf("%x\n", f1); // printf("%x\n", f2); // printf("%x\n", f3); // printf("%x\n", f4); // printf("%x\n", f5); // printf("%x\n", f6); // printf("%x\n", f7); // printf("%x\n", f8); // printf("%x\n", f9); // printf("\n"); // printf("%x\n", g0); // printf("%x\n", g1); // printf("%x\n", g2); // printf("%x\n", g3); // printf("%x\n", g4); // printf("%x\n", g5); // printf("%x\n", g6); // printf("%x\n", g7); // printf("%x\n", g8); // printf("%x\n", g9); } static void fe25519_sq(fe25519 h, const fe25519 f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); carry1 = (h1 + (int64_t)(1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); carry5 = (h5 + (int64_t)(1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); carry2 = (h2 + (int64_t)(1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); carry6 = (h6 + (int64_t)(1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); carry3 = (h3 + (int64_t)(1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); carry7 = (h7 + (int64_t)(1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); carry4 = (h4 + (int64_t)(1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); carry8 = (h8 + (int64_t)(1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); carry9 = (h9 + (int64_t)(1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); carry0 = (h0 + (int64_t)(1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } void fe25519_sqmul(fe25519 s, const int n, const fe25519 a) { int i; for (i = 0; i < n; i++) { fe25519_sq(s, s); } fe25519_mul(s, s, a); } /* * Inversion - returns 0 if z=0 */ void fe25519_invert(fe25519 out, const fe25519 z) { fe25519 t0, t1, t2, t3; int i; fe25519_sq(t0, z); fe25519_sq(t1, t0); fe25519_sq(t1, t1); fe25519_mul(t1, z, t1); fe25519_mul(t0, t0, t1); fe25519_sq(t2, t0); fe25519_mul(t1, t1, t2); fe25519_sq(t2, t1); for (i = 1; i < 5; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); fe25519_sq(t2, t1); for (i = 1; i < 10; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t2, t2, t1); fe25519_sq(t3, t2); for (i = 1; i < 20; ++i) { fe25519_sq(t3, t3); } fe25519_mul(t2, t3, t2); fe25519_sq(t2, t2); for (i = 1; i < 10; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); fe25519_sq(t2, t1); for (i = 1; i < 50; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t2, t2, t1); fe25519_sq(t3, t2); for (i = 1; i < 100; ++i) { fe25519_sq(t3, t3); } fe25519_mul(t2, t3, t2); fe25519_sq(t2, t2); for (i = 1; i < 50; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); fe25519_sq(t1, t1); for (i = 1; i < 5; ++i) { fe25519_sq(t1, t1); } fe25519_mul(out, t1, t0); } static void fe25519_pow22523(fe25519 out, const fe25519 z) { fe25519 t0, t1, t2; int i; fe25519_sq(t0, z); fe25519_sq(t1, t0); fe25519_sq(t1, t1); fe25519_mul(t1, z, t1); fe25519_mul(t0, t0, t1); fe25519_sq(t0, t0); fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for (i = 1; i < 5; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for (i = 1; i < 10; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t1, t1, t0); fe25519_sq(t2, t1); for (i = 1; i < 20; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); fe25519_sq(t1, t1); for (i = 1; i < 10; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t1, t0); for (i = 1; i < 50; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t1, t1, t0); fe25519_sq(t2, t1); for (i = 1; i < 100; ++i) { fe25519_sq(t2, t2); } fe25519_mul(t1, t2, t1); fe25519_sq(t1, t1); for (i = 1; i < 50; ++i) { fe25519_sq(t1, t1); } fe25519_mul(t0, t1, t0); fe25519_sq(t0, t0); fe25519_sq(t0, t0); fe25519_mul(out, t0, z); } void sc25519_reduce(unsigned char s[64]) { int64_t s0 = 2097151 & load_3(s); int64_t s1 = 2097151 & (load_4(s + 2) >> 5); int64_t s2 = 2097151 & (load_3(s + 5) >> 2); int64_t s3 = 2097151 & (load_4(s + 7) >> 7); int64_t s4 = 2097151 & (load_4(s + 10) >> 4); int64_t s5 = 2097151 & (load_3(s + 13) >> 1); int64_t s6 = 2097151 & (load_4(s + 15) >> 6); int64_t s7 = 2097151 & (load_3(s + 18) >> 3); int64_t s8 = 2097151 & load_3(s + 21); int64_t s9 = 2097151 & (load_4(s + 23) >> 5); int64_t s10 = 2097151 & (load_3(s + 26) >> 2); int64_t s11 = 2097151 & (load_4(s + 28) >> 7); int64_t s12 = 2097151 & (load_4(s + 31) >> 4); int64_t s13 = 2097151 & (load_3(s + 34) >> 1); int64_t s14 = 2097151 & (load_4(s + 36) >> 6); int64_t s15 = 2097151 & (load_3(s + 39) >> 3); int64_t s16 = 2097151 & load_3(s + 42); int64_t s17 = 2097151 & (load_4(s + 44) >> 5); int64_t s18 = 2097151 & (load_3(s + 47) >> 2); int64_t s19 = 2097151 & (load_4(s + 49) >> 7); int64_t s20 = 2097151 & (load_4(s + 52) >> 4); int64_t s21 = 2097151 & (load_3(s + 55) >> 1); int64_t s22 = 2097151 & (load_4(s + 57) >> 6); int64_t s23 = (load_4(s + 60) >> 3); int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } void sc25519_invert(unsigned char recip[32], const unsigned char s[32]) { unsigned char _10[32], _100[32], _1000[32], _10000[32], _100000[32], _1000000[32], _10010011[32], _10010111[32], _100110[32], _1010[32], _1010000[32], _1010011[32], _1011[32], _10110[32], _10111101[32], _11[32], _1100011[32], _1100111[32], _11010011[32], _1101011[32], _11100111[32], _11101011[32], _11110101[32]; sc25519_sq(_10, s); sc25519_mul(_11, s, _10); sc25519_mul(_100, s, _11); sc25519_sq(_1000, _100); sc25519_mul(_1010, _10, _1000); sc25519_mul(_1011, s, _1010); sc25519_sq(_10000, _1000); sc25519_sq(_10110, _1011); sc25519_mul(_100000, _1010, _10110); sc25519_mul(_100110, _10000, _10110); sc25519_sq(_1000000, _100000); sc25519_mul(_1010000, _10000, _1000000); sc25519_mul(_1010011, _11, _1010000); sc25519_mul(_1100011, _10000, _1010011); sc25519_mul(_1100111, _100, _1100011); sc25519_mul(_1101011, _100, _1100111); sc25519_mul(_10010011, _1000000, _1010011); sc25519_mul(_10010111, _100, _10010011); sc25519_mul(_10111101, _100110, _10010111); sc25519_mul(_11010011, _10110, _10111101); sc25519_mul(_11100111, _1010000, _10010111); sc25519_mul(_11101011, _100, _11100111); sc25519_mul(_11110101, _1010, _11101011); sc25519_mul(recip, _1011, _11110101); sc25519_sqmul(recip, 126, _1010011); sc25519_sqmul(recip, 9, _10); sc25519_mul(recip, recip, _11110101); sc25519_sqmul(recip, 7, _1100111); sc25519_sqmul(recip, 9, _11110101); sc25519_sqmul(recip, 11, _10111101); sc25519_sqmul(recip, 8, _11100111); sc25519_sqmul(recip, 9, _1101011); sc25519_sqmul(recip, 6, _1011); sc25519_sqmul(recip, 14, _10010011); sc25519_sqmul(recip, 10, _1100011); sc25519_sqmul(recip, 9, _10010111); sc25519_sqmul(recip, 10, _11110101); sc25519_sqmul(recip, 8, _11010011); sc25519_sqmul(recip, 8, _11101011); } int sc25519_is_canonical(const unsigned char s[32]) { /* 2^252+27742317777372353535851937790883648493 */ static const unsigned char L[32] = { 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 }; unsigned char c = 0; unsigned char n = 1; unsigned int i = 32; do { i--; c |= ((s[i] - L[i]) >> 8) & n; n &= ((s[i] ^ L[i]) - 1) >> 8; } while (i != 0); return (c != 0); } void ge25519_add_cached(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->YplusX); fe25519_mul(r->Y, r->Y, q->YminusX); fe25519_mul(r->T, q->T2d, p->T); fe25519_mul(r->X, p->Z, q->Z); fe25519_add(t0, r->X, r->X); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_add(r->Z, t0, r->T); fe25519_sub(r->T, t0, r->T); } static void slide_vartime(signed char *r, const unsigned char *a) { int i; int b; int k; int ribs; int cmp; for (i = 0; i < 256; ++i) { r[i] = 1 & (a[i >> 3] >> (i & 7)); } for (i = 0; i < 256; ++i) { if (! r[i]) { continue; } for (b = 1; b <= 6 && i + b < 256; ++b) { if (! r[i + b]) { continue; } ribs = r[i + b] << b; cmp = r[i] + ribs; if (cmp <= 15) { r[i] = cmp; r[i + b] = 0; } else { cmp = r[i] - ribs; if (cmp < -15) { break; } r[i] = cmp; for (k = i + b; k < 256; ++k) { if (! r[k]) { r[k] = 1; break; } r[k] = 0; } } } } } int ge25519_frombytes(ge25519_p3 *h, const unsigned char *s) { fe25519 u; fe25519 v; fe25519 v3; fe25519 vxx; fe25519 m_root_check, p_root_check; fe25519 negx; fe25519 x_sqrtm1; int has_m_root, has_p_root; fe25519_frombytes(h->Y, s); fe25519_1(h->Z); fe25519_sq(u, h->Y); fe25519_mul(v, u, ed25519_d); fe25519_sub(u, u, h->Z); /* u = y^2-1 */ fe25519_add(v, v, h->Z); /* v = dy^2+1 */ fe25519_sq(v3, v); // print_fe(v3); fe25519_mul(v3, v3, v); /* v3 = v^3 */ // print_fe(v3); fe25519_sq(h->X, v3); // print_fe(h->X); fe25519_mul(h->X, h->X, v); // print_fe(h->X); fe25519_mul(h->X, h->X, u); /* x = uv^7 */ // print_fe(h->X); fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ fe25519_mul(h->X, h->X, v3); fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ fe25519_sq(vxx, h->X); fe25519_mul(vxx, vxx, v); fe25519_sub(m_root_check, vxx, u); /* vx^2-u */ fe25519_add(p_root_check, vxx, u); /* vx^2+u */ has_m_root = fe25519_iszero(m_root_check); has_p_root = fe25519_iszero(p_root_check); fe25519_mul(x_sqrtm1, h->X, fe25519_sqrtm1); /* x*sqrt(-1) */ fe25519_cmov(h->X, x_sqrtm1, 1 - has_m_root); fe25519_neg(negx, h->X); fe25519_cmov(h->X, negx, fe25519_isnegative(h->X) ^ (s[31] >> 7)); fe25519_mul(h->T, h->X, h->Y); return (has_m_root | has_p_root) - 1; } int ge25519_frombytes_negate_vartime(ge25519_p3 *h, const unsigned char *s) { fe25519 u; fe25519 v; fe25519 v3; fe25519 vxx; fe25519 m_root_check, p_root_check; fe25519_frombytes(h->Y, s); fe25519_1(h->Z); fe25519_sq(u, h->Y); fe25519_mul(v, u, ed25519_d); fe25519_sub(u, u, h->Z); /* u = y^2-1 */ fe25519_add(v, v, h->Z); /* v = dy^2+1 */ fe25519_sq(v3, v); fe25519_mul(v3, v3, v); /* v3 = v^3 */ fe25519_sq(h->X, v3); fe25519_mul(h->X, h->X, v); fe25519_mul(h->X, h->X, u); /* x = uv^7 */ fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ fe25519_mul(h->X, h->X, v3); fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ fe25519_sq(vxx, h->X); fe25519_mul(vxx, vxx, v); fe25519_sub(m_root_check, vxx, u); /* vx^2-u */ if (fe25519_iszero(m_root_check) == 0) { fe25519_add(p_root_check, vxx, u); /* vx^2+u */ if (fe25519_iszero(p_root_check) == 0) { return -1; } fe25519_mul(h->X, h->X, fe25519_sqrtm1); } if (fe25519_isnegative(h->X) == (s[31] >> 7)) { fe25519_neg(h->X, h->X); } fe25519_mul(h->T, h->X, h->Y); return 0; } /* r = p + q */ static void ge25519_add_precomp(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->yplusx); fe25519_mul(r->Y, r->Y, q->yminusx); fe25519_mul(r->T, q->xy2d, p->T); fe25519_add(t0, p->Z, p->Z); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_add(r->Z, t0, r->T); fe25519_sub(r->T, t0, r->T); } /* r = p - q */ static void ge25519_sub_precomp(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->yminusx); fe25519_mul(r->Y, r->Y, q->yplusx); fe25519_mul(r->T, q->xy2d, p->T); fe25519_add(t0, p->Z, p->Z); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_sub(r->Z, t0, r->T); fe25519_add(r->T, t0, r->T); } /* r = p */ void ge25519_p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p) { fe25519_mul(r->X, p->X, p->T); fe25519_mul(r->Y, p->Y, p->Z); fe25519_mul(r->Z, p->Z, p->T); } /* r = p */ void ge25519_p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p) { fe25519_mul(r->X, p->X, p->T); fe25519_mul(r->Y, p->Y, p->Z); fe25519_mul(r->Z, p->Z, p->T); fe25519_mul(r->T, p->X, p->Y); } static void ge25519_p2_0(ge25519_p2 *h) { fe25519_0(h->X); fe25519_1(h->Y); fe25519_1(h->Z); } /* r = 2 * p */ static void ge25519_p2_dbl(ge25519_p1p1 *r, const ge25519_p2 *p) { fe25519 t0; fe25519_sq(r->X, p->X); fe25519_sq(r->Z, p->Y); fe25519_sq2(r->T, p->Z); fe25519_add(r->Y, p->X, p->Y); fe25519_sq(t0, r->Y); fe25519_add(r->Y, r->Z, r->X); fe25519_sub(r->Z, r->Z, r->X); fe25519_sub(r->X, t0, r->Y); fe25519_sub(r->T, r->T, r->Z); } static void ge25519_p3_0(ge25519_p3 *h) { fe25519_0(h->X); fe25519_1(h->Y); fe25519_1(h->Z); fe25519_0(h->T); } static void ge25519_cached_0(ge25519_cached *h) { fe25519_1(h->YplusX); fe25519_1(h->YminusX); fe25519_1(h->Z); fe25519_0(h->T2d); } /* r = p */ void ge25519_p3_to_cached(ge25519_cached *r, const ge25519_p3 *p) { fe25519_add(r->YplusX, p->Y, p->X); fe25519_sub(r->YminusX, p->Y, p->X); fe25519_copy(r->Z, p->Z); fe25519_mul(r->T2d, p->T, ed25519_d2); } static void ge25519_p3_to_precomp(ge25519_precomp *pi, const ge25519_p3 *p) { fe25519 recip; fe25519 x; fe25519 y; fe25519 xy; fe25519_invert(recip, p->Z); fe25519_mul(x, p->X, recip); fe25519_mul(y, p->Y, recip); fe25519_add(pi->yplusx, y, x); fe25519_sub(pi->yminusx, y, x); fe25519_mul(xy, x, y); fe25519_mul(pi->xy2d, xy, ed25519_d2); } /* r = p */ static void ge25519_p3_to_p2(ge25519_p2 *r, const ge25519_p3 *p) { fe25519_copy(r->X, p->X); fe25519_copy(r->Y, p->Y); fe25519_copy(r->Z, p->Z); } void ge25519_p3_tobytes(unsigned char *s, const ge25519_p3 *h) { fe25519 recip; fe25519 x; fe25519 y; fe25519_invert(recip, h->Z); fe25519_mul(x, h->X, recip); fe25519_mul(y, h->Y, recip); fe25519_tobytes(s, y); s[31] ^= fe25519_isnegative(x) << 7; } /* r = 2 * p */ static void ge25519_p3_dbl(ge25519_p1p1 *r, const ge25519_p3 *p) { ge25519_p2 q; ge25519_p3_to_p2(&q, p); ge25519_p2_dbl(r, &q); } static void ge25519_precomp_0(ge25519_precomp *h) { fe25519_1(h->yplusx); fe25519_1(h->yminusx); fe25519_0(h->xy2d); } static unsigned char equal(signed char b, signed char c) { unsigned char ub = b; unsigned char uc = c; unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ uint32_t y = (uint32_t) x; /* 0: yes; 1..255: no */ y -= 1; /* 4294967295: yes; 0..254: no */ y >>= 31; /* 1: yes; 0: no */ return y; } static unsigned char negative(signed char b) { /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ uint64_t x = b; x >>= 63; /* 1: yes; 0: no */ return x; } static void ge25519_cmov(ge25519_precomp *t, const ge25519_precomp *u, unsigned char b) { fe25519_cmov(t->yplusx, u->yplusx, b); fe25519_cmov(t->yminusx, u->yminusx, b); fe25519_cmov(t->xy2d, u->xy2d, b); } static void ge25519_cmov_cached(ge25519_cached *t, const ge25519_cached *u, unsigned char b) { fe25519_cmov(t->YplusX, u->YplusX, b); fe25519_cmov(t->YminusX, u->YminusX, b); fe25519_cmov(t->Z, u->Z, b); fe25519_cmov(t->T2d, u->T2d, b); } static void ge25519_cmov8(ge25519_precomp *t, const ge25519_precomp precomp[8], const signed char b) { ge25519_precomp minust; const unsigned char bnegative = negative(b); const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); // printf("babs: %d\nb: %d\nbneg: %d\n", babs, b, bnegative); ge25519_precomp_0(t); ge25519_cmov(t, &precomp[0], equal(babs, 1)); ge25519_cmov(t, &precomp[1], equal(babs, 2)); ge25519_cmov(t, &precomp[2], equal(babs, 3)); ge25519_cmov(t, &precomp[3], equal(babs, 4)); ge25519_cmov(t, &precomp[4], equal(babs, 5)); ge25519_cmov(t, &precomp[5], equal(babs, 6)); ge25519_cmov(t, &precomp[6], equal(babs, 7)); ge25519_cmov(t, &precomp[7], equal(babs, 8)); fe25519_copy(minust.yplusx, t->yminusx); fe25519_copy(minust.yminusx, t->yplusx); fe25519_neg(minust.xy2d, t->xy2d); ge25519_cmov(t, &minust, bnegative); } static void ge25519_cmov8_base(ge25519_precomp *t, const int pos, const signed char b) { static const ge25519_precomp