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// Copyright (c) 2017 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 field
import (
"bytes"
"crypto/rand"
"encoding/hex"
"io"
"math/big"
"math/bits"
mathrand "math/rand"
"reflect"
"testing"
"testing/quick"
)
func (v Element) String() string {
return hex.EncodeToString(v.Bytes())
}
// 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 generateFieldElement(rand *mathrand.Rand) Element {
const maskLow52Bits = (1 << 52) - 1
return Element{
rand.Uint64() & maskLow52Bits,
rand.Uint64() & maskLow52Bits,
rand.Uint64() & maskLow52Bits,
rand.Uint64() & maskLow52Bits,
rand.Uint64() & maskLow52Bits,
}
}
// weirdLimbs can be combined to generate a range of edge-case field elements.
// 0 and -1 are intentionally more weighted, as they combine well.
var (
weirdLimbs51 = []uint64{
0, 0, 0, 0,
1,
19 - 1,
19,
0x2aaaaaaaaaaaa,
0x5555555555555,
(1 << 51) - 20,
(1 << 51) - 19,
(1 << 51) - 1, (1 << 51) - 1,
(1 << 51) - 1, (1 << 51) - 1,
}
weirdLimbs52 = []uint64{
0, 0, 0, 0, 0, 0,
1,
19 - 1,
19,
0x2aaaaaaaaaaaa,
0x5555555555555,
(1 << 51) - 20,
(1 << 51) - 19,
(1 << 51) - 1, (1 << 51) - 1,
(1 << 51) - 1, (1 << 51) - 1,
(1 << 51) - 1, (1 << 51) - 1,
1 << 51,
(1 << 51) + 1,
(1 << 52) - 19,
(1 << 52) - 1,
}
)
func generateWeirdFieldElement(rand *mathrand.Rand) Element {
return Element{
weirdLimbs52[rand.Intn(len(weirdLimbs52))],
weirdLimbs51[rand.Intn(len(weirdLimbs51))],
weirdLimbs51[rand.Intn(len(weirdLimbs51))],
weirdLimbs51[rand.Intn(len(weirdLimbs51))],
weirdLimbs51[rand.Intn(len(weirdLimbs51))],
}
}
func (Element) Generate(rand *mathrand.Rand, size int) reflect.Value {
if rand.Intn(2) == 0 {
return reflect.ValueOf(generateWeirdFieldElement(rand))
}
return reflect.ValueOf(generateFieldElement(rand))
}
// isInBounds returns whether the element is within the expected bit size bounds
// after a light reduction.
func isInBounds(x *Element) bool {
return bits.Len64(x.l0) <= 52 &&
bits.Len64(x.l1) <= 52 &&
bits.Len64(x.l2) <= 52 &&
bits.Len64(x.l3) <= 52 &&
bits.Len64(x.l4) <= 52
}
func TestMultiplyDistributesOverAdd(t *testing.T) {
multiplyDistributesOverAdd := func(x, y, z Element) bool {
// Compute t1 = (x+y)*z
t1 := new(Element)
t1.Add(&x, &y)
t1.Multiply(t1, &z)
// Compute t2 = x*z + y*z
t2 := new(Element)
t3 := new(Element)
t2.Multiply(&x, &z)
t3.Multiply(&y, &z)
t2.Add(t2, t3)
return t1.Equal(t2) == 1 && isInBounds(t1) && isInBounds(t2)
}
if err := quick.Check(multiplyDistributesOverAdd, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestMul64to128(t *testing.T) {
a := uint64(5)
b := uint64(5)
r := mul64(a, b)
if r.lo != 0x19 || r.hi != 0 {
t.Errorf("lo-range wide mult failed, got %d + %d*(2**64)", r.lo, r.hi)
}
a = uint64(18014398509481983) // 2^54 - 1
b = uint64(18014398509481983) // 2^54 - 1
r = mul64(a, b)
if r.lo != 0xff80000000000001 || r.hi != 0xfffffffffff {
t.Errorf("hi-range wide mult failed, got %d + %d*(2**64)", r.lo, r.hi)
}
a = uint64(1125899906842661)
b = uint64(2097155)
r = mul64(a, b)
r = addMul64(r, a, b)
r = addMul64(r, a, b)
r = addMul64(r, a, b)
r = addMul64(r, a, b)
if r.lo != 16888498990613035 || r.hi != 640 {
t.Errorf("wrong answer: %d + %d*(2**64)", r.lo, r.hi)
}
}
func TestSetBytesRoundTrip(t *testing.T) {
f1 := func(in [32]byte, fe Element) bool {
fe.SetBytes(in[:])
// Mask the most significant bit as it's ignored by SetBytes. (Now
// instead of earlier so we check the masking in SetBytes is working.)
