package bls12381 import ( "bytes" "crypto/rand" "math/big" "testing" ) func TestFpSerialization(t *testing.T) { t.Run("zero", func(t *testing.T) { in := make([]byte, 48) fe, err := fromBytes(in) if err != nil { t.Fatal(err) } if !fe.isZero() { t.Fatal("bad serialization") } if !bytes.Equal(in, toBytes(fe)) { t.Fatal("bad serialization") } }) t.Run("bytes", func(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, err := fromBytes(toBytes(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad serialization") } } }) t.Run("string", func(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, err := fromString(toString(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad encoding or decoding") } } }) t.Run("big", func(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, err := fromBig(toBig(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad encoding or decoding") } } }) } func TestFpAdditionCrossAgainstBigInt(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) c := new(fe) big_a := toBig(a) big_b := toBig(b) big_c := new(big.Int) add(c, a, b) out_1 := toBytes(c) out_2 := padBytes(big_c.Add(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied A") } double(c, a) out_1 = toBytes(c) out_2 = padBytes(big_c.Add(big_a, big_a).Mod(big_c, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied B") } sub(c, a, b) out_1 = toBytes(c) out_2 = padBytes(big_c.Sub(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied C") } neg(c, a) out_1 = toBytes(c) out_2 = padBytes(big_c.Neg(big_a).Mod(big_c, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied D") } } } func TestFpAdditionCrossAgainstBigIntAssigned(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) big_a, big_b := toBig(a), toBig(b) addAssign(a, b) out_1 := toBytes(a) out_2 := padBytes(big_a.Add(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied A") } a, _ = new(fe).rand(rand.Reader) big_a = toBig(a) doubleAssign(a) out_1 = toBytes(a) out_2 = padBytes(big_a.Add(big_a, big_a).Mod(big_a, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied B") } a, _ = new(fe).rand(rand.Reader) b, _ = new(fe).rand(rand.Reader) big_a, big_b = toBig(a), toBig(b) subAssign(a, b) out_1 = toBytes(a) out_2 = padBytes(big_a.Sub(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied A") } } } func TestFpAdditionProperties(t *testing.T) { for i := 0; i < fuz; i++ { zero := new(fe).zero() a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) c_1, c_2 := new(fe), new(fe) add(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a + 0 == a") } sub(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a - 0 == a") } double(c_1, zero) if !c_1.equal(zero) { t.Fatal("2 * 0 == 0") } neg(c_1, zero) if !c_1.equal(zero) { t.Fatal("-0 == 0") } sub(c_1, zero, a) neg(c_2, a) if !c_1.equal(c_2) { t.Fatal("0-a == -a") } double(c_1, a) add(c_2, a, a) if !c_1.equal(c_2) { t.Fatal("2 * a == a + a") } add(c_1, a, b) add(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } sub(c_1, a, b) sub(c_2, b, a) neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } c_x, _ := new(fe).rand(rand.Reader) add(c_1, a, b) add(c_1, c_1, c_x) add(c_2, a, c_x) add(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a + b) + c == (a + c ) + b") } sub(c_1, a, b) sub(c_1, c_1, c_x) sub(c_2, a, c_x) sub(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a - b) - c == (a - c ) -b") } } } func TestFpAdditionPropertiesAssigned(t *testing.T) { for i := 0; i < fuz; i++ { zero := new(fe).zero() a, b := new(fe), new(fe) _, _ = a.rand(rand.Reader) b.set(a) addAssign(a, zero) if !a.equal(b) { t.Fatal("a + 0 == a") } subAssign(a, zero) if !a.equal(b) { t.Fatal("a - 0 == a") } a.set(zero) doubleAssign(a) if !a.equal(zero) { t.Fatal("2 * 0 == 0") } a.set(zero) subAssign(a, b) neg(b, b) if !a.equal(b) { t.Fatal("0-a == -a") } _, _ = a.rand(rand.Reader) b.set(a) doubleAssign(a) addAssign(b, b) if !a.equal(b) { t.Fatal("2 * a == a + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1, c_2 := new(fe).set(a), new(fe).set(b) addAssign(c_1, b) addAssign(c_2, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1.set(a) c_2.set(b) subAssign(c_1, b) subAssign(c_2, a) neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c, _ := new(fe).rand(rand.Reader) a0 := new(fe).set(a) addAssign(a, b) addAssign(a, c) addAssign(b, c) addAssign(b, a0) if !a.equal(b) { t.Fatal("(a + b) + c == (b + c) + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) _, _ = c.rand(rand.Reader) a0.set(a) subAssign(a, b) subAssign(a, c) subAssign(a0, c) subAssign(a0, b) if !a.equal(a0) { t.Fatal("(a - b) - c == (a - c) -b") } } } func TestFpLazyOperations(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) c, _ := new(fe).rand(rand.Reader) c0 := new(fe) c1 := new(fe) ladd(c0, a, b) add(c1, a, b) mul(c0, c0, c) mul(c1, c1, c) if !c0.equal(c1) { // l+ operator stands for lazy addition t.Fatal("(a + b) * c == (a l+ b) * c") } _, _ = a.rand(rand.Reader) b.set(a) ldouble(a, a) ladd(b, b, b) if !a.equal(b) { t.Fatal("2 l* a = a l+ a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) _, _ = c.rand(rand.Reader) a0 := new(fe).set(a) lsubAssign(a, b) laddAssign(a, &modulus) mul(a, a, c) subAssign(a0, b) mul(a0, a0, c) if !a.equal(a0) { t.Fatal("((a l- b) + p) * c = (a-b) * c") } } } func TestFpMultiplicationCrossAgainstBigInt(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) c := new(fe) big_a := toBig(a) big_b := toBig(b) big_c := new(big.Int) mul(c, a, b) out_1 := toBytes(c) out_2 := padBytes(big_c.Mul(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48) if !bytes.Equal(out_1, out_2) { t.Fatal("cross test against big.Int is not satisfied") } } } func TestFpMultiplicationProperties(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) zero, one := new(fe).zero(), new(fe).one() c_1, c_2 := new(fe), new(fe) mul(c_1, a, zero) if !c_1.equal(zero) { t.Fatal("a * 0 == 0") } mul(c_1, a, one) if !c_1.equal(a) { t.Fatal("a * 1 == a") } mul(c_1, a, b) mul(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a * b == b * a") } c_x, _ := new(fe).rand(rand.Reader) mul(c_1, a, b) mul(c_1, c_1, c_x) mul(c_2, c_x, b) mul(c_2, c_2, a) if !c_1.equal(c_2) { t.Fatal("(a * b) * c == (a * c) * b") } square(a, zero) if !a.equal(zero) { t.Fatal("0^2 == 0") } square(a, one) if !a.equal(one) { t.Fatal("1^2 == 1") } _, _ = a.rand(rand.Reader) square(c_1, a) mul(c_2, a, a) if !c_1.equal(c_1) { t.Fatal("a^2 == a*a") } } } func TestFpExponentiation(t *testing.T) { for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) u := new(fe) exp(u, a, big.NewInt(0)) if !u.isOne() { t.Fatal("a^0 == 1") } exp(u, a, big.NewInt(1)) if !u.equal(a) { t.Fatal("a^1 == a") } v := new(fe) mul(u, a, a) mul(u, u, u) mul(u, u, u) exp(v, a, big.NewInt(8)) if !u.equal(v) { t.Fatal("((a^2)^2)^2 == a^8") } p := modulus.big() exp(u, a, p) if !u.equal(a) { t.Fatal("a^p == a") } exp(u, a, p.Sub(p, big.NewInt(1))) if !u.isOne() { t.Fatal("a^(p-1) == 1") } } } func TestFpInversion(t *testing.T) { for i := 0; i < fuz; i++ { u := new(fe) zero, one := new(fe).zero(), new(fe).one() inverse(u, zero) if !u.equal(zero) { t.Fatal("(0^-1) == 0)") } inverse(u, one) if !u.equal(one) { t.Fatal("(1^-1) == 1)") } a, _ := new(fe).rand(rand.Reader) inverse(u, a) mul(u, u, a) if !u.equal(one) { t.Fatal("(r*a) * r*(a^-1) == r)") } v := new(fe) p := modulus.big() exp(u, a, p.Sub(p, big.NewInt(2))) inverse(v, a) if !v.equal(u) { t.Fatal("a^(p-2) == a^-1") } } } func TestFpSquareRoot(t *testing.T) { r := new(fe) if sqrt(r, nonResidue1) { t.Fatal("non residue cannot have a sqrt") } for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) aa, rr, r := &fe{}, &fe{}, &fe{} square(aa, a) if !sqrt(r, aa) { t.Fatal("bad sqrt 1") } square(rr, r) if !rr.equal(aa) { t.Fatal("bad sqrt 2") } } } func TestFpNonResidue(t *testing.T) { if !isQuadraticNonResidue(nonResidue1) { t.Fatal("element is quadratic non residue, 1") } if isQuadraticNonResidue(new(fe).one()) { t.Fatal("one is not quadratic non residue") } if !isQuadraticNonResidue(new(fe).zero()) { t.Fatal("should accept zero as quadratic non residue") } for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) square(a, a) if isQuadraticNonResidue(new(fe).one()) { t.Fatal("element is not quadratic non residue") } } for i := 0; i < fuz; i++ { a, _ := new(fe).rand(rand.Reader) if !sqrt(new(fe), a) { if !isQuadraticNonResidue(a) { t.Fatal("element is quadratic non residue, 2", i) } } else { i -= 1 } } } func TestFp2Serialization(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) b, err := field.fromBytes(field.toBytes(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad serialization") } } } func TestFp2AdditionProperties(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { zero := field.zero() a, _ := new(fe2).rand(rand.Reader) b, _ := new(fe2).rand(rand.Reader) c_1 := field.new() c_2 := field.new() field.add(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a + 0 == a") } field.sub(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a - 0 == a") } field.double(c_1, zero) if !c_1.equal(zero) { t.Fatal("2 * 0 == 0") } field.neg(c_1, zero) if !c_1.equal(zero) { t.Fatal("-0 == 0") } field.sub(c_1, zero, a) field.neg(c_2, a) if !c_1.equal(c_2) { t.Fatal("0-a == -a") } field.double(c_1, a) field.add(c_2, a, a) if !c_1.equal(c_2) { t.Fatal("2 * a == a + a") } field.add(c_1, a, b) field.add(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } field.sub(c_1, a, b) field.sub(c_2, b, a) field.neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } c_x, _ := new(fe2).rand(rand.Reader) field.add(c_1, a, b) field.add(c_1, c_1, c_x) field.add(c_2, a, c_x) field.add(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a + b) + c == (a + c ) + b") } field.sub(c_1, a, b) field.sub(c_1, c_1, c_x) field.sub(c_2, a, c_x) field.sub(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a - b) - c == (a - c ) -b") } } } func TestFp2AdditionPropertiesAssigned(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { