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#[macro_export]
macro_rules! bls12_range_field_pairing {
($range_field:ident, $quadratic_field:ident, $gt:ident, $g1_affine:ident, $pairng_coeff:ident, $bls_x:ident, $bls_x_is_negative:ident) => {
impl PairingRange for $range_field {
type G1Affine = $g1_affine;
type G2Coeff = $pairng_coeff;
type QuadraticField = $quadratic_field;
type Gt = $gt;
// twisting isomorphism from E to E'
fn untwist(self, coeffs: Self::G2Coeff, g1: Self::G1Affine) -> Self {
let mut c0 = coeffs.0;
let mut c1 = coeffs.1;
c0.0[0] *= g1.y;
c0.0[1] *= g1.y;
c1.0[0] *= g1.x;
c1.0[1] *= g1.x;
self.mul_by_014(coeffs.2, c1, c0)
}
fn mul_by_014(
mut self,
c0: Self::QuadraticField,
c1: Self::QuadraticField,
c4: Self::QuadraticField,
) -> Self {
let aa = self.0[0].mul_by_01(c0, c1);
let bb = self.0[1].mul_by_1(c4);
let o = c1 + c4;
let c1 = self.0[1] + self.0[0];
let c1 = c1.mul_by_01(c0, o);
let c1 = c1 - aa - bb;
let c0 = bb.mul_by_nonresidue();
let c0 = c0 + aa;
Self([c0, c1])
}
fn final_exp(self) -> Self::Gt {
#[must_use]
fn fp4_square(a: Fq2, b: Fq2) -> (Fq2, Fq2) {
let t0 = a.square();
let t1 = b.square();
let mut t2 = t1.mul_by_nonresidue();
let c0 = t2 + t0;
t2 = a + b;
t2 = t2.square();
t2 -= t0;
let c1 = t2 - t1;
(c0, c1)
}
// Adaptation of Algorithm 5.5.4, Guide to Pairing-Based Cryptography
// Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions
// https://eprint.iacr.org/2009/565.pdf
#[must_use]
fn cyclotomic_square(f: Fq12) -> Fq12 {
let mut z0 = f.0[0].0[0];
let mut z4 = f.0[0].0[1];
let mut z3 = f.0[0].0[2];
let mut z2 = f.0[1].0[0];
let mut z1 = f.0[1].0[1];
let mut z5 = f.0[1].0[2];
let (t0, t1) = fp4_square(z0, z1);
// For A
z0 = t0 - z0;
z0 = z0.double() + t0;
z1 = t1 + z1;
z1 = z1.double() + t1;
let (mut t0, t1) = fp4_square(z2, z3);
let (t2, t3) = fp4_square(z4, z5);
// For C
z4 = t0 - z4;
z4 = z4.double() + t0;
z5 = t1 + z5;
z5 = z5.double() + t1;
// For B
t0 = t3.mul_by_nonresidue();
z2 = t0 + z2;
z2 = z2.double() + t0;
z3 = t2 - z3;
z3 = z3.double() + t2;
Fq12([Fq6([z0, z4, z3]), Fq6([z2, z1, z5])])
}
#[must_use]
fn cycolotomic_exp(f: Fq12) -> Fq12 {
let mut tmp = Fq12::one();
let mut found_one = false;
for i in (0..64).rev().map(|b| ((BLS_X >> b) & 1) == 1) {
if found_one {
tmp = cyclotomic_square(tmp)
} else {
found_one = i;
}
if i {
tmp *= f;
}
}
tmp.conjugate()
}
