1052 lines
38 KiB
Go
1052 lines
38 KiB
Go
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// Copyright 2011 The Go Authors. All rights reserved.
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// Copyright 2011 ThePiachu. All rights reserved.
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// Copyright 2013-2016 The btcsuite developers
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// Use of this source code is governed by an ISC
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// license that can be found in the LICENSE file.
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package btcec
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import (
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"crypto/rand"
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"crypto/sha1"
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"encoding/hex"
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"fmt"
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"math/big"
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"testing"
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)
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// isJacobianOnS256Curve returns boolean if the point (x,y,z) is on the
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// secp256k1 curve.
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func isJacobianOnS256Curve(x, y, z *fieldVal) bool {
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// Elliptic curve equation for secp256k1 is: y^2 = x^3 + 7
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// In Jacobian coordinates, Y = y/z^3 and X = x/z^2
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// Thus:
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// (y/z^3)^2 = (x/z^2)^3 + 7
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// y^2/z^6 = x^3/z^6 + 7
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// y^2 = x^3 + 7*z^6
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var y2, z2, x3, result fieldVal
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y2.SquareVal(y).Normalize()
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z2.SquareVal(z)
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x3.SquareVal(x).Mul(x)
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result.SquareVal(&z2).Mul(&z2).MulInt(7).Add(&x3).Normalize()
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return y2.Equals(&result)
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}
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// TestAddJacobian tests addition of points projected in Jacobian coordinates.
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func TestAddJacobian(t *testing.T) {
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tests := []struct {
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x1, y1, z1 string // Coordinates (in hex) of first point to add
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x2, y2, z2 string // Coordinates (in hex) of second point to add
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x3, y3, z3 string // Coordinates (in hex) of expected point
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}{
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// Addition with a point at infinity (left hand side).
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// ∞ + P = P
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{
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"0",
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"0",
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"0",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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},
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// Addition with a point at infinity (right hand side).
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// P + ∞ = P
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{
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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"0",
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"0",
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"0",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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},
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// Addition with z1=z2=1 different x values.
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"1",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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"0cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a6",
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"e205f79361bbe0346b037b4010985dbf4f9e1e955e7d0d14aca876bfa79aad87",
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"44a5646b446e3877a648d6d381370d9ef55a83b666ebce9df1b1d7d65b817b2f",
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},
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// Addition with z1=z2=1 same x opposite y.
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// P(x, y, z) + P(x, -y, z) = infinity
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"1",
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
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"1",
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"0",
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"0",
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"0",
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},
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// Addition with z1=z2=1 same point.
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// P(x, y, z) + P(x, y, z) = 2P
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"1",
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"1",
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"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
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"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
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"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
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},
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// Addition with z1=z2 (!=1) different x values.
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"5d2fe112c21891d440f65a98473cb626111f8a234d2cd82f22172e369f002147",
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"98e3386a0a622a35c4561ffb32308d8e1c6758e10ebb1b4ebd3d04b4eb0ecbe8",
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"2",
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"cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a60",
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"817de4d86ef80d1ac0ded00426176fd3e787a5579f43452b2a1db021e6ac3778",
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"129591ad11b8e1de99235b4e04dc367bd56a0ed99baf3a77c6c75f5a6e05f08d",
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},
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// Addition with z1=z2 (!=1) same x opposite y.
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// P(x, y, z) + P(x, -y, z) = infinity
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"a470ab21467813b6e0496d2c2b70c11446bab4fcbc9a52b7f225f30e869aea9f",
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"2",
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"0",
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"0",
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"0",
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},
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// Addition with z1=z2 (!=1) same point.
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// P(x, y, z) + P(x, y, z) = 2P
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
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"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
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"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
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},
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// Addition with z1!=z2 and z2=1 different x values.
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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"3ef1f68795a6ccd1181e23eab80a1b9a2cebdcde755413bf097936eb5b91b4f3",
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"0bef26c377c068d606f6802130bb7e9f3c3d2abcfa1a295950ed81133561cb04",
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"252b235a2371c3bd3246b69c09b86cf7aad41db3375e74ef8d8ebeb4dc0be11a",
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},
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// Addition with z1!=z2 and z2=1 same x opposite y.
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// P(x, y, z) + P(x, -y, z) = infinity
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
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"1",
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"0",
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"0",
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"0",
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},
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// Addition with z1!=z2 and z2=1 same point.
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// P(x, y, z) + P(x, y, z) = 2P
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"1",
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"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
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"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
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"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
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},
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// Addition with z1!=z2 and z2!=1 different x values.
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// P(x, y, z) + P(x, y, z) = 2P
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"91abba6a34b7481d922a4bd6a04899d5a686f6cf6da4e66a0cb427fb25c04bd4",
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"03fede65e30b4e7576a2abefc963ddbf9fdccbf791b77c29beadefe49951f7d1",
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"3",
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"3f07081927fd3f6dadd4476614c89a09eba7f57c1c6c3b01fa2d64eac1eef31e",
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"949166e04ebc7fd95a9d77e5dfd88d1492ecffd189792e3944eb2b765e09e031",
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"eb8cba81bcffa4f44d75427506737e1f045f21e6d6f65543ee0e1d163540c931",
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}, // Addition with z1!=z2 and z2!=1 same x opposite y.
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// P(x, y, z) + P(x, -y, z) = infinity
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
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"cafc41904dd5428934f7d075129c8ba46eb622d4fc88d72cd1401452664add18",
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"3",
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"0",
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"0",
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"0",
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},
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// Addition with z1!=z2 and z2!=1 same point.
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// P(x, y, z) + P(x, y, z) = 2P
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{
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"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
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"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
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"2",
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"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
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"3503be6fb22abd76cb082f8aed63745b9149dd2b037728d32ebfebac99b51f17",
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"3",
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"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
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"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
|
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"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
|
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},
|
||
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}
|
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||
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t.Logf("Running %d tests", len(tests))
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for i, test := range tests {
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// Convert hex to field values.
