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// Copyright (c) 2019 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 edwards25519
import (
"testing"
"testing/quick"
)
var (
// a random scalar generated using dalek.
dalekScalar, _ = (&Scalar{}).SetCanonicalBytes([]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4})
// the above, times the edwards25519 basepoint.
dalekScalarBasepoint, _ = new(Point).SetBytes([]byte{0xf4, 0xef, 0x7c, 0xa, 0x34, 0x55, 0x7b, 0x9f, 0x72, 0x3b, 0xb6, 0x1e, 0xf9, 0x46, 0x9, 0x91, 0x1c, 0xb9, 0xc0, 0x6c, 0x17, 0x28, 0x2d, 0x8b, 0x43, 0x2b, 0x5, 0x18, 0x6a, 0x54, 0x3e, 0x48})
)
func TestScalarMultSmallScalars(t *testing.T) {
var z Scalar
var p Point
p.ScalarMult(&z, B)
if I.Equal(&p) != 1 {
t.Error("0*B != 0")
}
checkOnCurve(t, &p)
scEight, _ := (&Scalar{}).SetCanonicalBytes([]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
p.ScalarMult(scEight, B)
if B.Equal(&p) != 1 {
t.Error("1*B != 1")
}
checkOnCurve(t, &p)
}
func TestScalarMultVsDalek(t *testing.T) {
var p Point
p.ScalarMult(dalekScalar, B)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("Scalar mul does not match dalek")
}
checkOnCurve(t, &p)
}
func TestBaseMultVsDalek(t *testing.T) {
var p Point
p.ScalarBaseMult(dalekScalar)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("Scalar mul does not match dalek")
}
checkOnCurve(t, &p)
}
func TestVarTimeDoubleBaseMultVsDalek(t *testing.T) {
var p Point
var z Scalar
p.VarTimeDoubleScalarBaseMult(dalekScalar, B, &z)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("VarTimeDoubleScalarBaseMult fails with b=0")
}
checkOnCurve(t, &p)
p.VarTimeDoubleScalarBaseMult(&z, B, dalekScalar)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("VarTimeDoubleScalarBaseMult fails with a=0")
}
checkOnCurve(t, &p)
}
func TestScalarMultDistributesOverAdd(t *testing.T) {
scalarMultDistributesOverAdd := func(x, y Scalar) bool {
var z Scalar
z.Add(&x, &y)
var p, q, r, check Point
p.ScalarMult(&x, B)
q.ScalarMult(&y, B)
r.ScalarMult(&z, B)
check.Add(&p, &q)
checkOnCurve(t, &p, &q, &r, &check)
return check.Equal(&r) == 1
}
if err := quick.Check(scalarMultDistributesOverAdd, quickCheckConfig(32)); err != nil {
t.Error(err)
}
}
func TestScalarMultNonIdentityPoint(t *testing.T) {
// Check whether p.ScalarMult and q.ScalaBaseMult give the same,
// when p and q are originally set to the base point.
scalarMultNonIdentityPoint := func(x Scalar) bool {
var p, q Point
p.Set(B)
q.Set(B)
p.ScalarMult(&x, B)
q.ScalarBaseMult(&x)
checkOnCurve(t, &p, &q)
return p.Equal(&q) == 1
}
if err := quick.Check(scalarMultNonIdentityPoint, quickCheckConfig(32)); err != nil {
t.Error(err)
}
}
func TestBasepointTableGeneration(t *testing.T) {
// The basepoint table is 32 affineLookupTables,
// corresponding to (16^2i)*B for table i.
basepointTable := basepointTable()
tmp1 := &projP1xP1{}
tmp2 := &projP2{}
tmp3 := &Point{}
tmp3.Set(B)
table := make([]affineLookupTable, 32)
for i := 0; i < 32; i++ {
// Build the table
table[i].FromP3(tmp3)
// Assert equality with the hardcoded one
if table[i] != basepointTable[i] {
t.Errorf("Basepoint table %d does not match", i)
}
// Set p = (16^2)*p = 256*p = 2^8*p
tmp2.FromP3(tmp3)
for j := 0; j < 7; j++ {
tmp1.Double(tmp2)
tmp2.FromP1xP1(tmp1)
}
tmp1.Double(tmp2)
tmp3.fromP1xP1(tmp1)
checkOnCurve(t, tmp3)
}
}
func TestScalarMultMatchesBaseMult(t *testing.T) {
scalarMultMatchesBaseMult := func(x Scalar) bool {
var p, q Point
p.ScalarMult(&x, B)
q.ScalarBaseMult(&x)
checkOnCurve(t, &p, &q)
return p.Equal(&q) == 1
}
if err := quick.Check(scalarMultMatchesBaseMult, quickCheckConfig(32)); err != nil {
t.Error(err)
}
}
func TestBasepointNafTableGeneration(t *testing.T) {
var table nafLookupTable8
table.FromP3(B)
if table != *basepointNafTable() {
t.Error("BasepointNafTable does not match")
}
}
func TestVarTimeDoubleBaseMultMatchesBaseMult(t *testing.T) {
varTimeDoubleBaseMultMatchesBaseMult := func(x, y Scalar) bool {
var p, q1, q2, check Point
p.VarTimeDoubleScalarBaseMult(&x, B, &y)
q1.ScalarBaseMult(&x)
q2.ScalarBaseMult(&y)
check.Add(&q1, &q2)
checkOnCurve(t, &p, &check, &q1, &q2)
return p.Equal(&check) == 1
}
if err := quick.Check(varTimeDoubleBaseMultMatchesBaseMult, quickCheckConfig(32)); err != nil {
t.Error(err)
}
}
// Benchmarks.
func BenchmarkScalarBaseMult(b *testing.B) {
var p Point
for i := 0; i < b.N; i++ {
p.ScalarBaseMult(dalekScalar)
}
}
func BenchmarkScalarMult(b *testing.B) {
var p Point
for i := 0; i < b.N; i++ {
p.ScalarMult(dalekScalar, B)
}
}
func BenchmarkVarTimeDoubleScalarBaseMult(b *testing.B) {
var p Point
for i := 0; i < b.N; i++ {
p.VarTimeDoubleScalarBaseMult(dalekScalar, B, dalekScalar)
}
}