github.com/nova-foundation/go-ethereum@v1.0.1/crypto/bls12381/pairing_test.go (about)

     1  package bls12381
     2  
     3  import (
     4  	"math/big"
     5  	"testing"
     6  
     7  	"github.com/Nova-foundation/go-ethereum/common"
     8  )
     9  
    10  func TestPairingExpected(t *testing.T) {
    11  	bls := NewPairingEngine()
    12  	G1, G2 := bls.G1, bls.G2
    13  	GT := bls.GT()
    14  	expected, err := GT.FromBytes(
    15  		common.FromHex("" +
    16  			"0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
    17  			"04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
    18  			"03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
    19  			"11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
    20  			"06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
    21  			"19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
    22  			"018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
    23  			"01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
    24  			"193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
    25  			"1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
    26  			"089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
    27  			"1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
    28  		),
    29  	)
    30  	if err != nil {
    31  		t.Fatal(err)
    32  	}
    33  	r := bls.AddPair(G1.One(), G2.One()).Result()
    34  	if !r.Equal(expected) {
    35  		t.Fatal("bad pairing")
    36  	}
    37  	if !GT.IsValid(r) {
    38  		t.Fatal("element is not in correct subgroup")
    39  	}
    40  }
    41  
    42  func TestPairingNonDegeneracy(t *testing.T) {
    43  	bls := NewPairingEngine()
    44  	G1, G2 := bls.G1, bls.G2
    45  	g1Zero, g2Zero, g1One, g2One := G1.Zero(), G2.Zero(), G1.One(), G2.One()
    46  	GT := bls.GT()
    47  	// e(g1^a, g2^b) != 1
    48  	bls.Reset()
    49  	{
    50  		bls.AddPair(g1One, g2One)
    51  		e := bls.Result()
    52  		if e.IsOne() {
    53  			t.Fatal("pairing result is not expected to be one")
    54  		}
    55  		if !GT.IsValid(e) {
    56  			t.Fatal("pairing result is not valid")
    57  		}
    58  	}
    59  	// e(g1^a, 0) == 1
    60  	bls.Reset()
    61  	{
    62  		bls.AddPair(g1One, g2Zero)
    63  		e := bls.Result()
    64  		if !e.IsOne() {
    65  			t.Fatal("pairing result is expected to be one")
    66  		}
    67  	}
    68  	// e(0, g2^b) == 1
    69  	bls.Reset()
    70  	{
    71  		bls.AddPair(g1Zero, g2One)
    72  		e := bls.Result()
    73  		if !e.IsOne() {
    74  			t.Fatal("pairing result is expected to be one")
    75  		}
    76  	}
    77  	//
    78  	bls.Reset()
    79  	{
    80  		bls.AddPair(g1Zero, g2One)
    81  		bls.AddPair(g1One, g2Zero)
    82  		bls.AddPair(g1Zero, g2Zero)
    83  		e := bls.Result()
    84  		if !e.IsOne() {
    85  			t.Fatal("pairing result is expected to be one")
    86  		}
    87  	}
    88  	//
    89  	bls.Reset()
    90  	{
    91  		expected, err := GT.FromBytes(
    92  			common.FromHex("" +
    93  				"0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
    94  				"04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
    95  				"03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
    96  				"11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
    97  				"06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
    98  				"19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
    99  				"018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
   100  				"01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
   101  				"193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
   102  				"1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
   103  				"089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