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x1 := new(fieldVal).SetHex(test.x1)
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y1 := new(fieldVal).SetHex(test.y1)
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z1 := new(fieldVal).SetHex(test.z1)
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x2 := new(fieldVal).SetHex(test.x2)
|
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y2 := new(fieldVal).SetHex(test.y2)
|
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z2 := new(fieldVal).SetHex(test.z2)
|
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x3 := new(fieldVal).SetHex(test.x3)
|
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y3 := new(fieldVal).SetHex(test.y3)
|
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z3 := new(fieldVal).SetHex(test.z3)
|
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|
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|
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// Ensure the test data is using points that are actually on
|
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|
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// the curve (or the point at infinity).
|
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|
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if !z1.IsZero() && !isJacobianOnS256Curve(x1, y1, z1) {
|
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t.Errorf("#%d first point is not on the curve -- "+
|
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|
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"invalid test data", i)
|
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continue
|
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}
|
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|
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if !z2.IsZero() && !isJacobianOnS256Curve(x2, y2, z2) {
|
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|
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t.Errorf("#%d second point is not on the curve -- "+
|
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|
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"invalid test data", i)
|
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continue
|
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|
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}
|
||
|
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if !z3.IsZero() && !isJacobianOnS256Curve(x3, y3, z3) {
|
||
|
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t.Errorf("#%d expected point is not on the curve -- "+
|
||
|
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"invalid test data", i)
|
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|
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continue
|
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|
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}
|
||
|
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|
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|
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// Add the two points.
|
||
|
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rx, ry, rz := new(fieldVal), new(fieldVal), new(fieldVal)
|
||
|
|
S256().addJacobian(x1, y1, z1, x2, y2, z2, rx, ry, rz)
|
||
|
|
|
||
|
|
// Ensure result matches expected.
|
||
|
|
if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
|
||
|
|
t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
|
||
|
|
"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// TestAddAffine tests addition of points in affine coordinates.
|
||
|
|
func TestAddAffine(t *testing.T) {
|
||
|
|
tests := []struct {
|
||
|
|
x1, y1 string // Coordinates (in hex) of first point to add
|
||
|
|
x2, y2 string // Coordinates (in hex) of second point to add
|
||
|
|
x3, y3 string // Coordinates (in hex) of expected point
|
||
|
|
}{
|
||
|
|
// Addition with a point at infinity (left hand side).
|
||
|
|
// ∞ + P = P
|
||
|
|
{
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
|
||
|
|
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
|
||
|
|
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
|
||
|
|
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
|
||
|
|
},
|
||
|
|
// Addition with a point at infinity (right hand side).
|
||
|
|
// P + ∞ = P
|
||
|
|
{
|
||
|
|
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
|
||
|
|
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
|
||
|
|
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
|
||
|
|
},
|
||
|
|
|
||
|
|
// Addition with different x values.
|
||
|
|
{
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
|
||
|
|
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
|
||
|
|
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
|
||
|
|
"fd5b88c21d3143518d522cd2796f3d726793c88b3e05636bc829448e053fed69",
|
||
|
|
"21cf4f6a5be5ff6380234c50424a970b1f7e718f5eb58f68198c108d642a137f",
|
||
|
|
},
|
||
|
|
// Addition with same x opposite y.
|
||
|
|
// P(x, y) + P(x, -y) = infinity
|
||
|
|
{
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
},
|
||
|
|
// Addition with same point.
|
||
|
|
// P(x, y) + P(x, y) = 2P
|
||
|
|
{
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
|
||
|
|
"59477d88ae64a104dbb8d31ec4ce2d91b2fe50fa628fb6a064e22582196b365b",
|
||
|
|
"938dc8c0f13d1e75c987cb1a220501bd614b0d3dd9eb5c639847e1240216e3b6",
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
t.Logf("Running %d tests", len(tests))
|
||
|
|
for i, test := range tests {
|
||
|
|
// Convert hex to field values.
|
||
|
|
x1, y1 := fromHex(test.x1), fromHex(test.y1)
|
||
|
|
x2, y2 := fromHex(test.x2), fromHex(test.y2)
|
||
|
|
x3, y3 := fromHex(test.x3), fromHex(test.y3)
|
||
|
|
|
||
|
|
// Ensure the test data is using points that are actually on
|
||
|
|
// the curve (or the point at infinity).
|
||
|
|
if !(x1.Sign() == 0 && y1.Sign() == 0) && !S256().IsOnCurve(x1, y1) {
|
||
|
|
t.Errorf("#%d first point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
if !(x2.Sign() == 0 && y2.Sign() == 0) && !S256().IsOnCurve(x2, y2) {
|
||
|
|
t.Errorf("#%d second point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
if !(x3.Sign() == 0 && y3.Sign() == 0) && !S256().IsOnCurve(x3, y3) {
|
||
|
|
t.Errorf("#%d expected point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
|
||
|
|
// Add the two points.
|
||
|
|
rx, ry := S256().Add(x1, y1, x2, y2)
|
||
|
|
|
||
|
|
// Ensure result matches expected.
|
||
|
|
if rx.Cmp(x3) != 00 || ry.Cmp(y3) != 0 {
|
||
|
|
t.Errorf("#%d wrong result\ngot: (%x, %x)\n"+
|
||
|
|
"want: (%x, %x)", i, rx, ry, x3, y3)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// TestDoubleJacobian tests doubling of points projected in Jacobian
|
||
|
|
// coordinates.
|
||
|
|
func TestDoubleJacobian(t *testing.T) {
|
||
|
|
tests := []struct {
|
||
|
|
x1, y1, z1 string // Coordinates (in hex) of point to double
|
||
|
|
x3, y3, z3 string // Coordinates (in hex) of expected point
|
||
|
|
}{
|
||
|
|
// Doubling a point at infinity is still infinity.
|
||
|
|
{
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
},
|
||
|
|
// Doubling with z1=1.
|
||
|
|
{
|
||
|
|
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
|
||
|
|
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
|
||
|
|
"1",
|
||
|
|
"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
|
||
|
|
"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
|
||
|
|
"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
|
||
|
|
},
|
||
|
|
// Doubling with z1!=1.
|
||
|
|
{
|
||
|
|
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
|
||
|
|
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
|
||
|
|
"2",
|
||
|
|
"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
|
||
|
|
"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
|
||
|
|
"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
|
||
|
|
},
|
||
|
|
// From btcd issue #709.
|
||
|
|
{
|
||
|
|
"201e3f75715136d2f93c4f4598f91826f94ca01f4233a5bd35de9708859ca50d",
|
||
|
|
"bdf18566445e7562c6ada68aef02d498d7301503de5b18c6aef6e2b1722412e1",
|
||
|
|
"0000000000000000000000000000000000000000000000000000000000000001",
|
||
|
|
"4a5e0559863ebb4e9ed85f5c4fa76003d05d9a7626616e614a1f738621e3c220",
|
||
|
|
"00000000000000000000000000000000000000000000000000000001b1388778",
|
||
|
|
"7be30acc88bceac58d5b4d15de05a931ae602a07bcb6318d5dedc563e4482993",
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
t.Logf("Running %d tests", len(tests))
|
||
|
|
for i, test := range tests {
|
||
|
|
// Convert hex to field values.
