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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 (
"bytes"
"encoding/hex"
"math/big"
mathrand "math/rand"
"reflect"
"testing"
"testing/quick"
)
// Generate returns a valid (reduced modulo l) Scalar with a distribution
// weighted towards high, low, and edge values.
func (Scalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
s := scZero
diceRoll := rand.Intn(100)
switch {
case diceRoll == 0:
case diceRoll == 1:
s = scOne
case diceRoll == 2:
s = scMinusOne
case diceRoll < 5:
// Generate a low scalar in [0, 2^125).
rand.Read(s.s[:16])
s.s[15] &= (1 << 5) - 1
case diceRoll < 10:
// Generate a high scalar in [2^252, 2^252 + 2^124).
s.s[31] = 1 << 4
rand.Read(s.s[:16])
s.s[15] &= (1 << 4) - 1
default:
// Generate a valid scalar in [0, l) by returning [0, 2^252) which has a
// negligibly different distribution (the former has a 2^-127.6 chance
// of being out of the latter range).
rand.Read(s.s[:])
s.s[31] &= (1 << 4) - 1
}
return reflect.ValueOf(s)
}
// quickCheckConfig1024 will make each quickcheck test run (1024 * -quickchecks)
// times. The default value of -quickchecks is 100.
var quickCheckConfig1024 = &quick.Config{MaxCountScale: 1 << 10}
func TestScalarGenerate(t *testing.T) {
f := func(sc Scalar) bool {
return isReduced(&sc)
}
if err := quick.Check(f, quickCheckConfig1024); err != nil {
t.Errorf("generated unreduced scalar: %v", err)
}
}
func TestScalarSetCanonicalBytes(t *testing.T) {
f1 := func(in [32]byte, sc Scalar) bool {
// Mask out top 4 bits to guarantee value falls in [0, l).
in[len(in)-1] &= (1 << 4) - 1
if _, err := sc.SetCanonicalBytes(in[:]); err != nil {
return false
}
return bytes.Equal(in[:], sc.Bytes()) && isReduced(&sc)
}
if err := quick.Check(f1, quickCheckConfig1024); err != nil {
t.Errorf("failed bytes->scalar->bytes round-trip: %v", err)
}
f2 := func(sc1, sc2 Scalar) bool {
if _, err := sc2.SetCanonicalBytes(sc1.Bytes()); err != nil {
return false
}
return sc1 == sc2
}
if err := quick.Check(f2, quickCheckConfig1024); err != nil {
t.Errorf("failed scalar->bytes->scalar round-trip: %v", err)
}
b := scMinusOne.s
b[31] += 1
s := scOne
if out, err := s.SetCanonicalBytes(b[:]); err == nil {
t.Errorf("SetCanonicalBytes worked on a non-canonical value")
} else if s != scOne {
t.Errorf("SetCanonicalBytes modified its receiver")
} else if out != nil {
t.Errorf("SetCanonicalBytes did not return nil with an error")
}
}
func TestScalarSetUniformBytes(t *testing.T) {
mod, _ := new(big.Int).SetString("27742317777372353535851937790883648493", 10)
mod.Add(mod, new(big.Int).Lsh(big.NewInt(1), 252))
f := func(in [64]byte, sc Scalar) bool {
sc.SetUniformBytes(in[:])
if !isReduced(&sc) {
return false
}
scBig := bigIntFromLittleEndianBytes(sc.s[:])
inBig := bigIntFromLittleEndianBytes(in[:])
return inBig.Mod(inBig, mod).Cmp(scBig) == 0
}
if err := quick.Check(f, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestScalarSetBytesWithClamping(t *testing.T) {
// Generated with libsodium.js 1.0.18 crypto_scalarmult_ed25519_base.
