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1404 lines
30 KiB
1404 lines
30 KiB
4 years ago
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package bls12381
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import (
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"bytes"
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"crypto/rand"
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"math/big"
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"testing"
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)
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func TestFpSerialization(t *testing.T) {
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t.Run("zero", func(t *testing.T) {
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in := make([]byte, 48)
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fe, err := fromBytes(in)
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if err != nil {
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t.Fatal(err)
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}
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if !fe.isZero() {
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t.Fatal("bad serialization")
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}
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if !bytes.Equal(in, toBytes(fe)) {
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t.Fatal("bad serialization")
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}
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})
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t.Run("bytes", func(t *testing.T) {
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for i := 0; i < fuz; i++ {
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a, _ := new(fe).rand(rand.Reader)
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b, err := fromBytes(toBytes(a))
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if err != nil {
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t.Fatal(err)
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}
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if !a.equal(b) {
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t.Fatal("bad serialization")
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}
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}
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})
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t.Run("string", func(t *testing.T) {
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for i := 0; i < fuz; i++ {
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a, _ := new(fe).rand(rand.Reader)
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b, err := fromString(toString(a))
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if err != nil {
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t.Fatal(err)
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}
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if !a.equal(b) {
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t.Fatal("bad encoding or decoding")
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}
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}
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})
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t.Run("big", func(t *testing.T) {
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for i := 0; i < fuz; i++ {
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a, _ := new(fe).rand(rand.Reader)
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b, err := fromBig(toBig(a))
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if err != nil {
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t.Fatal(err)
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}
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if !a.equal(b) {
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t.Fatal("bad encoding or decoding")
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}
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}
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})
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}
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func TestFpAdditionCrossAgainstBigInt(t *testing.T) {
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for i := 0; i < fuz; i++ {
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a, _ := new(fe).rand(rand.Reader)
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b, _ := new(fe).rand(rand.Reader)
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c := new(fe)
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big_a := toBig(a)
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big_b := toBig(b)
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big_c := new(big.Int)
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add(c, a, b)
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out_1 := toBytes(c)
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out_2 := padBytes(big_c.Add(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied A")
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}
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double(c, a)
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out_1 = toBytes(c)
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out_2 = padBytes(big_c.Add(big_a, big_a).Mod(big_c, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied B")
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}
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sub(c, a, b)
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out_1 = toBytes(c)
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out_2 = padBytes(big_c.Sub(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied C")
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}
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neg(c, a)
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out_1 = toBytes(c)
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out_2 = padBytes(big_c.Neg(big_a).Mod(big_c, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied D")
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}
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}
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}
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func TestFpAdditionCrossAgainstBigIntAssigned(t *testing.T) {
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for i := 0; i < fuz; i++ {
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a, _ := new(fe).rand(rand.Reader)
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b, _ := new(fe).rand(rand.Reader)
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big_a, big_b := toBig(a), toBig(b)
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addAssign(a, b)
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out_1 := toBytes(a)
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out_2 := padBytes(big_a.Add(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied A")
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}
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a, _ = new(fe).rand(rand.Reader)
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big_a = toBig(a)
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doubleAssign(a)
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out_1 = toBytes(a)
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out_2 = padBytes(big_a.Add(big_a, big_a).Mod(big_a, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied B")
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}
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a, _ = new(fe).rand(rand.Reader)
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b, _ = new(fe).rand(rand.Reader)
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big_a, big_b = toBig(a), toBig(b)
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subAssign(a, b)
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out_1 = toBytes(a)
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out_2 = padBytes(big_a.Sub(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48)
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if !bytes.Equal(out_1, out_2) {
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t.Fatal("cross test against big.Int is not satisfied A")
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}
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}
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}
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func TestFpAdditionProperties(t *testing.T) {
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for i := 0; i < fuz; i++ {
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zero := new(fe).zero()
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a, _ := new(fe).rand(rand.Reader)
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b, _ := new(fe).rand(rand.Reader)
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c_1, c_2 := new(fe), new(fe)
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add(c_1, a, zero)
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if !c_1.equal(a) {
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t.Fatal("a + 0 == a")
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}
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sub(c_1, a, zero)
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if !c_1.equal(a) {
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t.Fatal("a - 0 == a")