zero := new(fe2).zero() a, b := new(fe2), new(fe2) _, _ = a.rand(rand.Reader) b.set(a) field.addAssign(a, zero) if !a.equal(b) { t.Fatal("a + 0 == a") } field.subAssign(a, zero) if !a.equal(b) { t.Fatal("a - 0 == a") } a.set(zero) field.doubleAssign(a) if !a.equal(zero) { t.Fatal("2 * 0 == 0") } a.set(zero) field.subAssign(a, b) field.neg(b, b) if !a.equal(b) { t.Fatal("0-a == -a") } _, _ = a.rand(rand.Reader) b.set(a) field.doubleAssign(a) field.addAssign(b, b) if !a.equal(b) { t.Fatal("2 * a == a + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1, c_2 := new(fe2).set(a), new(fe2).set(b) field.addAssign(c_1, b) field.addAssign(c_2, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1.set(a) c_2.set(b) field.subAssign(c_1, b) field.subAssign(c_2, a) field.neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c, _ := new(fe2).rand(rand.Reader) a0 := new(fe2).set(a) field.addAssign(a, b) field.addAssign(a, c) field.addAssign(b, c) field.addAssign(b, a0) if !a.equal(b) { t.Fatal("(a + b) + c == (b + c) + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) _, _ = c.rand(rand.Reader) a0.set(a) field.subAssign(a, b) field.subAssign(a, c) field.subAssign(a0, c) field.subAssign(a0, b) if !a.equal(a0) { t.Fatal("(a - b) - c == (a - c) -b") } } } func TestFp2LazyOperations(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) b, _ := new(fe2).rand(rand.Reader) c, _ := new(fe2).rand(rand.Reader) c0 := new(fe2) c1 := new(fe2) field.ladd(c0, a, b) field.add(c1, a, b) field.mulAssign(c0, c) field.mulAssign(c1, c) if !c0.equal(c1) { // l+ operator stands for lazy addition t.Fatal("(a + b) * c == (a l+ b) * c") } _, _ = a.rand(rand.Reader) b.set(a) field.ldouble(a, a) field.ladd(b, b, b) if !a.equal(b) { t.Fatal("2 l* a = a l+ a") } } } func TestFp2MultiplicationProperties(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) b, _ := new(fe2).rand(rand.Reader) zero := field.zero() one := field.one() c_1, c_2 := field.new(), field.new() field.mul(c_1, a, zero) if !c_1.equal(zero) { t.Fatal("a * 0 == 0") } field.mul(c_1, a, one) if !c_1.equal(a) { t.Fatal("a * 1 == a") } field.mul(c_1, a, b) field.mul(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a * b == b * a") } c_x, _ := new(fe2).rand(rand.Reader) field.mul(c_1, a, b) field.mul(c_1, c_1, c_x) field.mul(c_2, c_x, b) field.mul(c_2, c_2, a) if !c_1.equal(c_2) { t.Fatal("(a * b) * c == (a * c) * b") } field.square(a, zero) if !a.equal(zero) { t.Fatal("0^2 == 0") } field.square(a, one) if !a.equal(one) { t.Fatal("1^2 == 1") } _, _ = a.rand(rand.Reader) field.square(c_1, a) field.mul(c_2, a, a) if !c_2.equal(c_1) { t.Fatal("a^2 == a*a") } } } func TestFp2MultiplicationPropertiesAssigned(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) zero, one := new(fe2).zero(), new(fe2).one() field.mulAssign(a, zero) if !a.equal(zero) { t.Fatal("a * 0 == 0") } _, _ = a.rand(rand.Reader) a0 := new(fe2).set(a) field.mulAssign(a, one) if !a.equal(a0) { t.Fatal("a * 1 == a") } _, _ = a.rand(rand.Reader) b, _ := new(fe2).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(b, a0) if !a.equal(b) { t.Fatal("a * b == b * a") } c, _ := new(fe2).