base[32][8] = { /* base[i][j] = (j+1)*256^i*B */ # include "base.h" }; ge25519_cmov8(t, base[pos], b); } static void ge25519_cmov8_cached(ge25519_cached *t, const ge25519_cached cached[8], const signed char b) { ge25519_cached minust; const unsigned char bnegative = negative(b); const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); ge25519_cached_0(t); ge25519_cmov_cached(t, &cached[0], equal(babs, 1)); ge25519_cmov_cached(t, &cached[1], equal(babs, 2)); ge25519_cmov_cached(t, &cached[2], equal(babs, 3)); ge25519_cmov_cached(t, &cached[3], equal(babs, 4)); ge25519_cmov_cached(t, &cached[4], equal(babs, 5)); ge25519_cmov_cached(t, &cached[5], equal(babs, 6)); ge25519_cmov_cached(t, &cached[6], equal(babs, 7)); ge25519_cmov_cached(t, &cached[7], equal(babs, 8)); fe25519_copy(minust.YplusX, t->YminusX); fe25519_copy(minust.YminusX, t->YplusX); fe25519_copy(minust.Z, t->Z); fe25519_neg(minust.T2d, t->T2d); ge25519_cmov_cached(t, &minust, bnegative); } /* r = p - q */ void ge25519_sub_cached(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q) { fe25519 t0; fe25519_add(r->X, p->Y, p->X); fe25519_sub(r->Y, p->Y, p->X); fe25519_mul(r->Z, r->X, q->YminusX); fe25519_mul(r->Y, r->Y, q->YplusX); fe25519_mul(r->T, q->T2d, p->T); fe25519_mul(r->X, p->Z, q->Z); fe25519_add(t0, r->X, r->X); fe25519_sub(r->X, r->Z, r->Y); fe25519_add(r->Y, r->Z, r->Y); fe25519_sub(r->Z, t0, r->T); fe25519_add(r->T, t0, r->T); } void ge25519_tobytes(unsigned char *s, const ge25519_p2 *h) { fe25519 recip; fe25519 x; fe25519 y; fe25519_invert(recip, h->Z); fe25519_mul(x, h->X, recip); fe25519_mul(y, h->Y, recip); fe25519_tobytes(s, y); s[31] ^= fe25519_isnegative(x) << 7; } /* r = a * A + b * B where a = a[0]+256*a[1]+...+256^31 a[31]. and b = b[0]+256*b[1]+...+256^31 b[31]. B is the Ed25519 base point (x,4/5) with x positive. Only used for signatures verification. */ void ge25519_double_scalarmult_vartime(ge25519_p2 *r, const unsigned char *a, const ge25519_p3 *A, const unsigned char *b) { static const ge25519_precomp Bi[8] = { # include "base2.h" }; signed char aslide[256]; signed char bslide[256]; ge25519_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ ge25519_p1p1 t; ge25519_p3 u; ge25519_p3 A2; int i; slide_vartime(aslide, a); slide_vartime(bslide, b); ge25519_p3_to_cached(&Ai[0], A); ge25519_p3_dbl(&t, A); ge25519_p1p1_to_p3(&A2, &t); ge25519_add_cached(&t, &A2, &Ai[0]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[1], &u); ge25519_add_cached(&t, &A2, &Ai[1]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[2], &u); ge25519_add_cached(&t, &A2, &Ai[2]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[3], &u); ge25519_add_cached(&t, &A2, &Ai[3]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[4], &u); ge25519_add_cached(&t, &A2, &Ai[4]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[5], &u); ge25519_add_cached(&t, &A2, &Ai[5]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[6], &u); ge25519_add_cached(&t, &A2, &Ai[6]); ge25519_p1p1_to_p3(&u, &t); ge25519_p3_to_cached(&Ai[7], &u); ge25519_p2_0(r); for (i = 255; i >= 0; --i) { if (aslide[i] || bslide[i]) { break; } } for (; i >= 0; --i) { ge25519_p2_dbl(&t, r); if (aslide[i] > 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_add_cached(&t, &u, &Ai[aslide[i] / 2]); } else if (aslide[i] < 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_sub_cached(&t, &u, &Ai[(-aslide[i]) / 2]); } if (bslide[i] > 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_add_precomp(&t, &u, &Bi[bslide[i] / 2]); } else if (bslide[i] < 0) { ge25519_p1p1_to_p3(&u, &t); ge25519_sub_precomp(&t, &u, &Bi[(-bslide[i]) / 2]); } ge25519_p1p1_to_p2(r, &t); // if (i > 250) { printf("i: %d\naslide: %d\nbslide: %d\n", i, aslide[i], bslide[i]); print_ge2(r);} } } /* h = a * p where a = a[0]+256*a[1]+...