gmsm/internal/sm9/bn256/bn_pair_test.go

package bn256

import (
	"crypto/rand"
	"math/big"
	"testing"
)

var expected1 = &gfP12{}
var expected_b2 = &gfP12{}
var expected_b2_2 = &gfP12{}

func init() {
	expected1.x.x.x = *newGFpFromHex("4e378fb5561cd0668f906b731ac58fee25738edf09cadc7a29c0abc0177aea6d")
	expected1.x.x.y = *newGFpFromHex("28b3404a61908f5d6198815c99af1990c8af38655930058c28c21bb539ce0000")
	expected1.x.y.x = *newGFpFromHex("38bffe40a22d529a0c66124b2c308dac9229912656f62b4facfced408e02380f")
	expected1.x.y.y = *newGFpFromHex("a01f2c8bee81769609462c69c96aa923fd863e209d3ce26dd889b55e2e3873db")
	expected1.y.x.x = *newGFpFromHex("67e0e0c2eed7a6993dce28fe9aa2ef56834307860839677f96685f2b44d0911f")
	expected1.y.x.y = *newGFpFromHex("5a1ae172102efd95df7338dbc577c66d8d6c15e0a0158c7507228efb078f42a6")
	expected1.y.y.x = *newGFpFromHex("1604a3fcfa9783e667ce9fcb1062c2a5c6685c316dda62de0548baa6ba30038b")
	expected1.y.y.y = *newGFpFromHex("93634f44fa13af76169f3cc8fbea880adaff8475d5fd28a75deb83c44362b439")
	expected1.z.x.x = *newGFpFromHex("b3129a75d31d17194675a1bc56947920898fbf390a5bf5d931ce6cbb3340f66d")
	expected1.z.x.y = *newGFpFromHex("4c744e69c4a2e1c8ed72f796d151a17ce2325b943260fc460b9f73cb57c9014b")
	expected1.z.y.x = *newGFpFromHex("84b87422330d7936eaba1109fa5a7a7181ee16f2438b0aeb2f38fd5f7554e57a")
	expected1.z.y.y = *newGFpFromHex("aab9f06a4eeba4323a7833db202e4e35639d93fa3305af73f0f071d7d284fcfb")

	expected_b2.x.x.x = *newGFpFromHex("28542FB6954C84BE6A5F2988A31CB6817BA0781966FA83D9673A9577D3C0C134")
	expected_b2.x.x.y = *newGFpFromHex("5E27C19FC02ED9AE37F5BB7BE9C03C2B87DE027539CCF03E6B7D36DE4AB45CD1")
	expected_b2.x.y.x = *newGFpFromHex("A1ABFCD30C57DB0F1A838E3A8F2BF823479C978BD137230506EA6249C891049E")
	expected_b2.x.y.y = *newGFpFromHex("3497477913AB89F5E2960F382B1B5C8EE09DE0FA498BA95C4409D630D343DA40")
	expected_b2.y.x.x = *newGFpFromHex("4FEC93472DA33A4DB6599095C0CF895E3A7B993EE5E4EBE3B9AB7D7D5FF2A3D1")
	expected_b2.y.x.y = *newGFpFromHex("647BA154C3E8E185DFC33657C1F128D480F3F7E3F16801208029E19434C733BB")
	expected_b2.y.y.x = *newGFpFromHex("73F21693C66FC23724DB26380C526223C705DAF6BA18B763A68623C86A632B05")
	expected_b2.y.y.y = *newGFpFromHex("0F63A071A6D62EA45B59A1942DFF5335D1A232C9C5664FAD5D6AF54C11418B0D")
	expected_b2.z.x.x = *newGFpFromHex("8C8E9D8D905780D50E779067F2C4B1C8F83A8B59D735BB52AF35F56730BDE5AC")
	expected_b2.z.x.y = *newGFpFromHex("861CCD9978617267CE4AD9789F77739E62F2E57B48C2FF26D2E90A79A1D86B93")
	expected_b2.z.y.x = *newGFpFromHex("9B1CA08F64712E33AEDA3F44BD6CB633E0F722211E344D73EC9BBEBC92142765")
	expected_b2.z.y.y = *newGFpFromHex("6BA584CE742A2A3AB41C15D3EF94EDEB8EF74A2BDCDAAECC09ABA567981F6437")