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(a, c) field.mulAssign(a0, c) field.mulAssign(a0, b) if !a.equal(a0) { t.Fatal("(a * b) * c == (a * c) * b") } a0.set(a) field.squareAssign(a) field.mulAssign(a0, a0) if !a.equal(a0) { t.Fatal("a^2 == a*a") } } } func TestFp2Exponentiation(t *testing.T) { field := newFp2() for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) u := field.new() field.exp(u, a, big.NewInt(0)) if !u.equal(field.one()) { t.Fatal("a^0 == 1") } field.exp(u, a, big.NewInt(1)) if !u.equal(a) { t.Fatal("a^1 == a") } v := field.new() field.mul(u, a, a) field.mul(u, u, u) field.mul(u, u, u) field.exp(v, a, big.NewInt(8)) if !u.equal(v) { t.Fatal("((a^2)^2)^2 == a^8") } } } func TestFp2Inversion(t *testing.T) { field := newFp2() u := field.new() zero := field.zero() one := field.one() field.inverse(u, zero) if !u.equal(zero) { t.Fatal("(0 ^ -1) == 0)") } field.inverse(u, one) if !u.equal(one) { t.Fatal("(1 ^ -1) == 1)") } for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) field.inverse(u, a) field.mul(u, u, a) if !u.equal(one) { t.Fatal("(r * a) * r * (a ^ -1) == r)") } } } func TestFp2SquareRoot(t *testing.T) { field := newFp2() for z := 0; z < 1000; z++ { zi := new(fe) sub(zi, &modulus, &fe{uint64(z * z)}) // r = (-z*z, 0) r := &fe2{*zi, fe{0}} toMont(&r[0], &r[0]) toMont(&r[1], &r[1]) c := field.new() // sqrt((-z*z, 0)) = (0, z) if !field.sqrt(c, r) { t.Fatal("z*z does have a square root") } e := &fe2{fe{uint64(0)}, fe{uint64(z)}} toMont(&e[0], &e[0]) toMont(&e[1], &e[1]) field.square(e, e) field.square(c, c) if !e.equal(c) { t.Fatal("square root failed") } } if field.sqrt(field.new(), nonResidue2) { t.Fatal("non residue cannot have a sqrt") } for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) aa, rr, r := field.new(), field.new(), field.new() field.square(aa, a) if !field.sqrt(r, aa) { t.Fatal("bad sqrt 1") } field.square(rr, r) if !rr.equal(aa) { t.Fatal("bad sqrt 2") } } } func TestFp2NonResidue(t *testing.T) { field := newFp2() if !field.isQuadraticNonResidue(nonResidue2) { t.Fatal("element is quadratic non residue, 1") } if field.isQuadraticNonResidue(new(fe2).one()) { t.Fatal("one is not quadratic non residue") } if !field.isQuadraticNonResidue(new(fe2).zero()) { t.Fatal("should accept zero as quadratic non residue") } for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) field.squareAssign(a) if field.isQuadraticNonResidue(new(fe2).one()) { t.Fatal("element is not quadratic non residue") } } for i := 0; i < fuz; i++ { a, _ := new(fe2).rand(rand.Reader) if !field.sqrt(new(fe2), a) { if !field.isQuadraticNonResidue(a) { t.Fatal("element is quadratic non residue, 2", i) } } else { i -= 1 } } } func TestFp6Serialization(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { a, _ := new(fe6).rand(rand.Reader) b, err := field.fromBytes(field.toBytes(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad serialization") } } } func TestFp6AdditionProperties(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { zero := field.zero() a, _ := new(fe6).rand(rand.Reader) b, _ := new(fe6).rand(rand.Reader) c_1 := field.new() c_2 := field.new() field.add(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a + 0 == a") } field.sub(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a - 0 == a") } field.double(c_1, zero) if !c_1.equal(zero) { t.Fatal("2 * 0 == 0") } field.neg(c_1, zero) if !c_1.equal(zero) { t.Fatal("-0 == 0") } field.sub(c_1, zero, a) field.neg(c_2, a) if !c_1.equal(c_2) { t.Fatal("0-a == -a") } field.double(c_1, a) field.add(c_2, a, a) if !c_1.equal(c_2) { t.Fatal("2 * a == a + a") } field.add(c_1, a, b) field.add(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } field.sub(c_1, a, b) field.sub(c_2, b, a) field.neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } c_x, _ := new(fe6).rand(rand.Reader) field.add(c_1, a, b) field.add(c_1, c_1, c_x) field.add(c_2, a, c_x) field.add(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a + b) + c == (a + c ) + b") } field.sub(c_1, a, b) field.sub(c_1, c_1, c_x) field.sub(c_2, a, c_x) field.sub(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a - b) - c == (a - c ) -b") } } } func TestFp6AdditionPropertiesAssigned(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { zero := new(fe6).zero() a, b := new(fe6), new(fe6) _, _ = a.rand(rand.Reader) b.set(a) field.addAssign(a, zero) if !a.equal(b) { t.Fatal("a + 0 == a") } field.subAssign(a, zero) if !a.equal(b) { t.Fatal("a - 0 == a") } a.set(zero) field.doubleAssign(a) if !a.equal(zero) { t.Fatal("2 * 0 == 0") } a.set(zero) field.subAssign(a, b) field.neg(b, b) if !a.equal(b) { t.Fatal("0-a == -a") } _, _ = a.rand(rand.Reader) b.set(a) field.doubleAssign(a) field.addAssign(b, b) if !a.equal(b) { t.Fatal("2 * a == a + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1, c_2 := new(fe6).set(a), new(fe6).set(b) field.addAssign(c_1, b) field.addAssign(c_2, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c_1.set(a) c_2.set(b) field.subAssign(c_1, b) field.subAssign(c_2, a) field.neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) c, _ := new(fe6).rand(rand.Reader) a0 := new(fe6).set(a) field.addAssign(a, b) field.addAssign(a, c) field.addAssign(b, c) field.addAssign(b, a0) if !a.equal(b) { t.Fatal("(a + b) + c == (b + c) + a") } _, _ = a.rand(rand.Reader) _, _ = b.rand(rand.Reader) _, _ = c.rand(rand.Reader) a0.set(a) field.subAssign(a, b) field.subAssign(a, c) field.subAssign(a0, c) field.subAssign(a0, b) if !a.equal(a0) { t.Fatal("(a - b) - c == (a - c) -b") } } } func TestFp6SparseMultiplication(t *testing.T) { fp6 := newFp6(nil) var a, b, u *fe6 for j := 0; j < fuz; j++ { a, _ = new(fe6).rand(rand.Reader) b, _ = new(fe6).rand(rand.Reader) u, _ = new(fe6).rand(rand.Reader) b[2].zero() fp6.mul(u, a, b) fp6.mulBy01(a, a, &b[0], &b[1]) if !a.equal(u) { t.Fatal("bad mul by 01") } } for j := 0; j < fuz; j++ { a, _ = new(fe6).rand(rand.Reader) b, _ = new(fe6).rand(rand.Reader) u, _ = new(fe6).rand(rand.Reader) b[2].zero() b[0].zero() fp6.mul(u, a, b) fp6.mulBy1(a, a, &b[1]) if !a.equal(u) { t.Fatal("bad mul by 1") } } } func TestFp6MultiplicationProperties(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { a, _ := new(fe6).rand(rand.Reader) b, _ := new(fe6).rand(rand.Reader) zero := field.zero() one := field.one() c_1, c_2 := field.new(), field.new() field.mul(c_1, a, zero) if !c_1.equal(zero) { t.Fatal("a * 0 == 0") } field.mul(c_1, a, one) if !c_1.equal(a) { t.Fatal("a * 1 == a") } field.mul(c_1, a, b) field.mul(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a * b == b * a") } c_x, _ := new(fe6).rand(rand.Reader) field.mul(c_1, a, b) field.mul(c_1, c_1, c_x) field.mul(c_2, c_x, b) field.mul(c_2, c_2, a) if !c_1.equal(c_2) { t.Fatal("(a * b) * c == (a * c) * b") } field.square(a, zero) if !a.equal(zero) { t.Fatal("0^2 == 0") } field.square(a, one) if !a.equal(one) { t.Fatal("1^2 == 1") } _, _ = a.rand(rand.Reader) field.square(c_1, a) field.mul(c_2, a, a) if !c_2.equal(c_1) { t.Fatal("a^2 == a*a") } } } func TestFp6MultiplicationPropertiesAssigned(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { a, _ := new(fe6).rand(rand.Reader) zero, one := new(fe6).zero(), new(fe6).one() field.mulAssign(a, zero) if !a.equal(zero) { t.Fatal("a * 0 == 0") } _, _ = a.rand(rand.Reader) a0 := new(fe6).set(a) field.mulAssign(a, one) if !a.equal(a0) { t.Fatal("a * 1 == a") } _, _ = a.rand(rand.Reader) b, _ := new(fe6).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(b, a0) if !a.equal(b) { t.Fatal("a * b == b * a") } c, _ := new(fe6).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(a, c) field.mulAssign(a0, c) field.mulAssign(a0, b) if !a.equal(a0) { t.Fatal("(a * b) * c == (a * c) * b") } } } func TestFp6Exponentiation(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { a, _ := new(fe6).rand(rand.Reader) u := field.new() field.exp(u, a, big.NewInt(0)) if !u.equal(field.one()) { t.Fatal("a^0 == 1") } field.exp(u, a, big.NewInt(1)) if !u.equal(a) { t.Fatal("a^1 == a") } v := field.new() field.mul(u, a, a) field.mul(u, u, u) field.mul(u, u, u) field.exp(v, a, big.NewInt(8)) if !u.equal(v) { t.Fatal("((a^2)^2)^2 == a^8") } } } func TestFp6Inversion(t *testing.T) { field := newFp6(nil) for i := 0; i < fuz; i++ { u := field.new() zero := field.zero() one := field.one() field.inverse(u, zero) if !u.equal(zero) { t.Fatal("(0^-1) == 0)") } field.inverse(u, one) if !u.equal(one) { t.Fatal("(1^-1) == 1)") } a, _ := new(fe6).rand(rand.Reader) field.inverse(u, a) field.mul(u, u, a) if !u.equal(one) { t.Fatal("(r*a) * r*(a^-1) == r)") } } } func TestFp12Serialization(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { a, _ := new(fe12).rand(rand.Reader) b, err := field.fromBytes(field.toBytes(a)) if err != nil { t.Fatal(err) } if !a.equal(b) { t.Fatal("bad serialization") } } } func TestFp12AdditionProperties(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { zero := field.zero() a, _ := new(fe12).rand(rand.Reader) b, _ := new(fe12).rand(rand.Reader) c_1 := field.new() c_2 := field.new() field.add(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a + 0 == a") } field.sub(c_1, a, zero) if !c_1.equal(a) { t.Fatal("a - 0 == a") } field.double(c_1, zero) if !c_1.equal(zero) { t.Fatal("2 * 0 == 0") } field.neg(c_1, zero) if !c_1.equal(zero) { t.Fatal("-0 == 0") } field.sub(c_1, zero, a) field.neg(c_2, a) if !c_1.equal(c_2) { t.Fatal("0-a == -a") } field.double(c_1, a) field.add(c_2, a, a) if !c_1.equal(c_2) { t.Fatal("2 * a == a + a") } field.add(c_1, a, b) field.add(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a + b = b + a") } field.sub(c_1, a, b) field.sub(c_2, b, a) field.neg(c_2, c_2) if !c_1.equal(c_2) { t.Fatal("a - b = - ( b - a )") } c_x, _ := new(fe12).rand(rand.Reader) field.add(c_1, a, b) field.add(c_1, c_1, c_x) field.add(c_2, a, c_x) field.add(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a + b) + c == (a + c ) + b") } field.sub(c_1, a, b) field.sub(c_1, c_1, c_x) field.sub(c_2, a, c_x) field.sub(c_2, c_2, b) if !c_1.equal(c_2) { t.Fatal("(a - b) - c == (a - c ) -b") } } } func TestFp12MultiplicationProperties(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { a, _ := new(fe12).rand(rand.Reader) b, _ := new(fe12).rand(rand.Reader) zero := field.zero() one := field.one() c_1, c_2 := field.new(), field.new() field.mul(c_1, a, zero) if !c_1.equal(zero) { t.Fatal("a * 0 == 0") } field.mul(c_1, a, one) if !c_1.equal(a) { t.Fatal("a * 1 == a") } field.mul(c_1, a, b) field.mul(c_2, b, a) if !c_1.equal(c_2) { t.Fatal("a * b == b * a") } c_x, _ := new(fe12).rand(rand.Reader) field.mul(c_1, a, b) field.mul(c_1, c_1, c_x) field.mul(c_2, c_x, b) field.mul(c_2, c_2, a) if !c_1.equal(c_2) { t.Fatal("(a * b) * c == (a * c) * b") } field.square(a, zero) if !a.equal(zero) { t.Fatal("0^2 == 0") } field.square(a, one) if !a.equal(one) { t.Fatal("1^2 == 1") } _, _ = a.rand(rand.Reader) field.square(c_1, a) field.mul(c_2, a, a) if !c_2.equal(c_1) { t.Fatal("a^2 == a*a") } } } func TestFp12MultiplicationPropertiesAssigned(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { a, _ := new(fe12).rand(rand.Reader) zero, one := new(fe12).zero(), new(fe12).one() field.mulAssign(a, zero) if !a.equal(zero) { t.Fatal("a * 0 == 0") } _, _ = a.rand(rand.Reader) a0 := new(fe12).set(a) field.mulAssign(a, one) if !a.equal(a0) { t.Fatal("a * 1 == a") } _, _ = a.rand(rand.Reader) b, _ := new(fe12).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(b, a0) if !a.equal(b) { t.Fatal("a * b == b * a") } c, _ := new(fe12).rand(rand.Reader) a0.set(a) field.mulAssign(a, b) field.mulAssign(a, c) field.mulAssign(a0, c) field.mulAssign(a0, b) if !a.equal(a0) { t.Fatal("(a * b) * c == (a * c) * b") } } } func TestFp12SparseMultiplication(t *testing.T) { fp12 := newFp12(nil) var a, b, u *fe12 for j := 0; j < fuz; j++ { a, _ = new(fe12).rand(rand.Reader) b, _ = new(fe12).rand(rand.Reader) u, _ = new(fe12).rand(rand.Reader) b[0][2].zero() b[1][0].zero() b[1][2].zero() fp12.mul(u, a, b) fp12.mulBy014Assign(a, &b[0][0], &b[0][1], &b[1][1]) if !a.equal(u) { t.Fatal("bad mul by 01") } } } func TestFp12Exponentiation(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { a, _ := new(fe12).rand(rand.Reader) u := field.new() field.exp(u, a, big.NewInt(0)) if !u.equal(field.one()) { t.Fatal("a^0 == 1") } field.exp(u, a, big.NewInt(1)) if !u.equal(a) { t.Fatal("a^1 == a") } v := field.new() field.mul(u, a, a) field.mul(u, u, u) field.mul(u, u, u) field.exp(v, a, big.NewInt(8)) if !u.equal(v) { t.Fatal("((a^2)^2)^2 == a^8") } } } func TestFp12Inversion(t *testing.T) { field := newFp12(nil) for i := 0; i < fuz; i++ { u := field.new() zero := field.zero() one := field.one() field.inverse(u, zero) if !u.equal(zero) { t.Fatal("(0^-1) == 0)") } field.inverse(u, one) if !u.equal(one) { t.Fatal("(1^-1) == 1)") } a, _ := new(fe12).rand(rand.Reader) field.inverse(u, a) field.mul(u, u, a) if !u.equal(one) { t.Fatal("(r*a) * r*(a^-1) == r)") } } } func BenchmarkMultiplication(t *testing.B) { a, _ := new(fe).rand(rand.Reader) b, _ := new(fe).rand(rand.Reader) c, _ := new(fe).rand(rand.Reader) t.ResetTimer() for i := 0; i < t.N; i++ { mul(c, a, b) } } func padBytes(in []byte, size int) []byte { out := make([]byte, size) if len(in) > size { panic("bad input for padding") } copy(out[size-len(in):], in) return out }