+256^31 a[31] Preconditions: a[31] <= 127 p is public */ void ge25519_scalarmult(ge25519_p3 *h, const unsigned char *a, const ge25519_p3 *p) { signed char e[64]; signed char carry; ge25519_p1p1 r; ge25519_p2 s; ge25519_p1p1 t2, t3, t4, t5, t6, t7, t8; ge25519_p3 p2, p3, p4, p5, p6, p7, p8; ge25519_cached pi[8]; ge25519_cached t; int i; ge25519_p3_to_cached(&pi[1 - 1], p); /* p */ ge25519_p3_dbl(&t2, p); ge25519_p1p1_to_p3(&p2, &t2); ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */ ge25519_add_cached(&t3, p, &pi[2 - 1]); ge25519_p1p1_to_p3(&p3, &t3); ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */ ge25519_p3_dbl(&t4, &p2); ge25519_p1p1_to_p3(&p4, &t4); ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */ ge25519_add_cached(&t5, p, &pi[4 - 1]); ge25519_p1p1_to_p3(&p5, &t5); ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */ ge25519_p3_dbl(&t6, &p3); ge25519_p1p1_to_p3(&p6, &t6); ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */ ge25519_add_cached(&t7, p, &pi[6 - 1]); ge25519_p1p1_to_p3(&p7, &t7); ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */ ge25519_p3_dbl(&t8, &p4); ge25519_p1p1_to_p3(&p8, &t8); ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */ for (i = 0; i < 32; ++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ carry = 0; for (i = 0; i < 63; ++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry * ((signed char) 1 << 4); } e[63] += carry; /* each e[i] is between -8 and 8 */ ge25519_p3_0(h); for (i = 63; i != 0; i--) { ge25519_cmov8_cached(&t, pi, e[i]); ge25519_add_cached(&r, h, &t); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p3(h, &r); /* *16 */ } ge25519_cmov8_cached(&t, pi, e[i]); ge25519_add_cached(&r, h, &t); ge25519_p1p1_to_p3(h, &r); } /* h = a * B (with precomputation) where a = a[0]+256*a[1]+...+256^31 a[31] B is the Ed25519 base point (x,4/5) with x positive (as bytes: 0x5866666666666666666666666666666666666666666666666666666666666666) Preconditions: a[31] <= 127 */ void ge25519_scalarmult_base(ge25519_p3 *h, const unsigned char *a) { signed char e[64]; signed char carry; ge25519_p1p1 r; ge25519_p2 s; ge25519_precomp t; int i; for (i = 0; i < 32; ++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ carry = 0; for (i = 0; i < 63; ++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry * ((signed char) 1 << 4); } e[63] += carry; /* each e[i] is between -8 and 8 */ ge25519_p3_0(h); for (i = 1; i < 64; i += 2) { ge25519_cmov8_base(&t, i / 2, e[i]); ge25519_add_precomp(&r, h, &t); ge25519_p1p1_to_p3(h, &r); } ge25519_p3_dbl(&r, h); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p2(&s, &r); ge25519_p2_dbl(&r, &s); ge25519_p1p1_to_p3(h, &r); for (i = 0; i < 64; i += 2) { ge25519_cmov8_base(&t, i / 2, e[i]); ge25519_add_precomp(&r, h, &t); ge25519_p1p1_to_p3(h, &r); } } /* r = 2p */ static void ge25519_p3p3_dbl(ge25519_p3 *r, const ge25519_p3 *p) { ge25519_p1p1 p1p1; ge25519_p3_dbl(&p1p1, p); ge25519_p1p1_to_p3(r, &p1p1); } /* r = p+q */ static void ge25519_p3_add(ge25519_p3 *r, const ge25519_p3 *p, const ge25519_p3 *q) { ge25519_cached q_cached; ge25519_p1p1 p1p1; ge25519_p3_to_cached(&q_cached, q); ge25519_add_cached(&p1p1, p, &q_cached); ge25519_p1p1_to_p3(r, &p1p1); } /* r = r*(2^n)+q */ static void ge25519_p3_dbladd(ge25519_p3 *r, const int n, const ge25519_p3 *q) { ge25519_p2 p2; ge25519_p1p1 p1p1; int i; ge25519_p3_to_p2(&p2, r); for (i = 0; i < n; i++) { ge25519_p2_dbl(&p1p1, &p2); ge25519_p1p1_to_p2(&p2, &p1p1); } ge25519_p1p1_to_p3(r, &p1p1); ge25519_p3_add(r, r, q); } /* multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 */ static void