github.com/consensys/gnark-crypto@v0.14.0/internal/generator/tower/template/fq12over6over2/tests/fq12.go.tmpl

{{$Name := .Curve.Name}}
import (
	"math/big"
	"testing"

	"github.com/consensys/gnark-crypto/ecc/{{$Name}}/fp"
	"github.com/leanovate/gopter"
	"github.com/leanovate/gopter/prop"
)

// ------------------------------------------------------------
// tests

func TestE12Serialization(t *testing.T) {

	t.Parallel()
	parameters := gopter.DefaultTestParameters()
	if testing.Short() {
		parameters.MinSuccessfulTests = nbFuzzShort
	} else {
		parameters.MinSuccessfulTests = nbFuzz
	}

	properties := gopter.NewProperties(parameters)

	genA := GenE12()

	properties.Property("[{{ toUpper $Name}}] SetBytes(Bytes()) should stay constant", prop.ForAll(
		func(a *E12) bool {
			var b E12
			buf := a.Bytes()
			if err := b.SetBytes(buf[:]); err != nil {
				return false
			}
			return a.Equal(&b)
		},
		genA,
	))

	properties.TestingRun(t, gopter.ConsoleReporter(false))
}

func TestE12ReceiverIsOperand(t *testing.T) {

	parameters := gopter.DefaultTestParameters()
	if testing.Short() {
		parameters.MinSuccessfulTests = nbFuzzShort
	} else {
		parameters.MinSuccessfulTests = nbFuzz
	}

	properties := gopter.NewProperties(parameters)

	genA := GenE12()
	genB := GenE12()

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (addition) should output the same result", prop.ForAll(
		func(a, b *E12) bool {
			var c, d E12
			d.Set(a)
			c.Add(a, b)
			a.Add(a, b)
			b.Add(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (sub) should output the same result", prop.ForAll(
		func(a, b *E12) bool {
			var c, d E12
			d.Set(a)
			c.Sub(a, b)
			a.Sub(a, b)
			b.Sub(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (mul) should output the same result", prop.ForAll(
		func(a, b *E12) bool {
			var c, d E12
			d.Set(a)
			c.Mul(a, b)
			a.Mul(a, b)
			b.Mul(&d, b)
			return a.Equal(b) && a.Equal(&c) && b.Equal(&c)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (square) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Square(a)
			a.Square(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (double) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Double(a)
			a.Double(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Inverse) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Inverse(a)
			a.Inverse(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Cyclotomic square) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.CyclotomicSquare(a)
			a.CyclotomicSquare(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Conjugate) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Conjugate(a)
			a.Conjugate(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (Frobenius) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Frobenius(a)
			a.Frobenius(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name}}] Having the receiver as operand (FrobeniusSquare) should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.FrobeniusSquare(a)
			a.FrobeniusSquare(a)
			return a.Equal(&b)
		},
		genA,
	))

	properties.TestingRun(t, gopter.ConsoleReporter(false))
}

func TestE12Ops(t *testing.T) {

	parameters := gopter.DefaultTestParameters()
	if testing.Short() {
		parameters.MinSuccessfulTests = nbFuzzShort
	} else {
		parameters.MinSuccessfulTests = nbFuzz
	}

	properties := gopter.NewProperties(parameters)



	genA := GenE12()
	genB := GenE12()
	genExp := GenFp()

	properties.Property("[{{ toUpper $Name }}] sub & add should leave an element invariant", prop.ForAll(
		func(a, b *E12) bool {
			var c E12
			c.Set(a)
			c.Add(&c, b).Sub(&c, b)
			return c.Equal(a)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name }}] mul & inverse should leave an element invariant", prop.ForAll(
		func(a, b *E12) bool {
			var c, d E12
			d.Inverse(b)
			c.Set(a)
			c.Mul(&c, b).Mul(&c, &d)
			return c.Equal(a)
		},
		genA,
		genB,
	))

	properties.Property("[{{ toUpper $Name }}] inverse twice should leave an element invariant", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Inverse(a).Inverse(&b)
			return a.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] square and mul should output the same result", prop.ForAll(
		func(a *E12) bool {
			var b, c E12
			b.Mul(a, a)
			c.Square(a)
			return b.Equal(&c)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] a + pi(a), a-pi(a) should be real", prop.ForAll(
		func(a *E12) bool {
			var b, c, d E12
			var e, f, g E6
			b.Conjugate(a)
			c.Add(a, &b)
			d.Sub(a, &b)
			e.Double(&a.C0)
			f.Double(&a.C1)
			return c.C1.Equal(&g) && d.C0.Equal(&g) && e.Equal(&c.C0) && f.Equal(&d.C1)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Torus-based Compress/decompress E12 elements in the cyclotomic subgroup", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)

			c, _ := a.CompressTorus()
			d := c.DecompressTorus()
			return a.Equal(&d)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Torus-based batch Compress/decompress E12 elements in the cyclotomic subgroup", prop.ForAll(
		func(a, e, f *E12) bool {
			var b E12
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)

			e.CyclotomicSquare(a)
			f.CyclotomicSquare(e)