in[len(in)-1] &= (1 << 7) - 1
return bytes.Equal(in[:], fe.Bytes()) && isInBounds(&fe)
}
if err := quick.Check(f1, nil); err != nil {
t.Errorf("failed bytes->FE->bytes round-trip: %v", err)
}
f2 := func(fe, r Element) bool {
r.SetBytes(fe.Bytes())
// Intentionally not using Equal not to go through Bytes again.
// Calling reduce because both Generate and SetBytes can produce
// non-canonical representations.
fe.reduce()
r.reduce()
return fe == r
}
if err := quick.Check(f2, nil); err != nil {
t.Errorf("failed FE->bytes->FE round-trip: %v", err)
}
// Check some fixed vectors from dalek
type feRTTest struct {
fe Element
b []byte
}
var tests = []feRTTest{
{
fe: Element{358744748052810, 1691584618240980, 977650209285361, 1429865912637724, 560044844278676},
b: []byte{74, 209, 69, 197, 70, 70, 161, 222, 56, 226, 229, 19, 112, 60, 25, 92, 187, 74, 222, 56, 50, 153, 51, 233, 40, 74, 57, 6, 160, 185, 213, 31},
},
{
fe: Element{84926274344903, 473620666599931, 365590438845504, 1028470286882429, 2146499180330972},
b: []byte{199, 23, 106, 112, 61, 77, 216, 79, 186, 60, 11, 118, 13, 16, 103, 15, 42, 32, 83, 250, 44, 57, 204, 198, 78, 199, 253, 119, 146, 172, 3, 122},
},
}
for _, tt := range tests {
b := tt.fe.Bytes()
fe, _ := new(Element).SetBytes(tt.b)
if !bytes.Equal(b, tt.b) || fe.Equal(&tt.fe) != 1 {
t.Errorf("Failed fixed roundtrip: %v", tt)
}
}
}
func swapEndianness(buf []byte) []byte {
for i := 0; i < len(buf)/2; i++ {
buf[i], buf[len(buf)-i-1] = buf[len(buf)-i-1], buf[i]
}
return buf
}
func TestBytesBigEquivalence(t *testing.T) {
f1 := func(in [32]byte, fe, fe1 Element) bool {
fe.SetBytes(in[:])
in[len(in)-1] &= (1 << 7) - 1 // mask the most significant bit
b := new(big.Int).SetBytes(swapEndianness(in[:]))
fe1.fromBig(b)
if fe != fe1 {
return false
}
buf := make([]byte, 32)
buf = swapEndianness(fe1.toBig().FillBytes(buf))
return bytes.Equal(fe.Bytes(), buf) && isInBounds(&fe) && isInBounds(&fe1)
}
if err := quick.Check(f1, nil); err != nil {
t.Error(err)
}
}
// fromBig sets v = n, and returns v. The bit length of n must not exceed 256.
func (v *Element) fromBig(n *big.Int) *Element {
if n.BitLen() > 32*8 {
panic("edwards25519: invalid field element input size")
}
buf := make([]byte, 0, 32)
for _, word := range n.Bits() {
for i := 0; i < bits.UintSize; i += 8 {
if len(buf) >= cap(buf) {
break
}
buf = append(buf, byte(word))
word >>= 8
}
}
v.SetBytes(buf[:32])
return v
}
func (v *Element) fromDecimal(s string) *Element {
n, ok := new(big.Int).SetString(s, 10)
if !ok {
panic("not a valid decimal: " + s)
}
return v.fromBig(n)
}
// toBig returns v as a big.Int.
func (v *Element) toBig() *big.Int {
buf := v.Bytes()
words := make([]big.Word, 32*8/bits.UintSize)
for n := range words {
for i := 0; i < bits.UintSize; i += 8 {
if len(buf) == 0 {
break
}
words[n] |= big.Word(buf[0]) << big.Word(i)
buf = buf[1:]
}
}
return new(big.Int).SetBits(words)
}
func TestDecimalConstants(t *testing.T) {
sqrtM1String := "19681161376707505956807079304988542015446066515923890162744021073123829784752"
if exp := new(Element).fromDecimal(sqrtM1String); sqrtM1.Equal(exp) != 1 {
t.Errorf("sqrtM1 is %v, expected %v", sqrtM1, exp)
}
// d is in the parent package, and we don't want to expose d or fromDecimal.