ge25519_mul_l(ge25519_p3 *r, const ge25519_p3 *p) { ge25519_p3 _10, _11, _100, _110, _1000, _1011, _10000, _100000, _100110, _1000000, _1010000, _1010011, _1100011, _1100111, _1101011, _10010011, _10010111, _10111101, _11010011, _11100111, _11101101, _11110101; ge25519_p3p3_dbl(&_10, p); ge25519_p3_add(&_11, p, &_10); ge25519_p3_add(&_100, p, &_11); ge25519_p3_add(&_110, &_10, &_100); ge25519_p3_add(&_1000, &_10, &_110); ge25519_p3_add(&_1011, &_11, &_1000); ge25519_p3p3_dbl(&_10000, &_1000); ge25519_p3p3_dbl(&_100000, &_10000); ge25519_p3_add(&_100110, &_110, &_100000); ge25519_p3p3_dbl(&_1000000, &_100000); ge25519_p3_add(&_1010000, &_10000, &_1000000); ge25519_p3_add(&_1010011, &_11, &_1010000); ge25519_p3_add(&_1100011, &_10000, &_1010011); ge25519_p3_add(&_1100111, &_100, &_1100011); ge25519_p3_add(&_1101011, &_100, &_1100111); ge25519_p3_add(&_10010011, &_1000000, &_1010011); ge25519_p3_add(&_10010111, &_100, &_10010011); ge25519_p3_add(&_10111101, &_100110, &_10010111); ge25519_p3_add(&_11010011, &_1000000, &_10010011); ge25519_p3_add(&_11100111, &_1010000, &_10010111); ge25519_p3_add(&_11101101, &_110, &_11100111); ge25519_p3_add(&_11110101, &_1000, &_11101101); ge25519_p3_add(r, &_1011, &_11110101); ge25519_p3_dbladd(r, 126, &_1010011); ge25519_p3_dbladd(r, 9, &_10); ge25519_p3_add(r, r, &_11110101); ge25519_p3_dbladd(r, 7, &_1100111); ge25519_p3_dbladd(r, 9, &_11110101); ge25519_p3_dbladd(r, 11, &_10111101); ge25519_p3_dbladd(r, 8, &_11100111); ge25519_p3_dbladd(r, 9, &_1101011); ge25519_p3_dbladd(r, 6, &_1011); ge25519_p3_dbladd(r, 14, &_10010011); ge25519_p3_dbladd(r, 10, &_1100011); ge25519_p3_dbladd(r, 9, &_10010111); ge25519_p3_dbladd(r, 10, &_11110101); ge25519_p3_dbladd(r, 8, &_11010011); ge25519_p3_dbladd(r, 8, &_11101101); } /* montgomery to edwards */ static void ge25519_mont_to_ed(fe25519 xed, fe25519 yed, const fe25519 x, const fe25519 y) { fe25519 one; fe25519 x_plus_one; fe25519 x_minus_one; fe25519 x_plus_one_y_inv; fe25519_1(one); fe25519_add(x_plus_one, x, one); fe25519_sub(x_minus_one, x, one); /* xed = sqrt(-A-2)*x/y */ fe25519_mul(x_plus_one_y_inv, x_plus_one, y); fe25519_invert(x_plus_one_y_inv, x_plus_one_y_inv); /* 1/((x+1)*y) */ fe25519_mul(xed, x, ed25519_sqrtam2); fe25519_mul(xed, xed, x_plus_one_y_inv); /* sqrt(-A-2)*x/((x+1)*y) */ fe25519_mul(xed, xed, x_plus_one); /* yed = (x-1)/(x+1) */ fe25519_mul(yed, x_plus_one_y_inv, y); /* 1/(x+1) */ fe25519_mul(yed, yed, x_minus_one); fe25519_cmov(yed, one, fe25519_iszero(x_plus_one_y_inv)); } void zero (unsigned char *const c, const size_t len) { for (int i = 0U; i < len; i++) { c[i] = 0; } } static unsigned char a[32] = { 171, 69, 129, 47, 90, 82, 223, 134, 6, 147, 54, 76, 55, 148, 252, 37, 234, 216, 113, 62, 223, 49, 33, 36, 172, 246, 18, 226, 50, 249, 198, 231 }; unsigned char too_big[32]; static unsigned char b[32] = { 226, 38, 16, 80, 186, 183, 134, 239, 190, 24, 150, 125, 14, 254, 19, 44, 55, 112, 156, 5, 141, 230, 91, 84, 110, 130, 213, 39, 249, 107, 145, 140 }; static unsigned char c[32] = { 190, 24, 150, 125, 14, 254, 19, 44, 55, 112, 156, 5, 141, 230, 91, 84, 110, 130, 213, 39, 249, 107, 145, 140, 226, 38, 16, 80, 186, 183, 134, 239 }; static unsigned char c64[64] = { 190, 24, 150, 125, 14, 254, 19, 44, 55, 112, 156, 5, 141, 230, 91, 84, 110, 130, 213, 39, 249, 107, 145, 140, 226, 38, 16, 80, 186, 183, 134, 239, 190, 24, 150, 125, 14, 254, 19, 44, 55, 112, 156, 5, 141, 230, 91, 84, 110, 130, 213, 39, 249, 107, 145, 140, 226, 38, 16, 80, 186, 183, 134, 239 }; static const unsigned char p[32] = { 0x38, 0xf4, 0x69, 0x6f, 0xcf, 0x62, 0xa0, 0xfd, 0x5a, 0xb7, 0x6e, 0x9f, 0xcb, 0xcd, 0x95, 0x3f, 0xed, 0xba, 0x30, 0xb2, 0x64, 0x42, 0xa4, 0x52, 0x27, 0xa6, 