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perf(bn254): include G2 membership check in ML #1387

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perf(bn254): include G2 membership check in ML #1387

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3a20d3f
perf(bn254): include G2 membership check in ML
yelhousni Jan 7, 2025
16dfd2a
chore: update stats
yelhousni Jan 7, 2025
e2f1c55
Merge branch 'master' into perf/g2-membership-in-pairing
yelhousni Jan 8, 2025
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4 changes: 2 additions & 2 deletions internal/stats/latest_stats.csv
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Original file line number Diff line number Diff line change
Expand Up @@ -181,14 +181,14 @@ pairing_bls24315,bls24_315,plonk,0,0
pairing_bls24315,bls24_317,plonk,0,0
pairing_bls24315,bw6_761,plonk,0,0
pairing_bls24315,bw6_633,plonk,141249,141249
pairing_bn254,bn254,groth16,604783,990919
pairing_bn254,bn254,groth16,607378,995098
pairing_bn254,bls12_377,groth16,0,0
pairing_bn254,bls12_381,groth16,0,0
pairing_bn254,bls24_315,groth16,0,0
pairing_bn254,bls24_317,groth16,0,0
pairing_bn254,bw6_761,groth16,0,0
pairing_bn254,bw6_633,groth16,0,0
pairing_bn254,bn254,plonk,2319665,2030447
pairing_bn254,bn254,plonk,2329131,2039205
pairing_bn254,bls12_377,plonk,0,0
pairing_bn254,bls12_381,plonk,0,0
pairing_bn254,bls24_315,plonk,0,0
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2 changes: 1 addition & 1 deletion std/algebra/emulated/sw_bn254/g2.go
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Expand Up @@ -101,7 +101,7 @@ func (g2 *G2) phi(q *G2Affine) *G2Affine {
return &G2Affine{
P: g2AffP{
X: *x,
Y: q.P.Y,
Y: *g2.Ext2.Neg(&q.P.Y),
},
}
}
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1 change: 0 additions & 1 deletion std/algebra/emulated/sw_bn254/g2_test.go
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Expand Up @@ -126,7 +126,6 @@ type endomorphismG2Circuit struct {
func (c *endomorphismG2Circuit) Define(api frontend.API) error {
g2 := NewG2(api)
res1 := g2.phi(&c.In1)
res1 = g2.neg(res1)
res2 := g2.psi(&c.In1)
res2 = g2.psi(res2)
g2.AssertIsEqual(res1, res2)
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6 changes: 3 additions & 3 deletions std/algebra/emulated/sw_bn254/pairing.go
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Expand Up @@ -84,7 +84,7 @@ func NewPairing(api frontend.API) (*Pairing, error) {
// Pair calculates the reduced pairing for a set of points
// ∏ᵢ e(Pᵢ, Qᵢ).
//
// This function doesn't check that the inputs are in the correct subgroups. See AssertIsOnG1 and AssertIsOnG2.
// This function checks that the Qᵢ are in the correct subgroupsi, but does not check Pᵢ. See AssertIsOnG1.
func (pr Pairing) Pair(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
res, err := pr.MillerLoop(P, Q)
if err != nil {
Expand Down Expand Up @@ -209,7 +209,7 @@ func (pr Pairing) AssertFinalExponentiationIsOne(a *GTEl) {
// PairingCheck calculates the reduced pairing for a set of points and asserts if the result is One
// ∏ᵢ e(Pᵢ, Qᵢ) =? 1
//
// This function doesn't check that the inputs are in the correct subgroups. See AssertIsOnG1 and AssertIsOnG2.
// This function checks that the Qᵢ are in the correct subgroupsi, but does not check Pᵢ. See AssertIsOnG1.
func (pr Pairing) PairingCheck(P []*G1Affine, Q []*G2Affine) error {
f, err := pr.MillerLoop(P, Q)
if err != nil {
Expand Down Expand Up @@ -278,7 +278,7 @@ func (pr Pairing) computeG2ShortVector(Q *G2Affine) (_Q *G2Affine) {
psi3xxQ = pr.g2.psi(psi3xxQ)

// _Q = ψ³([2x₀]Q) - ψ²([x₀]Q) - ψ([x₀]Q) - [x₀]Q
_Q = pr.g2.sub(psi2xQ, psi3xxQ)
_Q = pr.g2.sub(psi3xxQ, psi2xQ)
_Q = pr.g2.sub(_Q, psixQ)
_Q = pr.g2.sub(_Q, xQ)
return _Q
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14 changes: 14 additions & 0 deletions std/algebra/emulated/sw_bn254/precomputations.go
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Expand Up @@ -31,6 +31,10 @@ func precomputeLines(Q bn254.G2Affine) lineEvaluations {

func (p *Pairing) computeLines(Q *g2AffP) lineEvaluations {

// check Q is on curve
Qaff := G2Affine{P: *Q, Lines: nil}
p.IsOnTwist(&Qaff)

var cLines lineEvaluations
Qacc := Q
n := len(bn254.LoopCounter)
Expand All @@ -50,6 +54,16 @@ func (p *Pairing) computeLines(Q *g2AffP) lineEvaluations {
}
}

// check Q is on G2 subgroup:
// [r]Q == 0 <==> [6x₀+2]Q + ψ(Q) + ψ³(Q) = ψ²(Q).
// At this point Qacc = [6x₀+2]Q
psiQ := p.g2.psi(&Qaff) // ψ(Q)
psi2Q := p.g2.phi(&Qaff) // ϕ(Q)=ψ²(Q)
psi3Q := p.g2.psi(psi2Q) // ψ³(Q)
lhs := p.g2.add(&G2Affine{P: *Qacc, Lines: nil}, psiQ)
lhs = p.g2.add(lhs, psi3Q)
p.g2.AssertIsEqual(lhs, psi2Q)

Q1X := p.Ext2.Conjugate(&Q.X)
Q1X = p.Ext2.MulByNonResidue1Power2(Q1X)
Q1Y := p.Ext2.Conjugate(&Q.Y)
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7 changes: 2 additions & 5 deletions std/evmprecompiles/08-bnpairing.go
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Expand Up @@ -40,11 +40,8 @@ func ECPair(api frontend.API, P []*sw_bn254.G1Affine, Q []*sw_bn254.G2Affine) {
if err != nil {
panic(err)
}
// 1- Check that Pᵢ are on G1 (done in the zkEVM ⚠️ )
// 2- Check that Qᵢ are on G2
for i := 0; i < len(Q); i++ {
pair.AssertIsOnG2(Q[i])
}
// 1- Check that Pᵢ are on G1 (done in the zkEVM ⚠️
// 2- Check that Qᵢ are on G2 (done in `computeLines` in `MillerLoopAndMul` and `MillerLoopAndFinalExpCheck)

// 3- Check that ∏ᵢ e(Pᵢ, Qᵢ) == 1
ml := pair.Ext12.One()
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