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- package bls12381
- import (
- "math/big"
- "testing"
- "github.com/ethereum/go-ethereum/common"
- )
- func TestPairingExpected(t *testing.T) {
- bls := NewPairingEngine()
- G1, G2 := bls.G1, bls.G2
- GT := bls.GT()
- expected, err := GT.FromBytes(
- common.FromHex("" +
- "0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
- "04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
- "03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
- "11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
- "06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
- "19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
- "018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
- "01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
- "193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
- "1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
- "089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
- "1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
- ),
- )
- if err != nil {
- t.Fatal(err)
- }
- r := bls.AddPair(G1.One(), G2.One()).Result()
- if !r.Equal(expected) {
- t.Fatal("bad pairing")
- }
- if !GT.IsValid(r) {
- t.Fatal("element is not in correct subgroup")
- }
- }
- func TestPairingNonDegeneracy(t *testing.T) {
- bls := NewPairingEngine()
- G1, G2 := bls.G1, bls.G2
- g1Zero, g2Zero, g1One, g2One := G1.Zero(), G2.Zero(), G1.One(), G2.One()
- GT := bls.GT()
- // e(g1^a, g2^b) != 1
- bls.Reset()
- {
- bls.AddPair(g1One, g2One)
- e := bls.Result()
- if e.IsOne() {
- t.Fatal("pairing result is not expected to be one")
- }
- if !GT.IsValid(e) {
- t.Fatal("pairing result is not valid")
- }
- }
- // e(g1^a, 0) == 1
- bls.Reset()
- {
- bls.AddPair(g1One, g2Zero)
- e := bls.Result()
- if !e.IsOne() {
- t.Fatal("pairing result is expected to be one")
- }
- }
- // e(0, g2^b) == 1
- bls.Reset()
- {
- bls.AddPair(g1Zero, g2One)
- e := bls.Result()
- if !e.IsOne() {
- t.Fatal("pairing result is expected to be one")
- }
- }
- //
- bls.Reset()
- {
- bls.AddPair(g1Zero, g2One)
- bls.AddPair(g1One, g2Zero)
- bls.AddPair(g1Zero, g2Zero)
- e := bls.Result()
- if !e.IsOne() {
- t.Fatal("pairing result is expected to be one")
- }
- }
- //
- bls.Reset()
- {
- expected, err := GT.FromBytes(
- common.FromHex("" +
- "0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
- "04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
- "03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
- "11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
- "06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
- "19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
- "018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
- "01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
- "193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
- "1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
- "089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
- "1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
- ),
- )
- if err != nil {
- t.Fatal(err)
- }
- bls.AddPair(g1Zero, g2One)
- bls.AddPair(g1One, g2Zero)
- bls.AddPair(g1Zero, g2Zero)
- bls.AddPair(g1One, g2One)
- e := bls.Result()
- if !e.Equal(expected) {
- t.Fatal("bad pairing")
- }
- }
- }
- func TestPairingBilinearity(t *testing.T) {
- bls := NewPairingEngine()
- g1, g2 := bls.G1, bls.G2
- gt := bls.GT()
- // e(a*G1, b*G2) = e(G1, G2)^c
- {
- a, b := big.NewInt(17), big.NewInt(117)
- c := new(big.Int).Mul(a, b)
- G1, G2 := g1.One(), g2.One()
- e0 := bls.AddPair(G1, G2).Result()
- P1, P2 := g1.New(), g2.New()
- g1.MulScalar(P1, G1, a)
- g2.MulScalar(P2, G2, b)
- e1 := bls.AddPair(P1, P2).Result()
- gt.Exp(e0, e0, c)
- if !e0.Equal(e1) {
- t.Fatal("bad pairing, 1")
- }
- }
- // e(a * G1, b * G2) = e((a + b) * G1, G2)
- {
- // scalars
- a, b := big.NewInt(17), big.NewInt(117)
- c := new(big.Int).Mul(a, b)
- // LHS
- G1, G2 := g1.One(), g2.One()
- g1.MulScalar(G1, G1, c)
- bls.AddPair(G1, G2)
- // RHS
- P1, P2 := g1.One(), g2.One()
- g1.MulScalar(P1, P1, a)
- g2.MulScalar(P2, P2, b)
- bls.AddPairInv(P1, P2)
- // should be one
- if !bls.Check() {
- t.Fatal("bad pairing, 2")
- }
- }
- // e(a * G1, b * G2) = e((a + b) * G1, G2)
- {
- // scalars
- a, b := big.NewInt(17), big.NewInt(117)
- c := new(big.Int).Mul(a, b)
- // LHS
- G1, G2 := g1.One(), g2.One()
- g2.MulScalar(G2, G2, c)
- bls.AddPair(G1, G2)
- // RHS
- H1, H2 := g1.One(), g2.One()
- g1.MulScalar(H1, H1, a)
- g2.MulScalar(H2, H2, b)
- bls.AddPairInv(H1, H2)
- // should be one
- if !bls.Check() {
- t.Fatal("bad pairing, 3")
- }
- }
- }
- func TestPairingMulti(t *testing.T) {
- // e(G1, G2) ^ t == e(a01 * G1, a02 * G2) * e(a11 * G1, a12 * G2) * ... * e(an1 * G1, an2 * G2)
- // where t = sum(ai1 * ai2)
- bls := NewPairingEngine()
- g1, g2 := bls.G1, bls.G2
- numOfPair := 100
- targetExp := new(big.Int)
- // RHS
- for i := 0; i < numOfPair; i++ {
- // (ai1 * G1, ai2 * G2)
- a1, a2 := randScalar(q), randScalar(q)
- P1, P2 := g1.One(), g2.One()
- g1.MulScalar(P1, P1, a1)
- g2.MulScalar(P2, P2, a2)
- bls.AddPair(P1, P2)
- // accumulate targetExp
- // t += (ai1 * ai2)
- a1.Mul(a1, a2)
- targetExp.Add(targetExp, a1)
- }
- // LHS
- // e(t * G1, G2)
- T1, T2 := g1.One(), g2.One()
- g1.MulScalar(T1, T1, targetExp)
- bls.AddPairInv(T1, T2)
- if !bls.Check() {
- t.Fatal("fail multi pairing")
- }
- }
- func TestPairingEmpty(t *testing.T) {
- bls := NewPairingEngine()
- if !bls.Check() {
- t.Fatal("empty check should be accepted")
- }
- if !bls.Result().IsOne() {
- t.Fatal("empty pairing result should be one")
- }
- }
- func BenchmarkPairing(t *testing.B) {
- bls := NewPairingEngine()
- g1, g2, gt := bls.G1, bls.G2, bls.GT()
- bls.AddPair(g1.One(), g2.One())
- e := gt.New()
- t.ResetTimer()
- for i := 0; i < t.N; i++ {
- e = bls.calculate()
- }
- _ = e
- }
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