890 lines
29 KiB
Go
890 lines
29 KiB
Go
// 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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"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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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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// Ensure the test data is using points that are actually on
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// the curve (or the point at infinity).
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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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"invalid test data", i)
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continue
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}
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if !z2.IsZero() && !isJacobianOnS256Curve(x2, y2, z2) {
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t.Errorf("#%d second point is not on the curve -- "+
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"invalid test data", i)
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continue
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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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continue
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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)
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S256().addJacobian(x1, y1, z1, x2, y2, z2, rx, ry, rz)
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// Ensure result matches expected.
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if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
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t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
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"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
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continue
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}
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}
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}
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// TestAddAffine tests addition of points in affine coordinates.
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func TestAddAffine(t *testing.T) {
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tests := []struct {
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x1, y1 string // Coordinates (in hex) of first point to add
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x2, y2 string // Coordinates (in hex) of second point to add
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x3, y3 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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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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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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"0",
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"0",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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},
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// Addition with different x values.
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"fd5b88c21d3143518d522cd2796f3d726793c88b3e05636bc829448e053fed69",
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"21cf4f6a5be5ff6380234c50424a970b1f7e718f5eb58f68198c108d642a137f",
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},
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// Addition with same x opposite y.
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// P(x, y) + P(x, -y) = infinity
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
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"0",
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"0",
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},
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// Addition with same point.
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// P(x, y) + P(x, y) = 2P
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{
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"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)
|
|
}
|
|
}
|
|
}
|