   104  				"1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
   105  			),
   106  		)
   107  		if err != nil {
   108  			t.Fatal(err)
   109  		}
   110  		bls.AddPair(g1Zero, g2One)
   111  		bls.AddPair(g1One, g2Zero)
   112  		bls.AddPair(g1Zero, g2Zero)
   113  		bls.AddPair(g1One, g2One)
   114  		e := bls.Result()
   115  		if !e.Equal(expected) {
   116  			t.Fatal("bad pairing")
   117  		}
   118  	}
   119  }
   120  
   121  func TestPairingBilinearity(t *testing.T) {
   122  	bls := NewPairingEngine()
   123  	g1, g2 := bls.G1, bls.G2
   124  	gt := bls.GT()
   125  	// e(a*G1, b*G2) = e(G1, G2)^c
   126  	{
   127  		a, b := big.NewInt(17), big.NewInt(117)
   128  		c := new(big.Int).Mul(a, b)
   129  		G1, G2 := g1.One(), g2.One()
   130  		e0 := bls.AddPair(G1, G2).Result()
   131  		P1, P2 := g1.New(), g2.New()
   132  		g1.MulScalar(P1, G1, a)
   133  		g2.MulScalar(P2, G2, b)
   134  		e1 := bls.AddPair(P1, P2).Result()
   135  		gt.Exp(e0, e0, c)
   136  		if !e0.Equal(e1) {
   137  			t.Fatal("bad pairing, 1")
   138  		}
   139  	}
   140  	// e(a * G1, b * G2) = e((a + b) * G1, G2)
   141  	{
   142  		// scalars
   143  		a, b := big.NewInt(17), big.NewInt(117)
   144  		c := new(big.Int).Mul(a, b)
   145  		// LHS
   146  		G1, G2 := g1.One(), g2.One()
   147  		g1.MulScalar(G1, G1, c)
   148  		bls.AddPair(G1, G2)
   149  		// RHS
   150  		P1, P2 := g1.One(), g2.One()
   151  		g1.MulScalar(P1, P1, a)
   152  		g2.MulScalar(P2, P2, b)
   153  		bls.AddPairInv(P1, P2)
   154  		// should be one
   155  		if !bls.Check() {
   156  			t.Fatal("bad pairing, 2")
   157  		}
   158  	}
   159  	// e(a * G1, b * G2) = e((a + b) * G1, G2)
   160  	{
   161  		// scalars
   162  		a, b := big.NewInt(17), big.NewInt(117)
   163  		c := new(big.Int).Mul(a, b)
   164  		// LHS
   165  		G1, G2 := g1.One(), g2.One()
   166  		g2.MulScalar(G2, G2, c)
   167  		bls.AddPair(G1, G2)
   168  		// RHS
   169  		H1, H2 := g1.One(), g2.One()
   170  		g1.MulScalar(H1, H1, a)
   171  		g2.MulScalar(H2, H2, b)
   172  		bls.AddPairInv(H1, H2)
   173  		// should be one
   174  		if !bls.Check() {
   175  			t.Fatal("bad pairing, 3")
   176  		}
   177  	}
   178  }
   179  
   180  func TestPairingMulti(t *testing.T) {
   181  	// e(G1, G2) ^ t == e(a01 * G1, a02 * G2) * e(a11 * G1, a12 * G2) * ... * e(an1 * G1, an2 * G2)
   182  	// where t = sum(ai1 * ai2)
   183  	bls := NewPairingEngine()
   184  	g1, g2 := bls.G1, bls.G2
   185  	numOfPair := 100
   186  	targetExp := new(big.Int)
   187  	// RHS
   188  	for i := 0; i < numOfPair; i++ {
   189  		// (ai1 * G1, ai2 * G2)
   190  		a1, a2 := randScalar(q), randScalar(q)
   191  		P1, P2 := g1.One(), g2.One()
   192  		g1.MulScalar(P1, P1, a1)
   193  		g2.MulScalar(P2, P2, a2)
   194  		bls.AddPair(P1, P2)
   195  		// accumulate targetExp
   196  		// t += (ai1 * ai2)
   197  		a1.Mul(a1, a2)
   198  		targetExp.Add(targetExp, a1)
   199  	}
   200  	// LHS
   201  	// e(t * G1, G2)
   202  	T1, T2 := g1.One(), g2.One()
   203  	g1.MulScalar(T1, T1, targetExp)
   204  	bls.AddPairInv(T1, T2)
   205  	if !bls.Check() {
   206  		t.Fatal("fail multi pairing")
   207  	}
   208  }
   209  
   210  func TestPairingEmpty(t *testing.T) {
   211  	bls := NewPairingEngine()
   212  	if !bls.Check() {
   213  		t.Fatal("empty check should be accepted")
   214  	}
   215  	if !bls.Result().IsOne() {
   216  		t.Fatal("empty pairing result should be one")
   217  	}
   218  }
   219  
   220  func BenchmarkPairing(t *testing.B) {
   221  	bls := NewPairingEngine()
   222  	g1, g2, gt := bls.G1, bls.G2, bls.GT()
   223  	bls.AddPair(g1.One(), g2.One())
   224  	e := gt.New()
   225  	t.ResetTimer()
   226  	for i := 0; i < t.N; i++ {
   227  		e = bls.calculate()
   228  	}
   229  	_ = e
   230  }