// dString := "37095705934669439343138083508754565189542113879843219016388785533085940283555"
// if exp := new(Element).fromDecimal(dString); d.Equal(exp) != 1 {
// t.Errorf("d is %v, expected %v", d, exp)
// }
}
func TestSetBytesRoundTripEdgeCases(t *testing.T) {
// TODO: values close to 0, close to 2^255-19, between 2^255-19 and 2^255-1,
// and between 2^255 and 2^256-1. Test both the documented SetBytes
// behavior, and that Bytes reduces them.
}
// Tests self-consistency between Multiply and Square.
func TestConsistency(t *testing.T) {
var x Element
var x2, x2sq Element
x = Element{1, 1, 1, 1, 1}
x2.Multiply(&x, &x)
x2sq.Square(&x)
if x2 != x2sq {
t.Fatalf("all ones failed\nmul: %x\nsqr: %x\n", x2, x2sq)
}
var bytes [32]byte
_, err := io.ReadFull(rand.Reader, bytes[:])
if err != nil {
t.Fatal(err)
}
x.SetBytes(bytes[:])
x2.Multiply(&x, &x)
x2sq.Square(&x)
if x2 != x2sq {
t.Fatalf("all ones failed\nmul: %x\nsqr: %x\n", x2, x2sq)
}
}
func TestEqual(t *testing.T) {
x := Element{1, 1, 1, 1, 1}
y := Element{5, 4, 3, 2, 1}
eq := x.Equal(&x)
if eq != 1 {
t.Errorf("wrong about equality")
}
eq = x.Equal(&y)
if eq != 0 {
t.Errorf("wrong about inequality")
}
}
func TestInvert(t *testing.T) {
x := Element{1, 1, 1, 1, 1}
one := Element{1, 0, 0, 0, 0}
var xinv, r Element
xinv.Invert(&x)
r.Multiply(&x, &xinv)
r.reduce()
if one != r {
t.Errorf("inversion identity failed, got: %x", r)
}
var bytes [32]byte
_, err := io.ReadFull(rand.Reader, bytes[:])
if err != nil {
t.Fatal(err)
}
x.SetBytes(bytes[:])
xinv.Invert(&x)
r.Multiply(&x, &xinv)
r.reduce()
if one != r {
t.Errorf("random inversion identity failed, got: %x for field element %x", r, x)
}
zero := Element{}
x.Set(&zero)
if xx := xinv.Invert(&x); xx != &xinv {
t.Errorf("inverting zero did not return the receiver")
} else if xinv.Equal(&zero) != 1 {
t.Errorf("inverting zero did not return zero")
}
}
func TestSelectSwap(t *testing.T) {
a := Element{358744748052810, 1691584618240980, 977650209285361, 1429865912637724, 560044844278676}
b := Element{84926274344903, 473620666599931, 365590438845504, 1028470286882429, 2146499180330972}
var c, d Element
c.Select(&a, &b, 1)
d.Select(&a, &b, 0)
if c.Equal(&a) != 1 || d.Equal(&b) != 1 {
t.Errorf("Select failed")
}
c.Swap(&d, 0)
if c.Equal(&a) != 1 || d.Equal(&b) != 1 {
t.Errorf("Swap failed")
}
c.Swap(&d, 1)
if c.Equal(&b) != 1 || d.Equal(&a) != 1 {
t.Errorf("Swap failed")
}
}
func TestMult32(t *testing.T) {
mult32EquivalentToMul := func(x Element, y uint32) bool {
t1 := new(Element)
for i := 0; i < 100; i++ {
t1.Mult32(&x, y)
}
ty := new(Element)
ty.l0 = uint64(y)
t2 := new(Element)
for i := 0; i < 100; i++ {
t2.Multiply(&x, ty)
}
return t1.Equal(t2) == 1 && isInBounds(t1) && isInBounds(t2)
}
if err := quick.Check(mult32EquivalentToMul, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestSqrtRatio(t *testing.T) {
// From draft-irtf-cfrg-ristretto255-decaf448-00, Appendix A.4.
type test struct {
u, v string
wasSquare int
r string
}
var tests = []test{
// If u is 0, the function is defined to return (0, TRUE), even if v
// is zero. Note that where used in this package, the denominator v
// is never zero.