|
||
|
|
x1 := new(fieldVal).SetHex(test.x1)
|
||
|
|
y1 := new(fieldVal).SetHex(test.y1)
|
||
|
|
z1 := new(fieldVal).SetHex(test.z1)
|
||
|
|
x3 := new(fieldVal).SetHex(test.x3)
|
||
|
|
y3 := new(fieldVal).SetHex(test.y3)
|
||
|
|
z3 := new(fieldVal).SetHex(test.z3)
|
||
|
|
|
||
|
|
// Ensure the test data is using points that are actually on
|
||
|
|
// the curve (or the point at infinity).
|
||
|
|
if !z1.IsZero() && !isJacobianOnS256Curve(x1, y1, z1) {
|
||
|
|
t.Errorf("#%d first point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
if !z3.IsZero() && !isJacobianOnS256Curve(x3, y3, z3) {
|
||
|
|
t.Errorf("#%d expected point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
|
||
|
|
// Double the point.
|
||
|
|
rx, ry, rz := new(fieldVal), new(fieldVal), new(fieldVal)
|
||
|
|
S256().doubleJacobian(x1, y1, z1, rx, ry, rz)
|
||
|
|
|
||
|
|
// Ensure result matches expected.
|
||
|
|
if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
|
||
|
|
t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
|
||
|
|
"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// TestDoubleAffine tests doubling of points in affine coordinates.
|
||
|
|
func TestDoubleAffine(t *testing.T) {
|
||
|
|
tests := []struct {
|
||
|
|
x1, y1 string // Coordinates (in hex) of point to double
|
||
|
|
x3, y3 string // Coordinates (in hex) of expected point
|
||
|
|
}{
|
||
|
|
// Doubling a point at infinity is still infinity.
|
||
|
|
// 2*∞ = ∞ (point at infinity)
|
||
|
|
|
||
|
|
{
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
"0",
|
||
|
|
},
|
||
|
|
|
||
|
|
// Random points.
|
||
|
|
{
|
||
|
|
"e41387ffd8baaeeb43c2faa44e141b19790e8ac1f7ff43d480dc132230536f86",
|
||
|
|
"1b88191d430f559896149c86cbcb703193105e3cf3213c0c3556399836a2b899",
|
||
|
|
"88da47a089d333371bd798c548ef7caae76e737c1980b452d367b3cfe3082c19",
|
||
|
|
"3b6f659b09a362821dfcfefdbfbc2e59b935ba081b6c249eb147b3c2100b1bc1",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"b3589b5d984f03ef7c80aeae444f919374799edf18d375cab10489a3009cff0c",
|
||
|
|
"c26cf343875b3630e15bccc61202815b5d8f1fd11308934a584a5babe69db36a",
|
||
|
|
"e193860172998751e527bb12563855602a227fc1f612523394da53b746bb2fb1",
|
||
|
|
"2bfcf13d2f5ab8bb5c611fab5ebbed3dc2f057062b39a335224c22f090c04789",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"2b31a40fbebe3440d43ac28dba23eee71c62762c3fe3dbd88b4ab82dc6a82340",
|
||
|
|
"9ba7deb02f5c010e217607fd49d58db78ec273371ea828b49891ce2fd74959a1",
|
||
|
|
"2c8d5ef0d343b1a1a48aa336078eadda8481cb048d9305dc4fdf7ee5f65973a2",
|
||
|
|
"bb4914ac729e26d3cd8f8dc8f702f3f4bb7e0e9c5ae43335f6e94c2de6c3dc95",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"61c64b760b51981fab54716d5078ab7dffc93730b1d1823477e27c51f6904c7a",
|
||
|
|
"ef6eb16ea1a36af69d7f66524c75a3a5e84c13be8fbc2e811e0563c5405e49bd",
|
||
|
|
"5f0dcdd2595f5ad83318a0f9da481039e36f135005420393e72dfca985b482f4",
|
||
|
|
"a01c849b0837065c1cb481b0932c441f49d1cab1b4b9f355c35173d93f110ae0",
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
t.Logf("Running %d tests", len(tests))
|
||
|
|
for i, test := range tests {
|
||
|
|
// Convert hex to field values.
|
||
|
|
x1, y1 := fromHex(test.x1), fromHex(test.y1)
|
||
|
|
x3, y3 := fromHex(test.x3), fromHex(test.y3)
|
||
|
|
|
||
|
|
// Ensure the test data is using points that are actually on
|
||
|
|
// the curve (or the point at infinity).
|
||
|
|
if !(x1.Sign() == 0 && y1.Sign() == 0) && !S256().IsOnCurve(x1, y1) {
|
||
|
|
t.Errorf("#%d first point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
if !(x3.Sign() == 0 && y3.Sign() == 0) && !S256().IsOnCurve(x3, y3) {
|
||
|
|
t.Errorf("#%d expected point is not on the curve -- "+
|
||
|
|
"invalid test data", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
|
||
|
|
// Double the point.
|
||
|
|
rx, ry := S256().Double(x1, y1)
|
||
|
|
|
||
|
|
// Ensure result matches expected.
|
||
|
|
if rx.Cmp(x3) != 00 || ry.Cmp(y3) != 0 {
|
||
|
|
t.Errorf("#%d wrong result\ngot: (%x, %x)\n"+
|
||
|
|
"want: (%x, %x)", i, rx, ry, x3, y3)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestOnCurve(t *testing.T) {
|
||
|
|
s256 := S256()
|
||
|
|
if !s256.IsOnCurve(s256.Params().Gx, s256.Params().Gy) {
|
||
|
|
t.Errorf("FAIL S256")
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
type baseMultTest struct {
|
||
|
|
k string
|
||
|
|
x, y string
|
||
|
|
}
|
||
|
|
|
||
|
|
//TODO: add more test vectors
|
||
|
|
var s256BaseMultTests = []baseMultTest{
|
||
|
|
{
|
||
|
|
"AA5E28D6A97A2479A65527F7290311A3624D4CC0FA1578598EE3C2613BF99522",
|
||
|
|
"34F9460F0E4F08393D192B3C5133A6BA099AA0AD9FD54EBCCFACDFA239FF49C6",
|
||
|
|
"B71EA9BD730FD8923F6D25A7A91E7DD7728A960686CB5A901BB419E0F2CA232",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"7E2B897B8CEBC6361663AD410835639826D590F393D90A9538881735256DFAE3",
|
||
|
|
"D74BF844B0862475103D96A611CF2D898447E288D34B360BC885CB8CE7C00575",
|
||
|
|
"131C670D414C4546B88AC3FF664611B1C38CEB1C21D76369D7A7A0969D61D97D",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"6461E6DF0FE7DFD05329F41BF771B86578143D4DD1F7866FB4CA7E97C5FA945D",
|
||
|
|
"E8AECC370AEDD953483719A116711963CE201AC3EB21D3F3257BB48668C6A72F",
|
||
|
|
"C25CAF2F0EBA1DDB2F0F3F47866299EF907867B7D27E95B3873BF98397B24EE1",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"376A3A2CDCD12581EFFF13EE4AD44C4044B8A0524C42422A7E1E181E4DEECCEC",
|
||
|
|
"14890E61FCD4B0BD92E5B36C81372CA6FED471EF3AA60A3E415EE4FE987DABA1",
|
||
|
|
"297B858D9F752AB42D3BCA67EE0EB6DCD1C2B7B0DBE23397E66ADC272263F982",
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"1B22644A7BE026548810C378D0B2994EEFA6D2B9881803CB02CEFF865287D1B9",
|
||
|
|
"F73C65EAD01C5126F28F442D087689BFA08E12763E0CEC1D35B01751FD735ED3",
|
||
|
|
"F449A8376906482A84ED01479BD18882B919C140D638307F0C0934BA12590BDE",
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
//TODO: test different curves as well?