	expected_b2_2.x.x.x = *newGFpFromHex("1052D6E9D13E381909DFF7B2B41E13C987D0A9068423B769480DACCE6A06F492")
	expected_b2_2.x.x.y = *newGFpFromHex("5FFEB92AD870F97DC0893114DA22A44DBC9E7A8B6CA31A0CF0467265A1FB48C7")
	expected_b2_2.x.y.x = *newGFpFromHex("2C5C3B37E4F2FF83DB33D98C0317BCBBBBF4AC6DF6B89ECA58268B280045E612")
	expected_b2_2.x.y.y = *newGFpFromHex("6CED9E2D7C9CD3D5AD630DEFAB0B831506218037EE0F861CF9B43C78434AEC38")
	expected_b2_2.y.x.x = *newGFpFromHex("0AE7BF3E1AEC0CB67A03440906C7DFB3BCD4B6EEEBB7E371F0094AD4A816088D")
	expected_b2_2.y.x.y = *newGFpFromHex("98DBC791D0671CACA12236CDF8F39E15AEB96FAEB39606D5B04AC581746A663D")
	expected_b2_2.y.y.x = *newGFpFromHex("00DD2B7416BAA91172E89D5309D834F78C1E31B4483BB97185931BAD7BE1B9B5")
	expected_b2_2.y.y.y = *newGFpFromHex("7EBAC0349F8544469E60C32F6075FB0468A68147FF013537DF792FFCE024F857")
	expected_b2_2.z.x.x = *newGFpFromHex("10CC2B561A62B62DA36AEFD60850714F49170FD94A0010C6D4B651B64F3A3A5E")
	expected_b2_2.z.x.y = *newGFpFromHex("58C9687BEDDCD9E4FEDAB16B884D1FE6DFA117B2AB821F74E0BF7ACDA2269859")
	expected_b2_2.z.y.x = *newGFpFromHex("2A430968F16086061904CE201847934B11CA0F9E9528F5A9D0CE8F015C9AEA79")
	expected_b2_2.z.y.y = *newGFpFromHex("934FDDA6D3AB48C8571CE2354B79742AA498CB8CDDE6BD1FA5946345A1A652F6")
}

func Test_Pairing_A2(t *testing.T) {
	pk := bigFromHex("0130E78459D78545CB54C587E02CF480CE0B66340F319F348A1D5B1F2DC5F4")
	g2 := &G2{}
	_, err := g2.ScalarBaseMult(NormalizeScalar(pk.Bytes()))
	if err != nil {
		t.Fatal(err)
	}
	ret := pairing(g2.p, curveGen)
	if ret.x != expected1.x || ret.y != expected1.y || ret.z != expected1.z {
		t.Errorf("not expected")
	}
}

func Test_Pairing_B2(t *testing.T) {
	deB := &twistPoint{}
	deB.x.x = *newGFpFromHex("74CCC3AC9C383C60AF083972B96D05C75F12C8907D128A17ADAFBAB8C5A4ACF7")
	deB.x.y = *newGFpFromHex("01092FF4DE89362670C21711B6DBE52DCD5F8E40C6654B3DECE573C2AB3D29B2")
	deB.y.x = *newGFpFromHex("44B0294AA04290E1524FF3E3DA8CFD432BB64DE3A8040B5B88D1B5FC86A4EBC1")
	deB.y.y = *newGFpFromHex("8CFC48FB4FF37F1E27727464F3C34E2153861AD08E972D1625FC1A7BD18D5539")
	deB.z.SetOne()
	deB.t.SetOne()

	rA := &curvePoint{}
	rA.x = *newGFpFromHex("7CBA5B19069EE66AA79D490413D11846B9BA76DD22567F809CF23B6D964BB265")
	rA.y = *newGFpFromHex("A9760C99CB6F706343FED05637085864958D6C90902ABA7D405FBEDF7B781599")
	rA.z = *one
	rA.t = *one

