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Pairing check optimisation #1335

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Merged
yelhousni merged 4 commits into from
Dec 5, 2024
Merged

Pairing check optimisation #1335

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1a916b7
em/bn254: cubicNonResiduePower E6
shramee Nov 30, 2024
3065f13
em/bls381: cubicNonResiduePower E6
shramee Nov 30, 2024
5defeaf
sw_bn254: cubicNonResiduePower E6
shramee Nov 30, 2024
468fc08
bls12377: cubicNonResiduePower E6
shramee Nov 30, 2024
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16 changes: 8 additions & 8 deletions std/algebra/emulated/fields_bls12381/e12_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -411,13 +411,10 @@ func (e Ext12) AssertFinalExponentiationIsOne(x *E12) {
},
}
// constrain cubicNonResiduePower to be in Fp6
scalingFactor := E12{
C0: E6{
B0: E2{A0: *res[12], A1: *res[13]},
B1: E2{A0: *res[14], A1: *res[15]},
B2: E2{A0: *res[16], A1: *res[17]},
},
C1: (*e.Ext6.Zero()),
scalingFactor := E6{
B0: E2{A0: *res[12], A1: *res[13]},
B1: E2{A0: *res[14], A1: *res[15]},
B2: E2{A0: *res[16], A1: *res[17]},
}

// Check that x * scalingFactor == residueWitness^(q-u)
Expand All @@ -428,7 +425,10 @@ func (e Ext12) AssertFinalExponentiationIsOne(x *E12) {
t1 := e.Expt(&residueWitness)
t0 = e.Mul(t0, t1)

t1 = e.Mul(x, &scalingFactor)
t1 = &E12{
C0: *e.Ext6.Mul(&x.C0, &scalingFactor),
C1: *e.Ext6.Mul(&x.C1, &scalingFactor),
}

e.AssertIsEqual(t0, t1)
}
Expand Down
16 changes: 8 additions & 8 deletions std/algebra/emulated/fields_bn254/e12_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -448,19 +448,19 @@ func (e Ext12) AssertFinalExponentiationIsOne(x *E12) {
},
}
// constrain cubicNonResiduePower to be in Fp6
cubicNonResiduePower := E12{
C0: E6{
B0: E2{A0: *res[12], A1: *res[13]},
B1: E2{A0: *res[14], A1: *res[15]},
B2: E2{A0: *res[16], A1: *res[17]},
},
C1: (*e.Ext6.Zero()),
cubicNonResiduePower := E6{
B0: E2{A0: *res[12], A1: *res[13]},
B1: E2{A0: *res[14], A1: *res[15]},
B2: E2{A0: *res[16], A1: *res[17]},
}

// Check that x * cubicNonResiduePower == residueWitness^λ
// where λ = 6u + 2 + q^3 - q^2 + q, with u the BN254 seed
// and residueWitness, cubicNonResiduePower from the hint.
t2 := e.Mul(&cubicNonResiduePower, x)
t2 := &E12{
C0: *e.Ext6.Mul(&x.C0, &cubicNonResiduePower),
C1: *e.Ext6.Mul(&x.C1, &cubicNonResiduePower),
}

t1 := e.FrobeniusCube(&residueWitness)
t0 := e.FrobeniusSquare(&residueWitness)
Expand Down
16 changes: 8 additions & 8 deletions std/algebra/emulated/sw_bn254/pairing.go
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Expand Up @@ -705,13 +705,10 @@ func (pr Pairing) millerLoopAndFinalExpResult(P *G1Affine, Q *G2Affine, previous
},
}
// constrain cubicNonResiduePower to be in Fp6
cubicNonResiduePower := fields_bn254.E12{
C0: fields_bn254.E6{
B0: fields_bn254.E2{A0: *hint[12], A1: *hint[13]},
B1: fields_bn254.E2{A0: *hint[14], A1: *hint[15]},
B2: fields_bn254.E2{A0: *hint[16], A1: *hint[17]},
},
C1: (*pr.Ext6.Zero()),
cubicNonResiduePower := fields_bn254.E6{
B0: fields_bn254.E2{A0: *hint[12], A1: *hint[13]},
B1: fields_bn254.E2{A0: *hint[14], A1: *hint[15]},
B2: fields_bn254.E2{A0: *hint[16], A1: *hint[17]},
}

// residueWitnessInv = 1 / residueWitness
Expand Down Expand Up @@ -795,7 +792,10 @@ func (pr Pairing) millerLoopAndFinalExpResult(P *G1Affine, Q *G2Affine, previous
// and residueWitnessInv, cubicNonResiduePower from the hint.
// Note that res is already MillerLoop(P,Q) * residueWitnessInv^{6x₀+2} since
// we initialized the Miller loop accumulator with residueWitnessInv.
t2 := pr.Mul(&cubicNonResiduePower, res)
t2 := &fields_bn254.E12{
C0: *pr.Ext6.Mul(&res.C0, &cubicNonResiduePower),
C1: *pr.Ext6.Mul(&res.C1, &cubicNonResiduePower),
}

t1 := pr.FrobeniusCube(residueWitnessInv)
t0 := pr.FrobeniusSquare(residueWitnessInv)
Expand Down
19 changes: 10 additions & 9 deletions std/algebra/native/fields_bls12377/e12_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -219,16 +219,16 @@ func (x *E12) AssertFinalExponentiationIsOne(api frontend.API) {
panic(err)
}

var residueWitness, scalingFactor, t0, t1 E12
var residueWitness, t0, t1 E12
var scalingFactor E6
residueWitness.assign(res[:12])
// constrain cubicNonResiduePower to be in Fp6
scalingFactor.C0.B0.A0 = res[12]
scalingFactor.C0.B0.A1 = res[13]
scalingFactor.C0.B1.A0 = res[14]
scalingFactor.C0.B1.A1 = res[15]
scalingFactor.C0.B2.A0 = res[16]
scalingFactor.C0.B2.A1 = res[17]
scalingFactor.C1.SetZero()
scalingFactor.B0.A0 = res[12]
scalingFactor.B0.A1 = res[13]
scalingFactor.B1.A0 = res[14]
scalingFactor.B1.A1 = res[15]
scalingFactor.B2.A0 = res[16]
scalingFactor.B2.A1 = res[17]

// Check that x * scalingFactor == residueWitness^(q-u)
// where u=0x8508c00000000001 is the BLS12-377 seed,
Expand All @@ -238,7 +238,8 @@ func (x *E12) AssertFinalExponentiationIsOne(api frontend.API) {
t1.ExpX0(api, residueWitness)
t0.DivUnchecked(api, t0, t1)

t1.Mul(api, *x, scalingFactor)
t1.C0.Mul(api, x.C0, scalingFactor)
t1.C1.Mul(api, x.C1, scalingFactor)

t0.AssertIsEqual(api, t1)
}