|
||
|
|
func TestBaseMult(t *testing.T) {
|
||
|
|
s256 := S256()
|
||
|
|
for i, e := range s256BaseMultTests {
|
||
|
|
k, ok := new(big.Int).SetString(e.k, 16)
|
||
|
|
if !ok {
|
||
|
|
t.Errorf("%d: bad value for k: %s", i, e.k)
|
||
|
|
}
|
||
|
|
x, y := s256.ScalarBaseMult(k.Bytes())
|
||
|
|
if fmt.Sprintf("%X", x) != e.x || fmt.Sprintf("%X", y) != e.y {
|
||
|
|
t.Errorf("%d: bad output for k=%s: got (%X, %X), want (%s, %s)", i, e.k, x, y, e.x, e.y)
|
||
|
|
}
|
||
|
|
if testing.Short() && i > 5 {
|
||
|
|
break
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestBaseMultVerify(t *testing.T) {
|
||
|
|
s256 := S256()
|
||
|
|
for bytes := 1; bytes < 40; bytes++ {
|
||
|
|
for i := 0; i < 30; i++ {
|
||
|
|
data := make([]byte, bytes)
|
||
|
|
_, err := rand.Read(data)
|
||
|
|
if err != nil {
|
||
|
|
t.Errorf("failed to read random data for %d", i)
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
x, y := s256.ScalarBaseMult(data)
|
||
|
|
xWant, yWant := s256.ScalarMult(s256.Gx, s256.Gy, data)
|
||
|
|
if x.Cmp(xWant) != 0 || y.Cmp(yWant) != 0 {
|
||
|
|
t.Errorf("%d: bad output for %X: got (%X, %X), want (%X, %X)", i, data, x, y, xWant, yWant)
|
||
|
|
}
|
||
|
|
if testing.Short() && i > 2 {
|
||
|
|
break
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestScalarMult(t *testing.T) {
|
||
|
|
tests := []struct {
|
||
|
|
x string
|
||
|
|
y string
|
||
|
|
k string
|
||
|
|
rx string
|
||
|
|
ry string
|
||
|
|
}{
|
||
|
|
// base mult, essentially.
|
||
|
|
{
|
||
|
|
"79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
|
||
|
|
"483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8",
|
||
|
|
"18e14a7b6a307f426a94f8114701e7c8e774e7f9a47e2c2035db29a206321725",
|
||
|
|
"50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352",
|
||
|
|
"2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6",
|
||
|
|
},
|
||
|
|
// From btcd issue #709.
|
||
|
|
{
|
||
|
|
"000000000000000000000000000000000000000000000000000000000000002c",
|
||
|
|
"420e7a99bba18a9d3952597510fd2b6728cfeafc21a4e73951091d4d8ddbe94e",
|
||
|
|
"a2e8ba2e8ba2e8ba2e8ba2e8ba2e8ba219b51835b55cc30ebfe2f6599bc56f58",
|
||
|
|
"a2112dcdfbcd10ae1133a358de7b82db68e0a3eb4b492cc8268d1e7118c98788",
|
||
|
|
"27fc7463b7bb3c5f98ecf2c84a6272bb1681ed553d92c69f2dfe25a9f9fd3836",
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
s256 := S256()
|
||
|
|
for i, test := range tests {
|
||
|
|
x, _ := new(big.Int).SetString(test.x, 16)
|
||
|
|
y, _ := new(big.Int).SetString(test.y, 16)
|
||
|
|
k, _ := new(big.Int).SetString(test.k, 16)
|
||
|
|
xWant, _ := new(big.Int).SetString(test.rx, 16)
|
||
|
|
yWant, _ := new(big.Int).SetString(test.ry, 16)
|
||
|
|
xGot, yGot := s256.ScalarMult(x, y, k.Bytes())
|
||
|
|
if xGot.Cmp(xWant) != 0 || yGot.Cmp(yWant) != 0 {
|
||
|
|
t.Fatalf("%d: bad output: got (%X, %X), want (%X, %X)", i, xGot, yGot, xWant, yWant)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestScalarMultRand(t *testing.T) {
|
||
|
|
// Strategy for this test:
|
||
|
|
// Get a random exponent from the generator point at first
|
||
|
|
// This creates a new point which is used in the next iteration
|
||
|
|
// Use another random exponent on the new point.
