tests/fuzzers/bn256: scale gnark result by constant

Author: MariusVanDerWijden

tests/fuzzers/bn256/bn256_fuzz.go

@@ -151,17 +151,34 @@ func FuzzPair(data []byte) int {
 	}
 
 	// Pair the two points and ensure they result in the same output
-	clPair := cloudflare.Pair(pc, tc).Marshal()
+	clPair := cloudflare.Pair(pc, tc).Marshal() // e_cloudflare(P, Q)
 	gPair := google.Pair(pg, tg).Marshal()
 	if !bytes.Equal(clPair, gPair) {
 		panic("pairing mismatch: cloudflare/google")
 	}
-
-	cPair, err := bn254.Pair([]bn254.G1Affine{*ps}, []bn254.G2Affine{*ts})
+	cPair, err := bn254.Pair([]bn254.G1Affine{*ps}, []bn254.G2Affine{*ts}) // e_gnark(-P, Q)
 	if err != nil {
 		panic(fmt.Sprintf("gnark/bn254 encountered error: %v", err))
 	}
-	if !bytes.Equal(clPair, cPair.Marshal()) {
+
+	// gnark uses a different pairing algorithm which might produce
+	// different but also correct outputs, we need to scale the output by s
+
+	u, _ := new(big.Int).SetString("0x44e992b44a6909f1", 0)
+	u_exp2 := new(big.Int).Exp(u, big.NewInt(2), nil)   // u^2
+	u_6_exp2 := new(big.Int).Mul(big.NewInt(6), u_exp2) // 6*u^2
+	u_3 := new(big.Int).Mul(big.NewInt(3), u)           // 3*u
+	inner := u_6_exp2.Add(u_6_exp2, u_3)                // 6*u^2 + 3*u
+	inner.Add(inner, big.NewInt(1))                     // 6*u^2 + 3*u + 1
+	u_2 := new(big.Int).Mul(big.NewInt(2), u)           // 2*u
+	s := u_2.Mul(u_2, inner)                            // 2*u(6*u^2 + 3*u + 1)
+
+	gRes := new(bn254.GT)
+	if err := gRes.SetBytes(clPair); err != nil {
+		panic(err)
+	}
+	gRes = gRes.Exp(*gRes, s)
+	if !bytes.Equal(cPair.Marshal(), gRes.Marshal()) {
 		panic("pairing mismatch: cloudflare/gnark")
 	}