// Copyright 2012 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 bn256
import (
"bytes"
"crypto/rand"
"math/big"
"testing"
)
func TestGFp2Invert(t *testing.T) {
pool := new(bnPool)
a := newGFp2(pool)
a.x.SetString("23423492374", 10)
a.y.SetString("12934872398472394827398470", 10)
inv := newGFp2(pool)
inv.Invert(a, pool)
b := newGFp2(pool).Mul(inv, a, pool)
if b.x.Int64() != 0 || b.y.Int64() != 1 {
t.Fatalf("bad result for a^-1*a: %s %s", b.x, b.y)
}
a.Put(pool)
b.Put(pool)
inv.Put(pool)
if c := pool.Count(); c > 0 {
t.Errorf("Pool count non-zero: %d\n", c)
}
}
func isZero(n *big.Int) bool {
return new(big.Int).Mod(n, P).Int64() == 0
}
func isOne(n *big.Int) bool {
return new(big.Int).Mod(n, P).Int64() == 1
}
func TestGFp6Invert(t *testing.T) {
pool := new(bnPool)
a := newGFp6(pool)
a.x.x.SetString("239487238491", 10)
a.x.y.SetString("2356249827341", 10)
a.y.x.SetString("082659782", 10)
a.y.y.SetString("182703523765", 10)
a.z.x.SetString("978236549263", 10)
a.z.y.SetString("64893242", 10)
inv := newGFp6(pool)
inv.Invert(a, pool)
b := newGFp6(pool).Mul(inv, a, pool)
if !isZero(b.x.x) ||
!isZero(b.x.y) ||
!isZero(b.y.x) ||
!isZero(b.y.y) ||
!isZero(b.z.x) ||
!isOne(b.z.y) {
t.Fatalf("bad result for a^-1*a: %s", b)
}
a.Put(pool)
b.Put(pool)
inv.Put(pool)
if c := pool.Count(); c > 0 {
t.Errorf("Pool count non-zero: %d\n", c)
}
}
func TestGFp12Invert(t *testing.T) {
pool := new(bnPool)
a := newGFp12(pool)
a.x.x.x.SetString("239846234862342323958623", 10)
a.x.x.y.SetString("2359862352529835623", 10)
a.x.y.x.SetString("928836523", 10)
a.x.y.y.SetString("9856234", 10)
a.x.z.x.SetString("235635286", 10)
a.x.z.y.SetString("5628392833", 10)
a.y.x.x.SetString("252936598265329856238956532167968", 10)
a.y.x.y.SetString("23596239865236954178968", 10)
a.y.y.x.SetString("95421692834", 10)
a.y.y.y.SetString("236548", 10)
a.y.z.x.SetString("924523", 10)
a.y.z.y.SetString("12954623", 10)
inv := newGFp12(pool)
inv.Invert(a, pool)
b := newGFp12(pool).Mul(inv, a, pool)
if !isZero(b.x.x.x) ||
!isZero(b.x.x.y) ||
!isZero(b.x.y.x) ||
!isZero(b.x.y.y) ||
!isZero(b.x.z.x) ||
!isZero(b.x.z.y) ||
!isZero(b.y.x.x) ||
!isZero(b.y.x.y) ||
!isZero(b.y.y.x) ||
!isZero(b.y.y.y) ||
!isZero(b.y.z.x) ||
!isOne(b.y.z.y) {
t.Fatalf("bad result for a^-1*a: %s", b)
}
a.Put(pool)
b.Put(pool)
inv.Put(pool)
if c := pool.Count(); c > 0 {
t.Errorf("Pool count non-zero: %d\n", c)
}
}
func TestCurveImpl(t *testing.T) {
pool := new(bnPool)
g := &curvePoint{
pool.Get().SetInt64(1),
pool.Get().SetInt64(-2),
pool.Get().SetInt64(1),
pool.Get().SetInt64(0),
}
x := pool.Get().SetInt64(32498273234)
X := newCurvePoint(pool).Mul(g, x, pool)
y := pool.Get().SetInt64(98732423523)
Y := newCurvePoint(pool).Mul(g, y, pool)
s1 := newCurvePoint(pool).Mul(X, y, pool).MakeAffine(pool)
s2 := newCurvePoint(pool).Mul(Y, x, pool).MakeAffine(pool)
if s1.x.Cmp(s2.x) != 0 ||
s2.x.Cmp(s1.x) != 0 {
t.Errorf("DH points don't match: (%s, %s) (%s, %s)", s1.x, s1.y, s2.x, s2.y)
}
pool.Put(x)
X.Put(pool)
pool.Put(y)
Y.Put(pool)
s1.Put(pool)
s2.Put(pool)
g.Put(pool)
if c := pool.Count(); c > 0 {
t.Errorf("Pool count non-zero: %d\n", c)
}
}