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}
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double(c_1, zero)
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if !c_1.equal(zero) {
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t.Fatal("2 * 0 == 0")
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}
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neg(c_1, zero)
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if !c_1.equal(zero) {
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t.Fatal("-0 == 0")
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}
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sub(c_1, zero, a)
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neg(c_2, a)
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if !c_1.equal(c_2) {
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t.Fatal("0-a == -a")
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}
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double(c_1, a)
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add(c_2, a, a)
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if !c_1.equal(c_2) {
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t.Fatal("2 * a == a + a")
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}
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add(c_1, a, b)
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add(c_2, b, a)
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if !c_1.equal(c_2) {
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t.Fatal("a + b = b + a")
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}
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sub(c_1, a, b)
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sub(c_2, b, a)
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neg(c_2, c_2)
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if !c_1.equal(c_2) {
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t.Fatal("a - b = - ( b - a )")
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}
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c_x, _ := new(fe).rand(rand.Reader)
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add(c_1, a, b)
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add(c_1, c_1, c_x)
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add(c_2, a, c_x)
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add(c_2, c_2, b)
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if !c_1.equal(c_2) {
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t.Fatal("(a + b) + c == (a + c ) + b")
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}
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sub(c_1, a, b)
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sub(c_1, c_1, c_x)
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sub(c_2, a, c_x)
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sub(c_2, c_2, b)
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if !c_1.equal(c_2) {
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t.Fatal("(a - b) - c == (a - c ) -b")
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}
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}
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}
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func TestFpAdditionPropertiesAssigned(t *testing.T) {
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for i := 0; i < fuz; i++ {
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zero := new(fe).zero()
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a, b := new(fe), new(fe)
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_, _ = a.rand(rand.Reader)
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b.set(a)
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addAssign(a, zero)
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if !a.equal(b) {
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t.Fatal("a + 0 == a")
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}
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subAssign(a, zero)
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if !a.equal(b) {
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t.Fatal("a - 0 == a")
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}
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a.set(zero)
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doubleAssign(a)
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if !a.equal(zero) {
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t.Fatal("2 * 0 == 0")
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}
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a.set(zero)
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subAssign(a, b)
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neg(b, b)
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if !a.equal(b) {
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t.Fatal("0-a == -a")
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}
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_, _ = a.rand(rand.Reader)
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b.set(a)
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doubleAssign(a)
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addAssign(b, b)
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if !a.equal(b) {
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t.Fatal("2 * a == a + a")
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}
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_, _ = a.rand(rand.Reader)
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_, _ = b.rand(rand.Reader)
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c_1, c_2 := new(fe).set(a), new(fe).set(b)
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addAssign(c_1, b)
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addAssign(c_2, a)
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if !c_1.equal(c_2) {
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t.Fatal("a + b = b + a")
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}
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_, _ = a.rand(rand.Reader)
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_, _ = b.rand(rand.Reader)
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c_1.set(a)
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c_2.set(b)
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subAssign(c_1, b)
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subAssign(c_2, a)
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neg(c_2, c_2)
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|
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if !c_1.equal(c_2) {
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t.Fatal("a - b = - ( b - a )")
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}
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_, _ = a.rand(rand.Reader)
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_, _ = b.rand(rand.Reader)
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c, _ := new(fe).rand(rand.Reader)
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a0 := new(fe).set(a)
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|
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addAssign(a, b)
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|
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addAssign(a, c)
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addAssign(b, c)
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addAssign(b, a0)
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|
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if !a.equal(b) {
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t.Fatal("(a + b) + c == (b + c) + a")
|
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|
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}
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|
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_, _ = a.rand(rand.Reader)
|
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_, _ = b.rand(rand.Reader)
|
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|
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_, _ = c.rand(rand.Reader)
|
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|
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a0.set(a)
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|
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subAssign(a, b)
|
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|
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subAssign(a, c)
|
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|
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subAssign(a0, c)
|
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|
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subAssign(a0, b)
|
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|
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if !a.equal(a0) {
|
||
|
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t.Fatal("(a - b) - c == (a - c) -b")
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
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func TestFpLazyOperations(t *testing.T) {
|
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|
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for i := 0; i < fuz; i++ {
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|
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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
|
||
|
|
}
|