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// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package elliptic
import (
"math/big"
"testing"
)
type scalarMultTest struct {
k string
xIn, yIn string
xOut, yOut string
}
var p256MultTests = []scalarMultTest{
{
"2a265f8bcbdcaf94d58519141e578124cb40d64a501fba9c11847b28965bc737",
"023819813ac969847059028ea88a1f30dfbcde03fc791d3a252c6b41211882ea",
"f93e4ae433cc12cf2a43fc0ef26400c0e125508224cdb649380f25479148a4ad",
"4d4de80f1534850d261075997e3049321a0864082d24a917863366c0724f5ae3",
"a22d2b7f7818a3563e0f7a76c9bf0921ac55e06e2e4d11795b233824b1db8cc0",
},
{
"313f72ff9fe811bf573176231b286a3bdb6f1b14e05c40146590727a71c3bccd",
"cc11887b2d66cbae8f4d306627192522932146b42f01d3c6f92bd5c8ba739b06",
"a2f08a029cd06b46183085bae9248b0ed15b70280c7ef13a457f5af382426031",
"831c3f6b5f762d2f461901577af41354ac5f228c2591f84f8a6e51e2e3f17991",
"93f90934cd0ef2c698cc471c60a93524e87ab31ca2412252337f364513e43684",
},
}
func TestP256BaseMult(t *testing.T) {
p256 := P256()
p256Generic := genericParamsForCurve(p256)
scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
for _, e := range p224BaseMultTests {
k, _ := new(big.Int).SetString(e.k, 10)
scalars = append(scalars, k)
}
k := new(big.Int).SetInt64(1)
k.Lsh(k, 500)
scalars = append(scalars, k)
for i, k := range scalars {
x, y := p256.ScalarBaseMult(k.Bytes())
x2, y2 := p256Generic.ScalarBaseMult(k.Bytes())
if x.Cmp(x2) != 0 || y.Cmp(y2) != 0 {
t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, x, y, x2, y2)
}
if testing.Short() && i > 5 {
break
}
}
}
func TestP256Mult(t *testing.T) {
p256 := P256()
for i, e := range p256MultTests {
x, _ := new(big.Int).SetString(e.xIn, 16)
y, _ := new(big.Int).SetString(e.yIn, 16)
k, _ := new(big.Int).SetString(e.k, 16)
expectedX, _ := new(big.Int).SetString(e.xOut, 16)
expectedY, _ := new(big.Int).SetString(e.yOut, 16)
xx, yy := p256.ScalarMult(x, y, k.Bytes())
if xx.Cmp(expectedX) != 0 || yy.Cmp(expectedY) != 0 {
t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, expectedX, expectedY)
}
}
}
type synthCombinedMult struct {
Curve
}
func (s synthCombinedMult) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
x1, y1 := s.ScalarBaseMult(baseScalar)
x2, y2 := s.ScalarMult(bigX, bigY, scalar)
return s.Add(x1, y1, x2, y2)
}
func TestP256CombinedMult(t *testing.T) {
type combinedMult interface {
Curve
CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
}
p256, ok := P256().(combinedMult)
if !ok {
p256 = &synthCombinedMult{P256()}
}
gx := p256.Params().Gx
gy := p256.Params().Gy
zero := make([]byte, 32)
one := make([]byte, 32)
one[31] = 1
two := make([]byte, 32)
two[31] = 2
// 0×G + 0×G = ∞
x, y := p256.CombinedMult(gx, gy, zero, zero)
if x.Sign() != 0 || y.Sign() != 0 {
t.Errorf("0×G + 0×G = (%d, %d), should be ∞", x, y)
}
// 1×G + 0×G = G
x, y = p256.CombinedMult(gx, gy, one, zero)
if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
t.Errorf("1×G + 0×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
}
// 0×G + 1×G = G
x, y = p256.CombinedMult(gx, gy, zero, one)
if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
t.Errorf("0×G + 1×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
}
// 1×G + 1×G = 2×G
x, y = p256.CombinedMult(gx, gy, one, one)
ggx, ggy := p256.ScalarBaseMult(two)
if x.Cmp(ggx) != 0 || y.Cmp(ggy) != 0 {
t.Errorf("1×G + 1×G = (%d, %d), should be (%d, %d)", x, y, ggx, ggy)
}
minusOne := new(big.Int).Sub(p256.Params().N, big.NewInt(1))
// 1×G + (-1)×G = ∞
x, y = p256.CombinedMult(gx, gy, one, minusOne.Bytes())
if x.Sign() != 0 || y.Sign() != 0 {
t.Errorf("1×G + (-1)×G = (%d, %d), should be ∞", x, y)
}
}
func TestIssue52075(t *testing.T) {
Gx, Gy := P256().Params().Gx, P256().Params().Gy
scalar := make([]byte, 33)
scalar[32] = 1
x, y := P256().ScalarBaseMult(scalar)
if x.Cmp(Gx) != 0 || y.Cmp(Gy) != 0 {
t.Errorf("unexpected output (%v,%v)", x, y)
}
x, y = P256().ScalarMult(Gx, Gy, scalar)
if x.Cmp(Gx) != 0 || y.Cmp(Gy) != 0 {
t.Errorf("unexpected output (%v,%v)", x, y)
}
}
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