|
||
|
|
// We use BaseMult to verify by multiplying the previous exponent
|
||
|
|
// and the new random exponent together (mod N)
|
||
|
|
s256 := S256()
|
||
|
|
x, y := s256.Gx, s256.Gy
|
||
|
|
exponent := big.NewInt(1)
|
||
|
|
for i := 0; i < 1024; i++ {
|
||
|
|
data := make([]byte, 32)
|
||
|
|
_, err := rand.Read(data)
|
||
|
|
if err != nil {
|
||
|
|
t.Fatalf("failed to read random data at %d", i)
|
||
|
|
break
|
||
|
|
}
|
||
|
|
x, y = s256.ScalarMult(x, y, data)
|
||
|
|
exponent.Mul(exponent, new(big.Int).SetBytes(data))
|
||
|
|
xWant, yWant := s256.ScalarBaseMult(exponent.Bytes())
|
||
|
|
if x.Cmp(xWant) != 0 || y.Cmp(yWant) != 0 {
|
||
|
|
t.Fatalf("%d: bad output for %X: got (%X, %X), want (%X, %X)", i, data, x, y, xWant, yWant)
|
||
|
|
break
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestSplitK(t *testing.T) {
|
||
|
|
tests := []struct {
|
||
|
|
k string
|
||
|
|
k1, k2 string
|
||
|
|
s1, s2 int
|
||
|
|
}{
|
||
|
|
{
|
||
|
|
"6df2b5d30854069ccdec40ae022f5c948936324a4e9ebed8eb82cfd5a6b6d766",
|
||
|
|
"00000000000000000000000000000000b776e53fb55f6b006a270d42d64ec2b1",
|
||
|
|
"00000000000000000000000000000000d6cc32c857f1174b604eefc544f0c7f7",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"6ca00a8f10632170accc1b3baf2a118fa5725f41473f8959f34b8f860c47d88d",
|
||
|
|
"0000000000000000000000000000000007b21976c1795723c1bfbfa511e95b84",
|
||
|
|
"00000000000000000000000000000000d8d2d5f9d20fc64fd2cf9bda09a5bf90",
|
||
|
|
1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"b2eda8ab31b259032d39cbc2a234af17fcee89c863a8917b2740b67568166289",
|
||
|
|
"00000000000000000000000000000000507d930fecda7414fc4a523b95ef3c8c",
|
||
|
|
"00000000000000000000000000000000f65ffb179df189675338c6185cb839be",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"f6f00e44f179936f2befc7442721b0633f6bafdf7161c167ffc6f7751980e3a0",
|
||
|
|
"0000000000000000000000000000000008d0264f10bcdcd97da3faa38f85308d",
|
||
|
|
"0000000000000000000000000000000065fed1506eb6605a899a54e155665f79",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"8679085ab081dc92cdd23091ce3ee998f6b320e419c3475fae6b5b7d3081996e",
|
||
|
|
"0000000000000000000000000000000089fbf24fbaa5c3c137b4f1cedc51d975",
|
||
|
|
"00000000000000000000000000000000d38aa615bd6754d6f4d51ccdaf529fea",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"6b1247bb7931dfcae5b5603c8b5ae22ce94d670138c51872225beae6bba8cdb3",
|
||
|
|
"000000000000000000000000000000008acc2a521b21b17cfb002c83be62f55d",
|
||
|
|
"0000000000000000000000000000000035f0eff4d7430950ecb2d94193dedc79",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"a2e8ba2e8ba2e8ba2e8ba2e8ba2e8ba219b51835b55cc30ebfe2f6599bc56f58",
|
||
|
|
"0000000000000000000000000000000045c53aa1bb56fcd68c011e2dad6758e4",
|
||
|
|
"00000000000000000000000000000000a2e79d200f27f2360fba57619936159b",
|
||
|
|
-1, -1,
|
||
|
|
},
|
||
|
|
}
|
||
|
|
|
||
|
|
s256 := S256()
|
||
|
|
for i, test := range tests {
|
||
|
|
k, ok := new(big.Int).SetString(test.k, 16)
|
||
|
|
if !ok {
|
||
|
|
t.Errorf("%d: bad value for k: %s", i, test.k)
|
||
|
|
}
|
||
|
|
k1, k2, k1Sign, k2Sign := s256.splitK(k.Bytes())
|
||
|
|
k1str := fmt.Sprintf("%064x", k1)
|
||
|
|
if test.k1 != k1str {
|
||
|
|
t.Errorf("%d: bad k1: got %v, want %v", i, k1str, test.k1)
|
||
|
|
}
|
||
|
|
k2str := fmt.Sprintf("%064x", k2)
|
||
|
|
if test.k2 != k2str {
|
||
|
|
t.Errorf("%d: bad k2: got %v, want %v", i, k2str, test.k2)
|
||
|
|
}
|
||
|
|
if test.s1 != k1Sign {
|
||
|
|
t.Errorf("%d: bad k1 sign: got %d, want %d", i, k1Sign, test.s1)
|
||
|
|
}
|
||
|
|
if test.s2 != k2Sign {
|
||
|
|
t.Errorf("%d: bad k2 sign: got %d, want %d", i, k2Sign, test.s2)
|
||
|
|
}
|
||
|
|
k1Int := new(big.Int).SetBytes(k1)
|
||
|
|
k1SignInt := new(big.Int).SetInt64(int64(k1Sign))
|
||
|
|
k1Int.Mul(k1Int, k1SignInt)
|
||
|
|
k2Int := new(big.Int).SetBytes(k2)
|
||
|
|
k2SignInt := new(big.Int).SetInt64(int64(k2Sign))
|
||
|
|
k2Int.Mul(k2Int, k2SignInt)
|
||
|
|
gotK := new(big.Int).Mul(k2Int, s256.lambda)
|
||
|
|
gotK.Add(k1Int, gotK)
|
||
|
|
gotK.Mod(gotK, s256.N)
|
||
|
|
if k.Cmp(gotK) != 0 {
|
||
|
|
t.Errorf("%d: bad k: got %X, want %X", i, gotK.Bytes(), k.Bytes())
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestSplitKRand(t *testing.T) {
|
||
|
|
s256 := S256()
|
||
|
|
for i := 0; i < 1024; i++ {
|
||
|
|
bytesK := make([]byte, 32)
|
||
|
|
_, err := rand.Read(bytesK)
|
||
|
|
if err != nil {
|
||
|
|
t.Fatalf("failed to read random data at %d", i)
|
||
|
|
break
|
||
|
|
}
|
||
|
|
k := new(big.Int).SetBytes(bytesK)
|
||
|
|
k1, k2, k1Sign, k2Sign := s256.splitK(bytesK)
|
||
|
|
k1Int := new(big.Int).SetBytes(k1)
|
||
|
|
k1SignInt := new(big.Int).SetInt64(int64(k1Sign))
|
||
|
|
k1Int.Mul(k1Int, k1SignInt)
|
||
|
|
k2Int := new(big.Int).SetBytes(k2)
|
||
|
|
k2SignInt := new(big.Int).SetInt64(int64(k2Sign))
|
||
|
|
k2Int.Mul(k2Int, k2SignInt)
|
||
|
|
gotK := new(big.Int).Mul(k2Int, s256.lambda)
|
||
|
|
gotK.Add(k1Int, gotK)
|
||
|
|
gotK.Mod(gotK, s256.N)
|
||
|
|
if k.Cmp(gotK) != 0 {
|
||
|
|
t.Errorf("%d: bad k: got %X, want %X", i, gotK.Bytes(), k.Bytes())
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Test this curve's usage with the ecdsa package.