func TestOrderG1(t *testing.T) {
g := new(G1).ScalarBaseMult(Order)
if !g.p.IsInfinity() {
t.Error("G1 has incorrect order")
}
one := new(G1).ScalarBaseMult(new(big.Int).SetInt64(1))
g.Add(g, one)
g.p.MakeAffine(nil)
if g.p.x.Cmp(one.p.x) != 0 || g.p.y.Cmp(one.p.y) != 0 {
t.Errorf("1+0 != 1 in G1")
}
}
func TestOrderG2(t *testing.T) {
g := new(G2).ScalarBaseMult(Order)
if !g.p.IsInfinity() {
t.Error("G2 has incorrect order")
}
one := new(G2).ScalarBaseMult(new(big.Int).SetInt64(1))
g.Add(g, one)
g.p.MakeAffine(nil)
if g.p.x.x.Cmp(one.p.x.x) != 0 ||
g.p.x.y.Cmp(one.p.x.y) != 0 ||
g.p.y.x.Cmp(one.p.y.x) != 0 ||
g.p.y.y.Cmp(one.p.y.y) != 0 {
t.Errorf("1+0 != 1 in G2")
}
}
func TestOrderGT(t *testing.T) {
gt := Pair(&G1{curveGen}, &G2{twistGen})
g := new(GT).ScalarMult(gt, Order)
if !g.p.IsOne() {
t.Error("GT has incorrect order")
}
}
func TestBilinearity(t *testing.T) {
for i := 0; i < 2; i++ {
a, p1, _ := RandomG1(rand.Reader)
b, p2, _ := RandomG2(rand.Reader)
e1 := Pair(p1, p2)
e2 := Pair(&G1{curveGen}, &G2{twistGen})
e2.ScalarMult(e2, a)
e2.ScalarMult(e2, b)
minusE2 := new(GT).Neg(e2)
e1.Add(e1, minusE2)
if !e1.p.IsOne() {
t.Fatalf("bad pairing result: %s", e1)
}
}
}
func TestG1Marshal(t *testing.T) {
g := new(G1).ScalarBaseMult(new(big.Int).SetInt64(1))
form := g.Marshal()
_, ok := new(G1).Unmarshal(form)
if !ok {
t.Fatalf("failed to unmarshal")
}
g.ScalarBaseMult(Order)
form = g.Marshal()
g2, ok := new(G1).Unmarshal(form)
if !ok {
t.Fatalf("failed to unmarshal ∞")
}
if !g2.p.IsInfinity() {
t.Fatalf("∞ unmarshaled incorrectly")
}
}
func TestG2Marshal(t *testing.T) {
g := new(G2).ScalarBaseMult(new(big.Int).SetInt64(1))
form := g.Marshal()
_, ok := new(G2).Unmarshal(form)
if !ok {
t.Fatalf("failed to unmarshal")
}
g.ScalarBaseMult(Order)
form = g.Marshal()
g2, ok := new(G2).Unmarshal(form)
if !ok {
t.Fatalf("failed to unmarshal ∞")
}
if !g2.p.IsInfinity() {
t.Fatalf("∞ unmarshaled incorrectly")
}
}
func TestG1Identity(t *testing.T) {
g := new(G1).ScalarBaseMult(new(big.Int).SetInt64(0))
if !g.p.IsInfinity() {
t.Error("failure")
}
}
func TestG2Identity(t *testing.T) {
g := new(G2).ScalarBaseMult(new(big.Int).SetInt64(0))
if !g.p.IsInfinity() {
t.Error("failure")
}
}
func TestTripartiteDiffieHellman(t *testing.T) {
a, _ := rand.Int(rand.Reader, Order)
b, _ := rand.Int(rand.Reader, Order)
c, _ := rand.Int(rand.Reader, Order)
pa, _ := new(G1).Unmarshal(new(G1).ScalarBaseMult(a).Marshal())
qa, _ := new(G2).Unmarshal(new(G2).ScalarBaseMult(a).Marshal())
pb, _ := new(G1).Unmarshal(new(G1).ScalarBaseMult(b).Marshal())
qb, _ := new(G2).Unmarshal(new(G2).ScalarBaseMult(b).Marshal())
pc, _ := new(G1).Unmarshal(new(G1).ScalarBaseMult(c).Marshal())
qc, _ := new(G2).Unmarshal(new(G2).ScalarBaseMult(c).Marshal())
k1 := Pair(pb, qc)
k1.ScalarMult(k1, a)
k1Bytes := k1.Marshal()
k2 := Pair(pc, qa)
k2.ScalarMult(k2, b)
k2Bytes := k2.Marshal()
k3 := Pair(pa, qb)
k3.ScalarMult(k3, c)
k3Bytes := k3.Marshal()
if !bytes.Equal(k1Bytes, k2Bytes) || !bytes.Equal(k2Bytes, k3Bytes) {
t.Errorf("keys didn't agree")
}
}
func BenchmarkPairing(b *testing.B) {
for i := 0; i < b.N; i++ {
Pair(&G1{curveGen}, &G2{twistGen})
}
}