random := "633d368491364dc9cd4c1bf891b1d59460face1644813240a313e61f2c88216e"
s := new(Scalar).SetBytesWithClamping(decodeHex(random))
p := new(Point).ScalarBaseMult(s)
want := "1d87a9026fd0126a5736fe1628c95dd419172b5b618457e041c9c861b2494a94"
if got := hex.EncodeToString(p.Bytes()); got != want {
t.Errorf("random: got %q, want %q", got, want)
}
zero := "0000000000000000000000000000000000000000000000000000000000000000"
s = new(Scalar).SetBytesWithClamping(decodeHex(zero))
p = new(Point).ScalarBaseMult(s)
want = "693e47972caf527c7883ad1b39822f026f47db2ab0e1919955b8993aa04411d1"
if got := hex.EncodeToString(p.Bytes()); got != want {
t.Errorf("zero: got %q, want %q", got, want)
}
one := "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
s = new(Scalar).SetBytesWithClamping(decodeHex(one))
p = new(Point).ScalarBaseMult(s)
want = "12e9a68b73fd5aacdbcaf3e88c46fea6ebedb1aa84eed1842f07f8edab65e3a7"
if got := hex.EncodeToString(p.Bytes()); got != want {
t.Errorf("one: got %q, want %q", got, want)
}
}
func bigIntFromLittleEndianBytes(b []byte) *big.Int {
bb := make([]byte, len(b))
for i := range b {
bb[i] = b[len(b)-i-1]
}
return new(big.Int).SetBytes(bb)
}
func TestScalarMultiplyDistributesOverAdd(t *testing.T) {
multiplyDistributesOverAdd := func(x, y, z Scalar) bool {
// Compute t1 = (x+y)*z
var t1 Scalar
t1.Add(&x, &y)
t1.Multiply(&t1, &z)
// Compute t2 = x*z + y*z
var t2 Scalar
var t3 Scalar
t2.Multiply(&x, &z)
t3.Multiply(&y, &z)
t2.Add(&t2, &t3)
return t1 == t2 && isReduced(&t1) && isReduced(&t3)
}
if err := quick.Check(multiplyDistributesOverAdd, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestScalarAddLikeSubNeg(t *testing.T) {
addLikeSubNeg := func(x, y Scalar) bool {
// Compute t1 = x - y
var t1 Scalar
t1.Subtract(&x, &y)
// Compute t2 = -y + x
var t2 Scalar
t2.Negate(&y)
t2.Add(&t2, &x)
return t1 == t2 && isReduced(&t1)
}
if err := quick.Check(addLikeSubNeg, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestScalarNonAdjacentForm(t *testing.T) {
s := Scalar{[32]byte{
0x1a, 0x0e, 0x97, 0x8a, 0x90, 0xf6, 0x62, 0x2d,
0x37, 0x47, 0x02, 0x3f, 0x8a, 0xd8, 0x26, 0x4d,
0xa7, 0x58, 0xaa, 0x1b, 0x88, 0xe0, 0x40, 0xd1,
0x58, 0x9e, 0x7b, 0x7f, 0x23, 0x76, 0xef, 0x09,
}}
expectedNaf := [256]int8{
0, 13, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -11, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1,
0, 0, 0, 0, 9, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 11, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0,
-9, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 9, 0,
0, 0, 0, -15, 0, 0, 0, 0, -7, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -3, 0,
0, 0, 0, -11, 0, 0, 0, 0, -7, 0, 0, 0, 0, -13, 0, 0, 0, 0, 11, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, -15, 0, 0, 0, 0, 1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 13, 0, 0, 0,
0, 0, 0, 11, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 7,
0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 15, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
}
sNaf := s.nonAdjacentForm(5)
for i := 0; i < 256; i++ {
if expectedNaf[i] != sNaf[i] {
t.Errorf("Wrong digit at position %d, got %d, expected %d", i, sNaf[i], expectedNaf[i])
}
}
}
type notZeroScalar Scalar
func (notZeroScalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
var s Scalar
for s == scZero {
s = Scalar{}.Generate(rand, size).Interface().(Scalar)
}
return reflect.ValueOf(notZeroScalar(s))
}
func TestScalarEqual(t *testing.T) {
if scOne.Equal(&scMinusOne) == 1 {
t.Errorf("scOne.Equal(&scMinusOne) is true")
}
if scMinusOne.Equal(&scMinusOne) == 0 {
t.Errorf("scMinusOne.Equal(&scMinusOne) is false")
}
}
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