sm9/bn256: add bilinearity test case

sm9/bn256/bn_pair_b6.go

@@ -50,7 +50,7 @@ func millerB6(q *twistPoint, p *curvePoint) *gfP12b6 {
 	r := &twistPoint{}
 	r.Set(aAffine)
 
-	r2 := (&gfP2{}).Square(&aAffine.y)
+	r2 := (&gfP2{}).SquareNC(&aAffine.y)
 
 	a, b, c := &gfP2{}, &gfP2{}, &gfP2{}
 	newR := &twistPoint{}

sm9/bn256/bn_pair_b6_test.go

@@ -1,6 +1,7 @@
 package bn256
 
 import (
+	"crypto/rand"
 	"fmt"
 	"math/big"
 	"testing"
@@ -81,6 +82,22 @@ func Test_PairingB6_B2_2(t *testing.T) {
 	}
 }
 
+func TestBilinearityB6(t *testing.T) {
+	for i := 0; i < 2; i++ {
+		a, p1, _ := RandomG1(rand.Reader)
+		b, p2, _ := RandomG2(rand.Reader)
+		e1 := pairingB6(p2.p, p1.p)
+
+		e2 := pairingB6(twistGen, curveGen)
+		e2.Exp(e2, a)
+		e2.Exp(e2, b)
+
+		if *e1 != *e2 {
+			t.Fatalf("bad pairing result: %s", e1)
+		}
+	}
+}
+
 func BenchmarkFinalExponentiationB6(b *testing.B) {
 	x := &gfP12b6{
 		p6,

sm9/bn256/bn_pair_test.go

@@ -1,6 +1,7 @@
 package bn256
 
 import (
+	"crypto/rand"
 	"math/big"
 	"testing"
 )
@@ -145,6 +146,22 @@ func Test_finalExponentiation(t *testing.T) {
 	}
 }
 
+func TestBilinearity(t *testing.T) {
+	for i := 0; i < 2; i++ {
+		a, p1, _ := RandomG1(rand.Reader)
+		b, p2, _ := RandomG2(rand.Reader)
+		e1 := Pair(p1, p2)
+
+		e2 := Pair(&G1{curveGen}, &G2{twistGen})
+		e2.ScalarMult(e2, a)
+		e2.ScalarMult(e2, b)
+
+		if *e1.p != *e2.p {
+			t.Fatalf("bad pairing result: %s", e1)
+		}
+	}
+}
+
 func BenchmarkFinalExponentiation(b *testing.B) {
 	x := testGfp12
 	exp := new(big.Int).Exp(p, big.NewInt(12), nil)

sm9/bn256/gfp6.go

@@ -156,7 +156,7 @@ func (e *gfP6) MulS(a *gfP6) *gfP6 {
 	tz := &gfP2{}
 
 	tz.x.Set(&a.x.y)
-	gfpAdd(&tz.y, &a.x.x, &a.x.x)
+	gfpDouble(&tz.y, &a.x.x)
 	gfpNeg(&tz.y, &tz.y)
 
 	e.y.Set(&a.z)

sm9/bn256/gfp_test.go

@@ -286,3 +286,23 @@ func BenchmarkGfPNeg2(b *testing.B) {
 		gfpSub(ret, zero, x)
 	}
 }
+
+func BenchmarkGfPInvert(b *testing.B) {
+	x := fromBigInt(bigFromHex("9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596"))
+	b.ReportAllocs()
+	b.ResetTimer()
+	ret := &gfP{}
+	for i := 0; i < b.N; i++ {
+		ret.Invert(x)
+	}
+}
+
+func BenchmarkGfPInvert2(b *testing.B) {
+	x := fromBigInt(bigFromHex("9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596"))
+	b.ReportAllocs()
+	b.ResetTimer()
+	ret := &gfP{}
+	for i := 0; i < b.N; i++ {
+		ret.exp(x, pMinus2)
+	}
+}