	ret := pairing(deB, rA)
	if ret.x != expected_b2.x || ret.y != expected_b2.y || ret.z != expected_b2.z {
		t.Errorf("not expected")
	}
}

func Test_Pairing_B2_2(t *testing.T) {
	pubE := &curvePoint{}
	pubE.x = *newGFpFromHex("9174542668E8F14AB273C0945C3690C66E5DD09678B86F734C4350567ED06283")
	pubE.y = *newGFpFromHex("54E598C6BF749A3DACC9FFFEDD9DB6866C50457CFC7AA2A4AD65C3168FF74210")
	pubE.z = *one
	pubE.t = *one

	ret := pairing(twistGen, pubE)
	ret.Exp(ret, bigFromHex("00018B98C44BEF9F8537FB7D071B2C928B3BC65BD3D69E1EEE213564905634FE"))
	if ret.x != expected_b2_2.x || ret.y != expected_b2_2.y || ret.z != expected_b2_2.z {
		t.Errorf("not expected")
	}
}

var testGfp12 = &gfP12{
	gfP4{
		gfP2{
			*newGFpFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141"),
			*newGFpFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B"),
		},
		gfP2{
			*newGFpFromHex("17509B092E845C1266BA0D262CBEE6ED0736A96FA347C8BD856DC76B84EBEB96"),
			*newGFpFromHex("A7CF28D519BE3DA65F3170153D278FF247EFBA98A71A08116215BBA5C999A7C7"),
		},
	},
	gfP4{
		gfP2{
			*newGFpFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141"),
			*newGFpFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B"),
		},
		gfP2{
			*newGFpFromHex("17509B092E845C1266BA0D262CBEE6ED0736A96FA347C8BD856DC76B84EBEB96"),
			*newGFpFromHex("A7CF28D519BE3DA65F3170153D278FF247EFBA98A71A08116215BBA5C999A7C7"),
		},
	},
	gfP4{
		gfP2{
			*newGFpFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141"),
			*newGFpFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B"),
		},
		gfP2{
			*newGFpFromHex("17509B092E845C1266BA0D262CBEE6ED0736A96FA347C8BD856DC76B84EBEB96"),
			*newGFpFromHex("A7CF28D519BE3DA65F3170153D278FF247EFBA98A71A08116215BBA5C999A7C7"),
		},
	},
}

func Test_finalExponentiation(t *testing.T) {
	x := testGfp12
	got := finalExponentiation(x)

	exp := new(big.Int).Exp(p, big.NewInt(12), nil)
	exp.Sub(exp, big.NewInt(1))
	exp.Div(exp, Order)
	expected := (&gfP12{}).Exp(x, exp)

	if got.x != expected.x || got.y != expected.y || got.z != expected.z {
		t.Errorf("got %v, expected %v\n", got, expected)
	}
}

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)
	exp.Sub(exp, big.NewInt(1))
	exp.Div(exp, Order)
	expected := (&gfP12{}).Exp(x, exp)

	b.ReportAllocs()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		got := finalExponentiation(x)
		if *got != *expected {
			b.Errorf("got %v, expected %v\n", got, expected)
		}
	}
}

func BenchmarkMiller(b *testing.B) {
	pk := bigFromHex("0130E78459D78545CB54C587E02CF480CE0B66340F319F348A1D5B1F2DC5F4")
	g2 := &G2{}
	_, err := g2.ScalarBaseMult(NormalizeScalar(pk.Bytes()))
	if err != nil {
		b.Fatal(err)
	}
	b.ReportAllocs()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		miller(g2.p, curveGen)
	}
}

func BenchmarkPairingB4(b *testing.B) {
	pk := bigFromHex("0130E78459D78545CB54C587E02CF480CE0B66340F319F348A1D5B1F2DC5F4")
	g2 := &G2{}
	_, err := g2.ScalarBaseMult(NormalizeScalar(pk.Bytes()))
	if err != nil {
		b.Fatal(err)
	}
	b.ReportAllocs()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		ret := pairing(g2.p, curveGen)
		if *ret != *expected1 {
			b.Errorf("not expected")
		}
	}
}