|
||
|
|
|
||
|
|
func testKeyGeneration(t *testing.T, c *KoblitzCurve, tag string) {
|
||
|
|
priv, err := NewPrivateKey(c)
|
||
|
|
if err != nil {
|
||
|
|
t.Errorf("%s: error: %s", tag, err)
|
||
|
|
return
|
||
|
|
}
|
||
|
|
if !c.IsOnCurve(priv.PublicKey.X, priv.PublicKey.Y) {
|
||
|
|
t.Errorf("%s: public key invalid: %s", tag, err)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestKeyGeneration(t *testing.T) {
|
||
|
|
testKeyGeneration(t, S256(), "S256")
|
||
|
|
}
|
||
|
|
|
||
|
|
func testSignAndVerify(t *testing.T, c *KoblitzCurve, tag string) {
|
||
|
|
priv, _ := NewPrivateKey(c)
|
||
|
|
pub := priv.PubKey()
|
||
|
|
|
||
|
|
hashed := []byte("testing")
|
||
|
|
sig, err := priv.Sign(hashed)
|
||
|
|
if err != nil {
|
||
|
|
t.Errorf("%s: error signing: %s", tag, err)
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
if !sig.Verify(hashed, pub) {
|
||
|
|
t.Errorf("%s: Verify failed", tag)
|
||
|
|
}
|
||
|
|
|
||
|
|
hashed[0] ^= 0xff
|
||
|
|
if sig.Verify(hashed, pub) {
|
||
|
|
t.Errorf("%s: Verify always works!", tag)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestSignAndVerify(t *testing.T) {
|
||
|
|
testSignAndVerify(t, S256(), "S256")
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestNAF(t *testing.T) {
|
||
|
|
tests := []string{
|
||
|
|
"6df2b5d30854069ccdec40ae022f5c948936324a4e9ebed8eb82cfd5a6b6d766",
|
||
|
|
"b776e53fb55f6b006a270d42d64ec2b1",
|
||
|
|
"d6cc32c857f1174b604eefc544f0c7f7",
|
||
|
|
"45c53aa1bb56fcd68c011e2dad6758e4",
|
||
|
|
"a2e79d200f27f2360fba57619936159b",
|
||
|
|
}
|
||
|
|
negOne := big.NewInt(-1)
|
||
|
|
one := big.NewInt(1)
|
||
|
|
two := big.NewInt(2)
|
||
|
|
for i, test := range tests {
|
||
|
|
want, _ := new(big.Int).SetString(test, 16)
|
||
|
|
nafPos, nafNeg := NAF(want.Bytes())
|
||
|
|
got := big.NewInt(0)
|
||
|
|
// Check that the NAF representation comes up with the right number
|
||
|
|
for i := 0; i < len(nafPos); i++ {
|
||
|
|
bytePos := nafPos[i]
|
||
|
|
byteNeg := nafNeg[i]
|
||
|
|
for j := 7; j >= 0; j-- {
|
||
|
|
got.Mul(got, two)
|
||
|
|
if bytePos&0x80 == 0x80 {
|
||
|
|
got.Add(got, one)
|
||
|
|
} else if byteNeg&0x80 == 0x80 {
|
||
|
|
got.Add(got, negOne)
|
||
|
|
}
|
||
|
|
bytePos <<= 1
|
||
|
|
byteNeg <<= 1
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if got.Cmp(want) != 0 {
|
||
|
|
t.Errorf("%d: Failed NAF got %X want %X", i, got, want)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestNAFRand(t *testing.T) {
|
||
|
|
negOne := big.NewInt(-1)
|
||
|
|
one := big.NewInt(1)
|
||
|
|
two := big.NewInt(2)
|
||
|
|
for i := 0; i < 1024; i++ {
|
||
|
|
data := make([]byte, 32)
|
||
|
|
_, err := rand.Read(data)
|
||
|
|
if err != nil {
|
||
|
|
t.Fatalf("failed to read random data at %d", i)
|
||
|
|
break
|
||
|
|
}
|
||
|
|
nafPos, nafNeg := NAF(data)
|
||
|
|
want := new(big.Int).SetBytes(data)
|
||
|
|
got := big.NewInt(0)
|
||
|
|
// Check that the NAF representation comes up with the right number
|
||
|
|
for i := 0; i < len(nafPos); i++ {
|
||
|
|
bytePos := nafPos[i]
|
||
|
|
byteNeg := nafNeg[i]
|
||
|
|
for j := 7; j >= 0; j-- {
|
||
|
|
got.Mul(got, two)
|
||
|
|
if bytePos&0x80 == 0x80 {
|
||
|
|
got.Add(got, one)
|
||
|
|
} else if byteNeg&0x80 == 0x80 {
|
||
|
|
got.Add(got, negOne)
|
||
|
|
}
|
||
|
|
bytePos <<= 1
|
||
|
|
byteNeg <<= 1
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if got.Cmp(want) != 0 {
|
||
|
|
t.Errorf("%d: Failed NAF got %X want %X", i, got, want)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// These test vectors were taken from
|
||
|
|
// http://csrc.nist.gov/groups/STM/cavp/documents/dss/ecdsatestvectors.zip
|
||
|
|
var testVectors = []struct {
|
||
|
|
msg string
|
||
|
|
Qx, Qy string
|
||
|
|
r, s string
|
||
|
|
ok bool
|
||
|
|
}{
|
||
|
|
/*
|
||
|
|
* All of these tests are disabled since they are for P224, not sec256k1.
|
||
|
|
* they are left here as an example of test vectors for when some *real*
|
||
|
|
* vectors may be found.
