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pairing_test.go
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/
pairing_test.go
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// Copyright 2020 Consensys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by consensys/gnark-crypto DO NOT EDIT
package bls12377
import (
"fmt"
"math/big"
"testing"
"github.com/consensys/gnark-crypto/ecc/bls12-377/fp"
"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
"github.com/leanovate/gopter"
"github.com/leanovate/gopter/prop"
)
// ------------------------------------------------------------
// tests
func TestPairing(t *testing.T) {
t.Parallel()
parameters := gopter.DefaultTestParameters()
if testing.Short() {
parameters.MinSuccessfulTests = nbFuzzShort
} else {
parameters.MinSuccessfulTests = nbFuzz
}
properties := gopter.NewProperties(parameters)
genA := GenE12()
genR1 := GenFr()
genR2 := GenFr()
properties.Property("[BLS12-377] Having the receiver as operand (final expo) should output the same result", prop.ForAll(
func(a GT) bool {
b := FinalExponentiation(&a)
a = FinalExponentiation(&a)
return a.Equal(&b)
},
genA,
))
properties.Property("[BLS12-377] Exponentiating FinalExpo(a) to r should output 1", prop.ForAll(
func(a GT) bool {
b := FinalExponentiation(&a)
return !a.IsInSubGroup() && b.IsInSubGroup()
},
genA,
))
properties.Property("[BLS12-377] Exp, CyclotomicExp and ExpGLV results must be the same in GT (small and big exponents)", prop.ForAll(
func(a GT, e fr.Element) bool {
var res bool
// exponent > r
{
a = FinalExponentiation(&a)
var _e big.Int
_e.SetString("169893631828481842931290008859743243489098146141979830311893424751855271950692001433356165550548410610101138388623573573742608490725625288296502860183437011025036209791574001140592327223981416956942076610555083128655330944007957223952510233203018053264066056080064687038560794652180979019775788172491868553073169893631828481842931290008859743243489098146141979830311893424751855271950692001433356165550548410610101138388623573573742608490725625288296502860183437011025036209791574001140592327223981416956942076610555083128655330944007957223952510233203018053264066056080064687038560794652180979019775788172491868553073", 10)
var b, c, d GT
b.Exp(a, &_e)
c.ExpGLV(a, &_e)
d.CyclotomicExp(a, &_e)
res = b.Equal(&c) && c.Equal(&d)
}
// exponent < r
{
a = FinalExponentiation(&a)
var _e big.Int
e.BigInt(&_e)
var b, c, d GT
b.Exp(a, &_e)
c.ExpGLV(a, &_e)
d.CyclotomicExp(a, &_e)
res = res && b.Equal(&c) && c.Equal(&d)
}
return res
},
genA,
genR1,
))
properties.Property("[BLS12-377] Expt(Expt) and Exp(t^2) should output the same result in the cyclotomic subgroup", prop.ForAll(
func(a GT) bool {
var b, c, d GT
b.Conjugate(&a)
a.Inverse(&a)
b.Mul(&b, &a)
a.FrobeniusSquare(&b).
