pairing_plus/bls12_381/
mod.rsmod cofactor;
mod ec;
mod fq;
mod fq12;
mod fq2;
mod fq6;
mod fr;
mod isogeny;
mod osswu_map;
#[cfg(test)]
mod tests;
pub(crate) use self::cofactor::ClearH;
pub use self::ec::{
G1Affine, G1Compressed, G1Prepared, G1Uncompressed, G2Affine, G2Compressed, G2Prepared,
G2Uncompressed, G1, G2,
};
pub use self::fq::{Fq, FqRepr};
pub use self::fq12::Fq12;
pub use self::fq2::Fq2;
pub use self::fq6::Fq6;
pub use self::fr::{Fr, FrRepr};
pub(crate) use self::isogeny::IsogenyMap;
pub(crate) use self::osswu_map::OSSWUMap;
pub mod transmute {
pub use super::ec::g1::transmute_affine as g1_affine;
pub use super::ec::g1::transmute_projective as g1_projective;
pub use super::ec::g2::transmute_affine as g2_affine;
pub use super::ec::g2::transmute_projective as g2_projective;
pub use super::fq::transmute as fq;
pub use super::fr::transmute as fr;
}
use super::{CurveAffine, Engine};
use ff::{BitIterator, Field, ScalarEngine};
const BLS_X: u64 = 0xd201000000010000;
const BLS_X_IS_NEGATIVE: bool = true;
#[derive(Clone, Debug)]
pub struct Bls12;
impl ScalarEngine for Bls12 {
type Fr = Fr;
}
impl Engine for Bls12 {
type G1 = G1;
type G1Affine = G1Affine;
type G2 = G2;
type G2Affine = G2Affine;
type Fq = Fq;
type Fqe = Fq2;
type Fqk = Fq12;
fn miller_loop<'a, I>(i: I) -> Self::Fqk
where
I: IntoIterator<
Item = &'a (
&'a <Self::G1Affine as CurveAffine>::Prepared,
&'a <Self::G2Affine as CurveAffine>::Prepared,
),
>,
{
let mut pairs = vec![];
for &(p, q) in i {
if !p.is_zero() && !q.is_zero() {
pairs.push((p, q.coeffs.iter()));
}
}
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);
f.mul_by_014(&coeffs.2, &c1, &c0);
}
let mut f = Fq12::one();
let mut found_one = false;
for i in BitIterator::new(&[BLS_X >> 1]) {
if !found_one {
found_one = i;
continue;
}
for &mut (p, ref mut coeffs) in &mut pairs {
ell(&mut f, coeffs.next().unwrap(), &p.0);
}
if i {
for &mut (p, ref mut coeffs) in &mut pairs {
ell(&mut f, coeffs.next().unwrap(), &p.0);
}
}
f.square();
}
for &mut (p, ref mut coeffs) in &mut pairs {
ell(&mut f, coeffs.next().unwrap(), &p.0);
}
if BLS_X_IS_NEGATIVE {
f.conjugate();
}
f
}
fn final_exponentiation(r: &Fq12) -> Option<Fq12> {
let mut f1 = *r;
f1.conjugate();
match r.inverse() {
Some(mut f2) => {
let mut r = f1;
r.mul_assign(&f2);
f2 = r;
r.frobenius_map(2);
r.mul_assign(&f2);
fn exp_by_x(f: &mut Fq12, x: u64) {
*f = f.pow(&[x]);
if BLS_X_IS_NEGATIVE {
f.conjugate();
}
}
let mut x = BLS_X;
let mut y0 = r;
y0.square();
let mut y1 = y0;
exp_by_x(&mut y1, x);
x >>= 1;
let mut y2 = y1;
exp_by_x(&mut y2, x);
x <<= 1;
let mut y3 = r;
y3.conjugate();
y1.mul_assign(&y3);
y1.conjugate();
y1.mul_assign(&y2);
y2 = y1;
exp_by_x(&mut y2, x);
y3 = y2;
exp_by_x(&mut y3, x);
y1.conjugate();
y3.mul_assign(&y1);
y1.conjugate();
y1.frobenius_map(3);
y2.frobenius_map(2);
y1.mul_assign(&y2);
y2 = y3;
exp_by_x(&mut y2, x);
y2.mul_assign(&y0);