|
||
|
|
* - oga@conformal.com
|
||
|
|
{
|
||
|
|
"09626b45493672e48f3d1226a3aff3201960e577d33a7f72c7eb055302db8fe8ed61685dd036b554942a5737cd1512cdf811ee0c00e6dd2f08c69f08643be396e85dafda664801e772cdb7396868ac47b172245b41986aa2648cb77fbbfa562581be06651355a0c4b090f9d17d8f0ab6cced4e0c9d386cf465a516630f0231bd",
|
||
|
|
"9504b5b82d97a264d8b3735e0568decabc4b6ca275bc53cbadfc1c40",
|
||
|
|
"03426f80e477603b10dee670939623e3da91a94267fc4e51726009ed",
|
||
|
|
"81d3ac609f9575d742028dd496450a58a60eea2dcf8b9842994916e1",
|
||
|
|
"96a8c5f382c992e8f30ccce9af120b067ec1d74678fa8445232f75a5",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"96b2b6536f6df29be8567a72528aceeaccbaa66c66c534f3868ca9778b02faadb182e4ed34662e73b9d52ecbe9dc8e875fc05033c493108b380689ebf47e5b062e6a0cdb3dd34ce5fe347d92768d72f7b9b377c20aea927043b509c078ed2467d7113405d2ddd458811e6faf41c403a2a239240180f1430a6f4330df5d77de37",
|
||
|
|
"851e3100368a22478a0029353045ae40d1d8202ef4d6533cfdddafd8",
|
||
|
|
"205302ac69457dd345e86465afa72ee8c74ca97e2b0b999aec1f10c2",
|
||
|
|
"4450c2d38b697e990721aa2dbb56578d32b4f5aeb3b9072baa955ee0",
|
||
|
|
"e26d4b589166f7b4ba4b1c8fce823fa47aad22f8c9c396b8c6526e12",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"86778dbb4a068a01047a8d245d632f636c11d2ad350740b36fad90428b454ad0f120cb558d12ea5c8a23db595d87543d06d1ef489263d01ee529871eb68737efdb8ff85bc7787b61514bed85b7e01d6be209e0a4eb0db5c8df58a5c5bf706d76cb2bdf7800208639e05b89517155d11688236e6a47ed37d8e5a2b1e0adea338e",
|
||
|
|
"ad5bda09d319a717c1721acd6688d17020b31b47eef1edea57ceeffc",
|
||
|
|
"c8ce98e181770a7c9418c73c63d01494b8b80a41098c5ea50692c984",
|
||
|
|
"de5558c257ab4134e52c19d8db3b224a1899cbd08cc508ce8721d5e9",
|
||
|
|
"745db7af5a477e5046705c0a5eff1f52cb94a79d481f0c5a5e108ecd",
|
||
|
|
true,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"4bc6ef1958556686dab1e39c3700054a304cbd8f5928603dcd97fafd1f29e69394679b638f71c9344ce6a535d104803d22119f57b5f9477e253817a52afa9bfbc9811d6cc8c8be6b6566c6ef48b439bbb532abe30627548c598867f3861ba0b154dc1c3deca06eb28df8efd28258554b5179883a36fbb1eecf4f93ee19d41e3d",
|
||
|
|
"cc5eea2edf964018bdc0504a3793e4d2145142caa09a72ac5fb8d3e8",
|
||
|
|
"a48d78ae5d08aa725342773975a00d4219cf7a8029bb8cf3c17c374a",
|
||
|
|
"67b861344b4e416d4094472faf4272f6d54a497177fbc5f9ef292836",
|
||
|
|
"1d54f3fcdad795bf3b23408ecbac3e1321d1d66f2e4e3d05f41f7020",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"bb658732acbf3147729959eb7318a2058308b2739ec58907dd5b11cfa3ecf69a1752b7b7d806fe00ec402d18f96039f0b78dbb90a59c4414fb33f1f4e02e4089de4122cd93df5263a95be4d7084e2126493892816e6a5b4ed123cb705bf930c8f67af0fb4514d5769232a9b008a803af225160ce63f675bd4872c4c97b146e5e",
|
||
|
|
"6234c936e27bf141fc7534bfc0a7eedc657f91308203f1dcbd642855",
|
||
|
|
"27983d87ca785ef4892c3591ef4a944b1deb125dd58bd351034a6f84",
|
||
|
|
"e94e05b42d01d0b965ffdd6c3a97a36a771e8ea71003de76c4ecb13f",
|
||
|
|
"1dc6464ffeefbd7872a081a5926e9fc3e66d123f1784340ba17737e9",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"7c00be9123bfa2c4290be1d8bc2942c7f897d9a5b7917e3aabd97ef1aab890f148400a89abd554d19bec9d8ed911ce57b22fbcf6d30ca2115f13ce0a3f569a23bad39ee645f624c49c60dcfc11e7d2be24de9c905596d8f23624d63dc46591d1f740e46f982bfae453f107e80db23545782be23ce43708245896fc54e1ee5c43",
|
||
|
|
"9f3f037282aaf14d4772edffff331bbdda845c3f65780498cde334f1",
|
||
|
|
"8308ee5a16e3bcb721b6bc30000a0419bc1aaedd761be7f658334066",
|
||
|
|
"6381d7804a8808e3c17901e4d283b89449096a8fba993388fa11dc54",
|
||
|
|
"8e858f6b5b253686a86b757bad23658cda53115ac565abca4e3d9f57",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cffc122a44840dc705bb37130069921be313d8bde0b66201aebc48add028ca131914ef2e705d6bedd19dc6cf9459bbb0f27cdfe3c50483808ffcdaffbeaa5f062e097180f07a40ef4ab6ed03fe07ed6bcfb8afeb42c97eafa2e8a8df469de07317c5e1494c41547478eff4d8c7d9f0f484ad90fedf6e1c35ee68fa73f1691601",
|
||
|
|
"a03b88a10d930002c7b17ca6af2fd3e88fa000edf787dc594f8d4fd4",
|
||
|
|
"e0cf7acd6ddc758e64847fe4df9915ebda2f67cdd5ec979aa57421f5",
|
||
|
|
"387b84dcf37dc343c7d2c5beb82f0bf8bd894b395a7b894565d296c1",
|
||
|
|
"4adc12ce7d20a89ce3925e10491c731b15ddb3f339610857a21b53b4",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"26e0e0cafd85b43d16255908ccfd1f061c680df75aba3081246b337495783052ba06c60f4a486c1591a4048bae11b4d7fec4f161d80bdc9a7b79d23e44433ed625eab280521a37f23dd3e1bdc5c6a6cfaa026f3c45cf703e76dab57add93fe844dd4cda67dc3bddd01f9152579e49df60969b10f09ce9372fdd806b0c7301866",
|
||
|
|
"9a8983c42f2b5a87c37a00458b5970320d247f0c8a88536440173f7d",
|
||
|
|
"15e489ec6355351361900299088cfe8359f04fe0cab78dde952be80c",
|
||
|
|
"929a21baa173d438ec9f28d6a585a2f9abcfc0a4300898668e476dc0",
|
||
|
|
"59a853f046da8318de77ff43f26fe95a92ee296fa3f7e56ce086c872",
|
||
|
|