Mul(&a, &b)
c.Expt(&a).Expt(&c)
d.Exp(a, &xGen).Exp(d, &xGen)
return c.Equal(&d)
},
genA,
))
properties.Property("[BLS12-377] bilinearity", prop.ForAll(
func(a, b fr.Element) bool {
var res, resa, resb, resab, zero GT
var ag1 G1Affine
var bg2 G2Affine
var abigint, bbigint, ab big.Int
a.BigInt(&abigint)
b.BigInt(&bbigint)
ab.Mul(&abigint, &bbigint)
ag1.ScalarMultiplication(&g1GenAff, &abigint)
bg2.ScalarMultiplication(&g2GenAff, &bbigint)
res, _ = Pair([]G1Affine{g1GenAff}, []G2Affine{g2GenAff})
resa, _ = Pair([]G1Affine{ag1}, []G2Affine{g2GenAff})
resb, _ = Pair([]G1Affine{g1GenAff}, []G2Affine{bg2})
resab.Exp(res, &ab)
resa.Exp(resa, &bbigint)
resb.Exp(resb, &abigint)
return resab.Equal(&resa) && resab.Equal(&resb) && !res.Equal(&zero)
},
genR1,
genR2,
))
properties.Property("[BLS12-377] PairingCheck", prop.ForAll(
func(a, b fr.Element) bool {
var g1GenAffNeg G1Affine
g1GenAffNeg.Neg(&g1GenAff)
tabP := []G1Affine{g1GenAff, g1GenAffNeg}
tabQ := []G2Affine{g2GenAff, g2GenAff}
res, _ := PairingCheck(tabP, tabQ)
return res
},
genR1,
genR2,
))
properties.TestingRun(t, gopter.ConsoleReporter(false))
}
func TestMillerLoop(t *testing.T) {
t.Parallel()
parameters := gopter.DefaultTestParameters()
if testing.Short() {
parameters.MinSuccessfulTests = nbFuzzShort
} else {
parameters.MinSuccessfulTests = nbFuzz
}
properties := gopter.NewProperties(parameters)
genR1 := GenFr()
genR2 := GenFr()
properties.Property("[BLS12-377] MillerLoop of pairs should be equal to the product of MillerLoops", prop.ForAll(
func(a, b fr.Element) bool {
var simpleProd, factorizedProd GT
var ag1 G1Affine
var bg2 G2Affine
var abigint, bbigint big.Int
a.BigInt(&abigint)
b.BigInt(&bbigint)
ag1.ScalarMultiplication(&g1GenAff, &abigint)
bg2.ScalarMultiplication(&g2GenAff, &bbigint)
P0 := []G1Affine{g1GenAff}
P1 := []G1Affine{ag1}
Q0 := []G2Affine{g2GenAff}
Q1 := []G2Affine{bg2}
// FE( ML(a,b) * ML(c,d) * ML(e,f) * ML(g,h) )
M1, _ := MillerLoop(P0, Q0)
M2, _ := MillerLoop(P1, Q0)
M3, _ := MillerLoop(P0, Q1)
M4, _ := MillerLoop(P1, Q1)
simpleProd.Mul(&M1, &M2).Mul(&simpleProd, &M3).Mul(&simpleProd, &M4)
simpleProd = FinalExponentiation(&simpleProd)
tabP := []G1Affine{g1GenAff, ag1, g1GenAff, ag1}
tabQ := []G2Affine{g2GenAff, g2GenAff, bg2, bg2}
// FE( ML([a,c,e,g] ; [b,d,f,h]) ) -> saves 3 squares in Fqk
factorizedProd, _ = Pair(tabP, tabQ)
return simpleProd.Equal(&factorizedProd)
},
genR1,
genR2,
))
properties.Property("[BLS12-377] MillerLoop should skip pairs with a point at infinity", prop.ForAll(
func(a, b fr.Element) bool {
var one GT
var ag1, g1Inf G1Affine
var bg2, g2Inf G2Affine
var abigint, bbigint big.Int
one.SetOne()
a.BigInt(&abigint)
b.BigInt(&bbigint)
ag1.ScalarMultiplication(&g1GenAff, &abigint)
bg2.ScalarMultiplication(&g2GenAff, &bbigint)
g1Inf.FromJacobian(&g1Infinity)
g2Inf.FromJacobian(&g2Infinity)
// e([0,c] ; [b,d])
tabP := []G1Affine{g1Inf, ag1}
tabQ := []G2Affine{g2GenAff, bg2}