0x3e, 0xd2, 0xc8, 0xac, 0xa4, 0xed }; static const unsigned char pk_test[32] = { 0xd7, 0x5a, 0x98, 0x01, 0x82, 0xb1, 0x0a, 0xb7, 0xd5, 0x4b, 0xfe, 0xd3, 0xc9, 0x64, 0x07, 0x3a, 0x0e, 0xe1, 0x72, 0xf3, 0xda, 0xa6, 0x23, 0x25, 0xaf, 0x02, 0x1a, 0x68, 0xf7, 0x07, 0x51, 0x1a }; int main (int argc, char *argv[]) { static fe25519 f; static fe25519 g; static fe25519 h; static fe25519 f_; static fe25519 g_; ge25519_p3 ge; ge25519_p3 gf; char s[32]; unsigned char s64[64]; static unsigned char res[32]; static char hex[32]; static char hex64[64]; int i; ////////////////////////////////////////////// fe25519_frombytes(f, a); fe25519_frombytes(g, b); fe25519_mul(h, f, g); fe25519_tobytes(res, h); // // printf("\na _____________\n"); // // for (i = 0; i < 10; i++) printf("a%d: %08x\n", i, f[i]); // // printf("\nb _____________\n"); // // for (i = 0; i < 10; i++) printf("b%d: %08x\n", i, g[i]); memset(hex, 0, sizeof hex); bin2hex(hex, sizeof hex, res, sizeof res); printf("fe_mul: %s\n", hex); // fe25519_sq(h, f); // fe25519_tobytes(res, h); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_sq: %s\n", hex); // memset(too_big, 128, sizeof too_big); // fe25519_frombytes(f, b); // fe25519_tobytes(res, f); // // bin2hex(hex, sizeof hex, res, sizeof res); // // printf("%s\n", hex); // fe25519_reduce(h, f); // fe25519_tobytes(res, h); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_red: %s\n", hex); // fe25519_frombytes(f, a); // fe25519_frombytes(g, b); // fe25519_sqmul(f, 8734U, g); // fe25519_tobytes(res, f); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_sqm: %s\n", hex); // fe25519_invert(f, f); // fe25519_tobytes(res, f); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_inv: %s\n", hex); // fe25519_pow22523(f, f); // fe25519_tobytes(res, f); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_p25: %s\n", hex); // fe25519_cneg(f, f, 1); // fe25519_tobytes(res, f); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("fe_cng: %s\n", hex); // sc25519_mul(res, a, b); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("sc_mul: %s\n", hex); // sc25519_muladd(res, a, b, c); // memset(hex, 0, sizeof hex); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("sc_mad: %s\n", hex); // memcpy(&s64, &c64, sizeof c64); // sc25519_reduce(s64); // bin2hex(hex, sizeof hex, s64, (sizeof s64) / 2); // printf("sc_red: %s\n", hex); // sc25519_invert(res, c); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("sc_inv: %s\n", hex); // ge25519_mont_to_ed(f_, g_, f, g); // fe25519_tobytes(res, f_); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("g_m2ex: %s \n", hex); // fe25519_tobytes(res, g_); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("g_m2ey: %s \n", hex); // memset(&ge, 0, sizeof ge); // ge25519_frombytes(&ge, p); // ge25519_p3_tobytes(res, &ge); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("p : %s \n", hex); // ge25519_mul_l(&gf, &ge); // ge25519_p3_tobytes(res, &gf); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("mul_l : %s \n", hex); // ge25519_scalarmult_base(&gf, c); // ge25519_p3_tobytes(res, &gf); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("smultb: %s \n", hex); // ge25519_scalarmult(&ge, b, &gf); // ge25519_p3_tobytes(res, &ge); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("smult : %s \n", hex); // ge25519_double_scalarmult_vartime(&gf, a, &ge, b); // ge25519_p3_tobytes(res, &gf); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("scdbl : %s \n", hex); // ge25519_frombytes_negate_vartime(&gf, pk_test); // ge25519_p3_tobytes(res, &gf); // bin2hex(hex, sizeof hex, res, sizeof res); // printf("scdbl : %s \n", hex); int canon = sc25519_is_canonical(b); printf("canon: %d\n", canon); return 1; }