let mut f = self;
let mut t0 = f.frobenius_maps(6);
$gt(f
.invert()
.map(|mut t1| {
let mut t2 = t0 * t1;
t1 = t2;
t2 = t2.frobenius_maps(2);
t2 *= t1;
t1 = cyclotomic_square(t2).conjugate();
let mut t3 = cycolotomic_exp(t2);
let mut t4 = cyclotomic_square(t3);
let mut t5 = t1 * t3;
t1 = cycolotomic_exp(t5);
t0 = cycolotomic_exp(t1);
let mut t6 = cycolotomic_exp(t0);
t6 *= t4;
t4 = cycolotomic_exp(t6);
t5 = t5.conjugate();
t4 *= t5 * t2;
t5 = t2.conjugate();
t1 *= t2;
t1 = t1.frobenius_maps(3);
t6 *= t5;
t6 = t6.frobenius_map();
t3 *= t0;
t3 = t3.frobenius_maps(2);
t3 *= t1;
t3 *= t6;
f = t3 * t4;
f
})
.unwrap())
}
}
impl $range_field {
pub const fn generator() -> Self {
Fq12([
Fq6([
Fq2([
Fq([
0x1972e433a01f85c5,
0x97d32b76fd772538,
0xc8ce546fc96bcdf9,
0xcef63e7366d40614,
0xa611342781843780,
0x13f3448a3fc6d825,
]),
Fq([
0xd26331b02e9d6995,
0x9d68a482f7797e7d,
0x9c9b29248d39ea92,
0xf4801ca2e13107aa,
0xa16c0732bdbcb066,
0x083ca4afba360478,
]),
]),
Fq2([
Fq([
0x59e261db0916b641,
0x2716b6f4b23e960d,
0xc8e55b10a0bd9c45,
0x0bdb0bd99c4deda8,
0x8cf89ebf57fdaac5,
0x12d6b7929e777a5e,
]),
Fq([
0x5fc85188b0e15f35,
0x34a06e3a8f096365,
0xdb3126a6e02ad62c,
0xfc6f5aa97d9a990b,
0xa12f55f5eb89c210,
0x1723703a926f8889,
]),
]),
Fq2([
Fq([
0x93588f2971828778,
0x43f65b8611ab7585,
0x3183aaf5ec279fdf,
0xfa73d7e18ac99df6,
0x64e176a6a64c99b0,
0x179fa78c58388f1f,
]),
Fq([
0x672a0a11ca2aef12,
0x0d11b9b52aa3f16b,
0xa44412d0699d056e,
0xc01d0177221a5ba5,
0x66e0cede6c735529,
0x05f5a71e9fddc339,
]),
]),
]),
Fq6([
Fq2([
Fq([
0xd30a88a1b062c679,
0x5ac56a5d35fc8304,
0xd0c834a6a81f290d,
0xcd5430c2da3707c7,
0xf0c27ff780500af0,
0x09245da6e2d72eae,
]),
Fq([
0x9f2e0676791b5156,
0xe2d1c8234918fe13,
0x4c9e459f3c561bf4,
0xa3e85e53b9d3e3c1,
0x820a121e21a70020,
0x15af618341c59acc,
]),
]),
Fq2([
Fq([
0x7c95658c24993ab1,
0x73eb38721ca886b9,
0x5256d749477434bc,
0x8ba41902ea504a8b,
0x04a3d3f80c86ce6d,
0x18a64a87fb686eaa,
]),
Fq([
0xbb83e71bb920cf26,
0x2a5277ac92a73945,
0xfc0ee59f94f046a0,
0x7158cdf3786058f7,
0x7cc1061b82f945f6,
0x03f847aa9fdbe567,
]),
]),
Fq2([
Fq([
0x8078dba56134e657,
0x1cd7ec9a43998a6e,
0xb1aa599a1a993766,
0xc9a0f62f0842ee44,
0x8e159be3b605dffa,
0x0c86ba0d4af13fc2,
]),
Fq([
0xe80ff2a06a52ffb1,
0x7694ca48721a906c,
0x7583183e03b08514,
0xf567afdd40cee4e2,
0x9a6d96d2e526a5fc,
0x197e9f49861f2242,
]),
]),
]),
])
}
}
};
}
pub use bls12_range_field_pairing;