{
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
1, "0000000000000000000000000000000000000000000000000000000000000000",
},
// 0/1 == 0²
{
"0000000000000000000000000000000000000000000000000000000000000000",
"0100000000000000000000000000000000000000000000000000000000000000",
1, "0000000000000000000000000000000000000000000000000000000000000000",
},
// If u is non-zero and v is zero, defined to return (0, FALSE).
{
"0100000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
0, "0000000000000000000000000000000000000000000000000000000000000000",
},
// 2/1 is not square in this field.
{
"0200000000000000000000000000000000000000000000000000000000000000",
"0100000000000000000000000000000000000000000000000000000000000000",
0, "3c5ff1b5d8e4113b871bd052f9e7bcd0582804c266ffb2d4f4203eb07fdb7c54",
},
// 4/1 == 2²
{
"0400000000000000000000000000000000000000000000000000000000000000",
"0100000000000000000000000000000000000000000000000000000000000000",
1, "0200000000000000000000000000000000000000000000000000000000000000",
},
// 1/4 == (2⁻¹)² == (2^(p-2))² per Euler's theorem
{
"0100000000000000000000000000000000000000000000000000000000000000",
"0400000000000000000000000000000000000000000000000000000000000000",
1, "f6ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f",
},
}
for i, tt := range tests {
u, _ := new(Element).SetBytes(decodeHex(tt.u))
v, _ := new(Element).SetBytes(decodeHex(tt.v))
want, _ := new(Element).SetBytes(decodeHex(tt.r))
got, wasSquare := new(Element).SqrtRatio(u, v)
if got.Equal(want) == 0 || wasSquare != tt.wasSquare {
t.Errorf("%d: got (%v, %v), want (%v, %v)", i, got, wasSquare, want, tt.wasSquare)
}
}
}
func TestCarryPropagate(t *testing.T) {
asmLikeGeneric := func(a [5]uint64) bool {
t1 := &Element{a[0], a[1], a[2], a[3], a[4]}
t2 := &Element{a[0], a[1], a[2], a[3], a[4]}
t1.carryPropagate()
t2.carryPropagateGeneric()
if *t1 != *t2 {
t.Logf("got: %#v,\nexpected: %#v", t1, t2)
}
return *t1 == *t2 && isInBounds(t2)
}
if err := quick.Check(asmLikeGeneric, quickCheckConfig1024); err != nil {
t.Error(err)
}
if !asmLikeGeneric([5]uint64{0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff}) {
t.Errorf("failed for {0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff}")
}
}
func TestFeSquare(t *testing.T) {
asmLikeGeneric := func(a Element) bool {
t1 := a
t2 := a
feSquareGeneric(&t1, &t1)
feSquare(&t2, &t2)
if t1 != t2 {
t.Logf("got: %#v,\nexpected: %#v", t1, t2)
}
return t1 == t2 && isInBounds(&t2)
}
if err := quick.Check(asmLikeGeneric, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func TestFeMul(t *testing.T) {
asmLikeGeneric := func(a, b Element) bool {
a1 := a
a2 := a
b1 := b
b2 := b
feMulGeneric(&a1, &a1, &b1)
feMul(&a2, &a2, &b2)
if a1 != a2 || b1 != b2 {
t.Logf("got: %#v,\nexpected: %#v", a1, a2)
t.Logf("got: %#v,\nexpected: %#v", b1, b2)
}
return a1 == a2 && isInBounds(&a2) &&
b1 == b2 && isInBounds(&b2)
}
if err := quick.Check(asmLikeGeneric, quickCheckConfig1024); err != nil {
t.Error(err)
}
}
func decodeHex(s string) []byte {
b, err := hex.DecodeString(s)
if err != nil {
panic(err)
}
return b
}