res1, _ := Pair(tabP, tabQ)
// e([a,c] ; [0,d])
tabP = []G1Affine{g1GenAff, ag1}
tabQ = []G2Affine{g2Inf, bg2}
res2, _ := Pair(tabP, tabQ)
// e([0,c] ; [d,0])
tabP = []G1Affine{g1Inf, ag1}
tabQ = []G2Affine{bg2, g2Inf}
res3, _ := Pair(tabP, tabQ)
return res1.Equal(&res2) && !res2.Equal(&res3) && res3.Equal(&one)
},
genR1,
genR2,
))
properties.Property("[BLS12-377] compressed pairing", prop.ForAll(
func(a, b fr.Element) bool {
var ag1 G1Affine
var bg2 G2Affine
var abigint, bbigint big.Int
a.BigInt(&abigint)
b.BigInt(&bbigint)
ag1.ScalarMultiplication(&g1GenAff, &abigint)
bg2.ScalarMultiplication(&g2GenAff, &bbigint)
res, _ := Pair([]G1Affine{ag1}, []G2Affine{bg2})
compressed, _ := res.CompressTorus()
decompressed := compressed.DecompressTorus()
return decompressed.Equal(&res)
},
genR1,
genR2,
))
properties.TestingRun(t, gopter.ConsoleReporter(false))
}
// ------------------------------------------------------------
// benches
func BenchmarkPairing(b *testing.B) {
var g1GenAff G1Affine
var g2GenAff G2Affine
g1GenAff.FromJacobian(&g1Gen)
g2GenAff.FromJacobian(&g2Gen)
b.ResetTimer()
for i := 0; i < b.N; i++ {
Pair([]G1Affine{g1GenAff}, []G2Affine{g2GenAff})
}
}
func BenchmarkMillerLoop(b *testing.B) {
var g1GenAff G1Affine
var g2GenAff G2Affine
g1GenAff.FromJacobian(&g1Gen)
g2GenAff.FromJacobian(&g2Gen)
b.ResetTimer()
for i := 0; i < b.N; i++ {
MillerLoop([]G1Affine{g1GenAff}, []G2Affine{g2GenAff})
}
}
func BenchmarkFinalExponentiation(b *testing.B) {
var a GT
a.SetRandom()
b.ResetTimer()
for i := 0; i < b.N; i++ {
FinalExponentiation(&a)
}
}
func BenchmarkMultiMiller(b *testing.B) {
var g1GenAff G1Affine
var g2GenAff G2Affine
g1GenAff.FromJacobian(&g1Gen)
g2GenAff.FromJacobian(&g2Gen)
n := 10
P := make([]G1Affine, n)
Q := make([]G2Affine, n)
for i := 2; i <= n; i++ {
for j := 0; j < i; j++ {
P[j].Set(&g1GenAff)
Q[j].Set(&g2GenAff)
}
b.Run(fmt.Sprintf("%d pairs", i), func(b *testing.B) {
b.ResetTimer()
for i := 0; i < b.N; i++ {
MillerLoop(P, Q)
}
})
}
}
func BenchmarkMultiPair(b *testing.B) {
var g1GenAff G1Affine
var g2GenAff G2Affine
g1GenAff.FromJacobian(&g1Gen)
g2GenAff.FromJacobian(&g2Gen)
n := 10
P := make([]G1Affine, n)
Q := make([]G2Affine, n)
for i := 2; i <= n; i++ {
for j := 0; j < i; j++ {
P[j].Set(&g1GenAff)
Q[j].Set(&g2GenAff)
}
b.Run(fmt.Sprintf("%d pairs", i), func(b *testing.B) {
b.ResetTimer()
for i := 0; i < b.N; i++ {
Pair(P, Q)
}
})
}
}
func BenchmarkExpGT(b *testing.B) {
var a GT
a.SetRandom()
a = FinalExponentiation(&a)
var e fp.Element
e.SetRandom()
k := new(big.Int).SetUint64(12)
e.Exp(e, k)
var _e big.Int
e.BigInt(&_e)
b.Run("Naive windowed Exp", func(b *testing.B) {
b.ResetTimer()
for i := 0; i < b.N; i++ {
a.Exp(a, &_e)
}
})
b.Run("2-NAF cyclotomic Exp", func(b *testing.B) {
b.ResetTimer()
for i := 0; i < b.N; i++ {
a.CyclotomicExp(a, &_e)
}
})
b.Run("windowed 2-dim GLV Exp", func(b *testing.B) {
b.ResetTimer()
for i := 0; i < b.N; i++ {
a.ExpGLV(a, &_e)
}
})
}