y2.mul_assign(&r);
y1.mul_assign(&y2);
y2 = y3;
y2.frobenius_map(1);
y1.mul_assign(&y2);
Some(y1)
}
None => None,
}
}
}
impl G2Prepared {
pub fn is_zero(&self) -> bool {
self.infinity
}
pub fn from_affine(q: G2Affine) -> Self {
if q.is_zero() {
return G2Prepared {
coeffs: vec![],
infinity: true,
};
}
fn doubling_step(r: &mut G2) -> (Fq2, Fq2, Fq2) {
let mut tmp0 = r.x;
tmp0.square();
let mut tmp1 = r.y;
tmp1.square();
let mut tmp2 = tmp1;
tmp2.square();
let mut tmp3 = tmp1;
tmp3.add_assign(&r.x);
tmp3.square();
tmp3.sub_assign(&tmp0);
tmp3.sub_assign(&tmp2);
tmp3.double();
let mut tmp4 = tmp0;
tmp4.double();
tmp4.add_assign(&tmp0);
let mut tmp6 = r.x;
tmp6.add_assign(&tmp4);
let mut tmp5 = tmp4;
tmp5.square();
let mut zsquared = r.z;
zsquared.square();
r.x = tmp5;
r.x.sub_assign(&tmp3);
r.x.sub_assign(&tmp3);
r.z.add_assign(&r.y);
r.z.square();
r.z.sub_assign(&tmp1);
r.z.sub_assign(&zsquared);
r.y = tmp3;
r.y.sub_assign(&r.x);
r.y.mul_assign(&tmp4);
tmp2.double();
tmp2.double();
tmp2.double();
r.y.sub_assign(&tmp2);
tmp3 = tmp4;
tmp3.mul_assign(&zsquared);
tmp3.double();
tmp3.negate();
tmp6.square();
tmp6.sub_assign(&tmp0);
tmp6.sub_assign(&tmp5);
tmp1.double();
tmp1.double();
tmp6.sub_assign(&tmp1);
tmp0 = r.z;
tmp0.mul_assign(&zsquared);
tmp0.double();
(tmp0, tmp3, tmp6)
}
fn addition_step(r: &mut G2, q: &G2Affine) -> (Fq2, Fq2, Fq2) {
let mut zsquared = r.z;
zsquared.square();
let mut ysquared = q.y;
ysquared.square();
let mut t0 = zsquared;
t0.mul_assign(&q.x);
let mut t1 = q.y;
t1.add_assign(&r.z);
t1.square();
t1.sub_assign(&ysquared);
t1.sub_assign(&zsquared);
t1.mul_assign(&zsquared);
let mut t2 = t0;
t2.sub_assign(&r.x);
let mut t3 = t2;
t3.square();
let mut t4 = t3;
t4.double();
t4.double();
let mut t5 = t4;
t5.mul_assign(&t2);
let mut t6 = t1;
t6.sub_assign(&r.y);
t6.sub_assign(&r.y);
let mut t9 = t6;
t9.mul_assign(&q.x);
let mut t7 = t4;
t7.mul_assign(&r.x);
r.x = t6;
r.x.square();
r.x.sub_assign(&t5);
r.x.sub_assign(&t7);
r.x.sub_assign(&t7);
r.z.add_assign(&t2);
r.z.square();
r.z.sub_assign(&zsquared);
r.z.sub_assign(&t3);
let mut t10 = q.y;
t10.add_assign(&r.z);
let mut t8 = t7;
t8.sub_assign(&r.x);
t8.mul_assign(&t6);
t0 = r.y;
t0.mul_assign(&t5);
t0.double();
r.y = t8;
r.y.sub_assign(&t0);
t10.square();
t10.sub_assign(&ysquared);
let mut ztsquared = r.z;
ztsquared.square();
t10.sub_assign(&ztsquared);
t9.double();
t9.sub_assign(&t10);
t10 = r.z;
t10.double();
t6.negate();
t1 = t6;
t1.double();
(t10, t1, t9)
}
let mut coeffs = vec![];
let mut r: G2 = q.into();
let mut found_one = false;
for i in BitIterator::new([BLS_X >> 1]) {
if !found_one {
found_one = i;
continue;
}
coeffs.push(doubling_step(&mut r));
if i {
coeffs.push(addition_step(&mut r, &q));
}
}
coeffs.push(doubling_step(&mut r));
G2Prepared {
coeffs,
infinity: false,
}
}
}
#[test]
fn bls12_engine_tests() {
::tests::engine::engine_tests::<Bls12>();
}