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use super::fq12::Fq12; | ||
use super::fq2::Fq2; | ||
use super::{Fr, G1Affine, G2Affine, BLS_X, G1, G2}; | ||
use crate::ff_ext::quadratic::QuadSparseMul; | ||
use crate::ff_ext::ExtField; | ||
use core::borrow::Borrow; | ||
use core::iter::Sum; | ||
use core::ops::{Add, Mul, Neg, Sub}; | ||
use ff::Field; | ||
use ff::PrimeField; | ||
use group::prime::PrimeCurveAffine; | ||
use group::Group; | ||
use pairing::{Engine, MillerLoopResult, MultiMillerLoop, PairingCurveAffine}; | ||
use rand::RngCore; | ||
use std::ops::MulAssign; | ||
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq}; | ||
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crate::impl_gt!(Gt, Fq12, Fr); | ||
crate::impl_miller_loop_components!(Bls12381, G1, G1Affine, G2, G2Affine, Fq12, Gt, Fr); | ||
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impl MillerLoopResult for Fq12 { | ||
type Gt = Gt; | ||
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fn final_exponentiation(&self) -> Gt { | ||
#[must_use] | ||
fn exp_by_x(f: Fq12) -> Fq12 { | ||
let mut acc = Fq12::one(); | ||
for (i, b) in BLS_X.into_iter().enumerate() { | ||
(i != 0).then(|| acc.cyclotomic_square()); | ||
(b == 1).then(|| acc *= f); | ||
} | ||
acc.conjugate(); | ||
acc | ||
} | ||
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let mut t0 = *self; | ||
t0.frobenius_map(6); | ||
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Gt(self | ||
.invert() | ||
.map(|mut t1| { | ||
let mut t2 = t0 * t1; | ||
t1 = t2; | ||
t2.frobenius_map(2); | ||
t2 *= t1; | ||
t1 = t2; | ||
t1.cyclotomic_square(); | ||
t1.conjugate(); | ||
let mut t3 = exp_by_x(t2); | ||
let mut t4 = t3; | ||
t4.cyclotomic_square(); | ||
let mut t5 = t1 * t3; | ||
t1 = exp_by_x(t5); | ||
t0 = exp_by_x(t1); | ||
let mut t6 = exp_by_x(t0) * t4; | ||
t4 = exp_by_x(t6); | ||
t5.conjugate(); | ||
t4 *= t5 * t2; | ||
t1 *= t2; | ||
t1.frobenius_map(3); | ||
t2.conjugate(); | ||
t6 *= t2; | ||
t6.frobenius_map(1); | ||
t3 *= t0; | ||
t3.frobenius_map(2); | ||
t3 * t4 * t1 * t6 | ||
}) | ||
.unwrap()) | ||
} | ||
} | ||
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pub fn multi_miller_loop(terms: &[(&G1Affine, &G2Affine)]) -> Fq12 { | ||
let terms = terms | ||
.iter() | ||
.filter_map(|&(p, q)| { | ||
if bool::from(p.is_identity()) || bool::from(q.is_identity()) { | ||
None | ||
} else { | ||
Some((p, q)) | ||
} | ||
}) | ||
.collect::<Vec<_>>(); | ||
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let mut f = Fq12::one(); | ||
let mut r = terms.iter().map(|(_, q)| q.to_curve()).collect::<Vec<_>>(); | ||
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for (i, x) in BLS_X.iter().map(|&b| b == 1).skip(1).enumerate() { | ||
if i != 0 { | ||
f.square_assign(); | ||
} | ||
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terms.iter().zip(r.iter_mut()).for_each(|((p, _), r)| { | ||
double(&mut f, r, p); | ||
}); | ||
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if x { | ||
for ((p, q), r) in terms.iter().zip(r.iter_mut()) { | ||
add(&mut f, r, q, p); | ||
} | ||
} | ||
} | ||
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f.conjugate(); | ||
f | ||
} | ||
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fn ell(f: &mut Fq12, coeffs: &(Fq2, Fq2, Fq2), p: &G1Affine) { | ||
let mut c0 = coeffs.0; | ||
let mut c1 = coeffs.1; | ||
c0.c0.mul_assign(&p.y); | ||
c0.c1.mul_assign(&p.y); | ||
c1.c0.mul_assign(&p.x); | ||
c1.c1.mul_assign(&p.x); | ||
Fq12::mul_by_014(f, &coeffs.2, &c1, &c0); | ||
} | ||
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#[cfg(test)] | ||
mod test { | ||
use super::super::{Bls12381, Fr, G1, G2}; | ||
use super::{multi_miller_loop, Fq12, G1Affine, G2Affine, Gt}; | ||
use ff::Field; | ||
use group::{prime::PrimeCurveAffine, Curve, Group}; | ||
use pairing::{Engine as _, MillerLoopResult, PairingCurveAffine}; | ||
use rand_core::OsRng; | ||
crate::test_pairing!(Bls12381, G1, G1Affine, G2, G2Affine, Fq12, Gt, Fr); | ||
} |
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use core::convert::TryInto; | ||
use halo2derive::impl_field; | ||
use rand::RngCore; | ||
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption}; | ||
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impl_field!( | ||
bls12381_base, | ||
Fq, | ||
modulus = "1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", | ||
mul_gen = "2", | ||
zeta = "1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac", | ||
from_uniform = [64, 96], | ||
endian = "big", | ||
); | ||
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crate::extend_field_legendre!(Fq); | ||
crate::impl_binops_calls!(Fq); | ||
crate::impl_binops_additive!(Fq, Fq); | ||
crate::impl_binops_multiplicative!(Fq, Fq); | ||
crate::field_bits!(Fq); | ||
crate::serialize_deserialize_primefield!(Fq); | ||
crate::impl_from_u64!(Fq); | ||
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use ff::Field; | ||
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use crate::ff_ext::ExtField; | ||
const NEGATIVE_ONE: Fq = Fq::ZERO.sub_const(&Fq::ONE); | ||
impl ExtField for Fq { | ||
const NON_RESIDUE: Self = NEGATIVE_ONE; | ||
fn mul_by_nonresidue(&self) -> Self { | ||
self.neg() | ||
} | ||
fn frobenius_map(&mut self, _: usize) {} | ||
} | ||
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#[cfg(test)] | ||
mod test { | ||
use super::*; | ||
crate::field_testing_suite!(Fq, "field_arithmetic"); | ||
crate::field_testing_suite!(Fq, "conversion"); | ||
crate::field_testing_suite!(Fq, "serialization"); | ||
crate::field_testing_suite!(Fq, "quadratic_residue"); | ||
crate::field_testing_suite!(Fq, "bits"); | ||
crate::field_testing_suite!(Fq, "serialization_check"); | ||
crate::field_testing_suite!(Fq, "constants"); | ||
crate::field_testing_suite!(Fq, "sqrt"); | ||
crate::field_testing_suite!(Fq, "zeta"); | ||
crate::field_testing_suite!(Fq, "from_uniform_bytes", 64, 96); | ||
#[test] | ||
fn test_fq_mul_nonresidue() { | ||
let e = Fq::random(rand_core::OsRng); | ||
let a0 = e.mul_by_nonresidue(); | ||
let a1 = e * Fq::NON_RESIDUE; | ||
assert_eq!(a0, a1); | ||
} | ||
} |
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