			c, _ := BatchCompressTorus([]E12{*a, *e, *f})
			d, _ := BatchDecompressTorus(c)
			return a.Equal(&d[0]) && e.Equal(&d[1]) && f.Equal(&d[2])
		},
		genA,
		genA,
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] pi**12=id", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.Frobenius(a).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b).
				Frobenius(&b)
			return b.Equal(a)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] (pi**2)**6=id", prop.ForAll(
		func(a *E12) bool {
			var b E12
			b.FrobeniusSquare(a).
				FrobeniusSquare(&b).
				FrobeniusSquare(&b).
				FrobeniusSquare(&b).
				FrobeniusSquare(&b).
				FrobeniusSquare(&b)
			return b.Equal(a)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] cyclotomic square (Granger-Scott) and square should be the same in the cyclotomic subgroup", prop.ForAll(
		func(a *E12) bool {
			var b, c, d E12
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)
			c.Square(a)
			d.CyclotomicSquare(a)
			return c.Equal(&d)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] compressed cyclotomic square (Karabina) and square should be the same in the cyclotomic subgroup", prop.ForAll(
		func(a *E12) bool {
			var _a, b, c, d, _c, _d E12
			_a.SetOne().Double(&_a)

			// put a and _a in the cyclotomic subgroup
			// a (g3 != 0 probably)
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)
			// _a (g3 == 0)
			b.Conjugate(&_a)
			_a.Inverse(&_a)
			b.Mul(&b, &_a)
			_a.FrobeniusSquare(&b).Mul(&_a, &b)

			// case g3 != 0
			c.Square(a)
			d.CyclotomicSquareCompressed(a).DecompressKarabina(&d)

			// case g3 == 0
			_c.Square(&_a)
			_d.CyclotomicSquareCompressed(&_a).DecompressKarabina(&_d)

			return c.Equal(&d)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] batch decompress and individual decompress (Karabina) should be the same", prop.ForAll(
		func(a *E12) bool {
			var _a, b E12
			_a.SetOne().Double(&_a)

			// put a and _a in the cyclotomic subgroup
			// a (g3 !=0 probably)
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)
			// _a (g3 == 0)
			b.Conjugate(&_a)
			_a.Inverse(&_a)
			b.Mul(&b, &_a)
			_a.FrobeniusSquare(&b).Mul(&_a, &b)
 
			var a2, a4, a17 E12
			a2.Set(&_a)
            a4.Set(a)
            a17.Set(a)
			a2.nSquareCompressed(2) // case g3 == 0
			a4.nSquareCompressed(4)
			a17.nSquareCompressed(17)
			batch := BatchDecompressKarabina([]E12{a2, a4, a17})
			a2.DecompressKarabina(&a2)
			a4.DecompressKarabina(&a4)
			a17.DecompressKarabina(&a17)

			return a2.Equal(&batch[0]) && a4.Equal(&batch[1]) && a17.Equal(&batch[2])
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] Exp and CyclotomicExp results must be the same in the cyclotomic subgroup", prop.ForAll(
		func(a *E12, e fp.Element) bool {
			var b, c, d E12
			// put in the cyclo subgroup
			b.Conjugate(a)
			a.Inverse(a)
			b.Mul(&b, a)
			a.FrobeniusSquare(&b).Mul(a, &b)

			var _e big.Int
			k := new(big.Int).SetUint64(12)
			e.Exp(e, k)
			e.BigInt(&_e)

			c.Exp(*a, &_e)
			d.CyclotomicExp(*a, &_e)

			return c.Equal(&d)
		},
		genA,
		genExp,
	))

	properties.Property("[{{ toUpper $Name }}] Frobenius of x in E12 should be equal to x^q", prop.ForAll(
		func(a *E12) bool {
			var b, c E12
			q := fp.Modulus()
			b.Frobenius(a)
			c.Exp(*a, q)
			return c.Equal(&b)
		},
		genA,
	))

	properties.Property("[{{ toUpper $Name }}] FrobeniusSquare of x in E12 should be equal to x^(q^2)", prop.ForAll(
		func(a *E12) bool {
			var b, c E12
			q := fp.Modulus()
			b.FrobeniusSquare(a)
			c.Exp(*a, q).Exp(c, q)
			return c.Equal(&b)
		},
		genA,
	))

	properties.TestingRun(t, gopter.ConsoleReporter(false))

}

// ------------------------------------------------------------
// benches

func BenchmarkE12Add(b *testing.B) {
	var a, c E12
_,_ =	a.SetRandom()
_,_ =	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Add(&a, &c)
	}
}

func BenchmarkE12Sub(b *testing.B) {
	var a, c E12
_,_ =	a.SetRandom()
_,_ =	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Sub(&a, &c)
	}
}

func BenchmarkE12Mul(b *testing.B) {
	var a, c E12
_,_ =	a.SetRandom()
_,_ =	c.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Mul(&a, &c)
	}
}

func BenchmarkE12Cyclosquare(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.CyclotomicSquare(&a)
	}
}

func BenchmarkE12Square(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Square(&a)
	}
}

func BenchmarkE12Inverse(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Inverse(&a)
	}
}

func BenchmarkE12Conjugate(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Conjugate(&a)
	}
}

func BenchmarkE12Frobenius(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Frobenius(&a)
	}
}

func BenchmarkE12FrobeniusSquare(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.FrobeniusSquare(&a)
	}
}

func BenchmarkE12Expt(b *testing.B) {
	var a E12
_,_ =	a.SetRandom()
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		a.Expt(&a)
	}
}

{{ template "base" .}}