true,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"1078eac124f48ae4f807e946971d0de3db3748dd349b14cca5c942560fb25401b2252744f18ad5e455d2d97ed5ae745f55ff509c6c8e64606afe17809affa855c4c4cdcaf6b69ab4846aa5624ed0687541aee6f2224d929685736c6a23906d974d3c257abce1a3fb8db5951b89ecb0cda92b5207d93f6618fd0f893c32cf6a6e",
|
||
|
|
"d6e55820bb62c2be97650302d59d667a411956138306bd566e5c3c2b",
|
||
|
|
"631ab0d64eaf28a71b9cbd27a7a88682a2167cee6251c44e3810894f",
|
||
|
|
"65af72bc7721eb71c2298a0eb4eed3cec96a737cc49125706308b129",
|
||
|
|
"bd5a987c78e2d51598dbd9c34a9035b0069c580edefdacee17ad892a",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"919deb1fdd831c23481dfdb2475dcbe325b04c34f82561ced3d2df0b3d749b36e255c4928973769d46de8b95f162b53cd666cad9ae145e7fcfba97919f703d864efc11eac5f260a5d920d780c52899e5d76f8fe66936ff82130761231f536e6a3d59792f784902c469aa897aabf9a0678f93446610d56d5e0981e4c8a563556b",
|
||
|
|
"269b455b1024eb92d860a420f143ac1286b8cce43031562ae7664574",
|
||
|
|
"baeb6ca274a77c44a0247e5eb12ca72bdd9a698b3f3ae69c9f1aaa57",
|
||
|
|
"cb4ec2160f04613eb0dfe4608486091a25eb12aa4dec1afe91cfb008",
|
||
|
|
"40b01d8cd06589481574f958b98ca08ade9d2a8fe31024375c01bb40",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"6e012361250dacf6166d2dd1aa7be544c3206a9d43464b3fcd90f3f8cf48d08ec099b59ba6fe7d9bdcfaf244120aed1695d8be32d1b1cd6f143982ab945d635fb48a7c76831c0460851a3d62b7209c30cd9c2abdbe3d2a5282a9fcde1a6f418dd23c409bc351896b9b34d7d3a1a63bbaf3d677e612d4a80fa14829386a64b33f",
|
||
|
|
"6d2d695efc6b43b13c14111f2109608f1020e3e03b5e21cfdbc82fcd",
|
||
|
|
"26a4859296b7e360b69cf40be7bd97ceaffa3d07743c8489fc47ca1b",
|
||
|
|
"9a8cb5f2fdc288b7183c5b32d8e546fc2ed1ca4285eeae00c8b572ad",
|
||
|
|
"8c623f357b5d0057b10cdb1a1593dab57cda7bdec9cf868157a79b97",
|
||
|
|
true,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"bf6bd7356a52b234fe24d25557200971fc803836f6fec3cade9642b13a8e7af10ab48b749de76aada9d8927f9b12f75a2c383ca7358e2566c4bb4f156fce1fd4e87ef8c8d2b6b1bdd351460feb22cdca0437ac10ca5e0abbbce9834483af20e4835386f8b1c96daaa41554ceee56730aac04f23a5c765812efa746051f396566",
|
||
|
|
"14250131b2599939cf2d6bc491be80ddfe7ad9de644387ee67de2d40",
|
||
|
|
"b5dc473b5d014cd504022043c475d3f93c319a8bdcb7262d9e741803",
|
||
|
|
"4f21642f2201278a95339a80f75cc91f8321fcb3c9462562f6cbf145",
|
||
|
|
"452a5f816ea1f75dee4fd514fa91a0d6a43622981966c59a1b371ff8",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"0eb7f4032f90f0bd3cf9473d6d9525d264d14c031a10acd31a053443ed5fe919d5ac35e0be77813071b4062f0b5fdf58ad5f637b76b0b305aec18f82441b6e607b44cdf6e0e3c7c57f24e6fd565e39430af4a6b1d979821ed0175fa03e3125506847654d7e1ae904ce1190ae38dc5919e257bdac2db142a6e7cd4da6c2e83770",
|
||
|
|
"d1f342b7790a1667370a1840255ac5bbbdc66f0bc00ae977d99260ac",
|
||
|
|
"76416cabae2de9a1000b4646338b774baabfa3db4673790771220cdb",
|
||
|
|
"bc85e3fc143d19a7271b2f9e1c04b86146073f3fab4dda1c3b1f35ca",
|
||
|
|
"9a5c70ede3c48d5f43307a0c2a4871934424a3303b815df4bb0f128e",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"5cc25348a05d85e56d4b03cec450128727bc537c66ec3a9fb613c151033b5e86878632249cba83adcefc6c1e35dcd31702929c3b57871cda5c18d1cf8f9650a25b917efaed56032e43b6fc398509f0d2997306d8f26675f3a8683b79ce17128e006aa0903b39eeb2f1001be65de0520115e6f919de902b32c38d691a69c58c92",
|
||
|
|
"7e49a7abf16a792e4c7bbc4d251820a2abd22d9f2fc252a7bf59c9a6",
|
||
|
|
"44236a8fb4791c228c26637c28ae59503a2f450d4cfb0dc42aa843b9",
|
||
|
|
"084461b4050285a1a85b2113be76a17878d849e6bc489f4d84f15cd8",
|
||
|
|
"079b5bddcc4d45de8dbdfd39f69817c7e5afa454a894d03ee1eaaac3",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"1951533ce33afb58935e39e363d8497a8dd0442018fd96dff167b3b23d7206a3ee182a3194765df4768a3284e23b8696c199b4686e670d60c9d782f08794a4bccc05cffffbd1a12acd9eb1cfa01f7ebe124da66ecff4599ea7720c3be4bb7285daa1a86ebf53b042bd23208d468c1b3aa87381f8e1ad63e2b4c2ba5efcf05845",
|
||
|
|
"31945d12ebaf4d81f02be2b1768ed80784bf35cf5e2ff53438c11493",
|
||
|
|
"a62bebffac987e3b9d3ec451eb64c462cdf7b4aa0b1bbb131ceaa0a4",
|
||
|
|
"bc3c32b19e42b710bca5c6aaa128564da3ddb2726b25f33603d2af3c",
|
||
|
|
"ed1a719cc0c507edc5239d76fe50e2306c145ad252bd481da04180c0",
|
||
|
|
false,
|
||
|
|
},
|
||
|
|
*/
|
||
|
|
}
|
||
|
|
|
||
|
|
func TestVectors(t *testing.T) {
|
||
|
|
sha := sha1.New()
|
||
|
|
|
||
|
|
for i, test := range testVectors {
|
||
|
|
pub := PublicKey{
|
||
|
|
Curve: S256(),
|
||
|
|
X: fromHex(test.Qx),
|
||
|
|
Y: fromHex(test.Qy),
|
||
|
|
}
|
||
|
|
msg, _ := hex.DecodeString(test.msg)
|
||
|
|
sha.Reset()
|
||
|
|
sha.Write(msg)
|
||
|
|
hashed := sha.Sum(nil)
|
||
|
|
sig := Signature{R: fromHex(test.r), S: fromHex(test.s)}
|
||
|
|
if verified := sig.Verify(hashed, &pub); verified != test.ok {
|
||
|
|
t.Errorf("%d: bad result %v instead of %v", i, verified,
|
||
|
|
test.ok)
|
||
|
|
}
|
||
|
|
if testing.Short() {
|
||
|
|
break
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|