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use crate::{
templates::{
bls12::{Bls12Parameters, TwistType},
short_weierstrass_jacobian::{Affine, Projective},
},
traits::{AffineCurve, ShortWeierstrassParameters},
};
use snarkvm_fields::{Field, Fp2, One, Zero};
use snarkvm_utilities::{bititerator::BitIteratorBE, serialize::*, ToBytes};
use std::io::{Result as IoResult, Write};
pub type G2Affine<P> = Affine<<P as Bls12Parameters>::G2Parameters>;
pub type G2Projective<P> = Projective<<P as Bls12Parameters>::G2Parameters>;
type CoeffTriplet<T> = (Fp2<T>, Fp2<T>, Fp2<T>);
#[allow(clippy::derive_partial_eq_without_eq)]
#[derive(Clone, Debug, PartialEq, Eq, Hash, CanonicalSerialize, CanonicalDeserialize)]
pub struct G2Prepared<P: Bls12Parameters> {
pub ell_coeffs: Vec<CoeffTriplet<P::Fp2Params>>,
pub infinity: bool,
}
#[derive(Copy, Clone, Debug)]
struct G2HomProjective<P: Bls12Parameters> {
x: Fp2<P::Fp2Params>,
y: Fp2<P::Fp2Params>,
z: Fp2<P::Fp2Params>,
}
impl<P: Bls12Parameters> Default for G2Prepared<P> {
fn default() -> Self {
Self::from_affine(G2Affine::<P>::prime_subgroup_generator())
}
}
impl<P: Bls12Parameters> ToBytes for G2Prepared<P> {
fn write_le<W: Write>(&self, mut writer: W) -> IoResult<()> {
(self.ell_coeffs.len() as u32).write_le(&mut writer)?;
for coeff in &self.ell_coeffs {
coeff.0.write_le(&mut writer)?;
coeff.1.write_le(&mut writer)?;
coeff.2.write_le(&mut writer)?;
}
self.infinity.write_le(writer)
}
}
impl<P: Bls12Parameters> FromBytes for G2Prepared<P> {
fn read_le<R: Read>(mut reader: R) -> IoResult<Self> {
let ell_coeffs_len: u32 = FromBytes::read_le(&mut reader)?;
let mut ell_coeffs = Vec::with_capacity(ell_coeffs_len as usize);
for _ in 0..ell_coeffs_len {
let coeff_1: Fp2<P::Fp2Params> = FromBytes::read_le(&mut reader)?;
let coeff_2: Fp2<P::Fp2Params> = FromBytes::read_le(&mut reader)?;
let coeff_3: Fp2<P::Fp2Params> = FromBytes::read_le(&mut reader)?;
ell_coeffs.push((coeff_1, coeff_2, coeff_3));
}
let infinity: bool = FromBytes::read_le(&mut reader)?;
Ok(Self { ell_coeffs, infinity })
}
}
impl<P: Bls12Parameters> G2Prepared<P> {
pub fn is_zero(&self) -> bool {
self.infinity
}
pub fn from_affine(q: G2Affine<P>) -> Self {
if q.is_zero() {
return Self { ell_coeffs: vec![], infinity: true };
}
let mut r = G2HomProjective { x: q.x, y: q.y, z: Fp2::one() };
let bit_iterator = BitIteratorBE::new(P::X);
let mut ell_coeffs = Vec::with_capacity(bit_iterator.len());
let one_half = P::Fp::half();
for i in bit_iterator.skip(1) {
ell_coeffs.push(doubling_step::<P>(&mut r, &one_half));
if i {
ell_coeffs.push(addition_step::<P>(&mut r, &q));
}
}
Self { ell_coeffs, infinity: false }
}
}
#[allow(clippy::many_single_char_names)]
fn doubling_step<B: Bls12Parameters>(r: &mut G2HomProjective<B>, two_inv: &B::Fp) -> CoeffTriplet<B::Fp2Params> {
let mut a = r.x * r.y;
a.mul_by_fp(two_inv);
let b = r.y.square();
let c = r.z.square();
let e = B::G2Parameters::WEIERSTRASS_B * (c.double() + c);
let f = e.double() + e;
let mut g = b + f;
g.mul_by_fp(two_inv);
let h = (r.y + r.z).square() - (b + c);
let i = e - b;
let j = r.x.square();
let e_square = e.square();
r.x = a * (b - f);
r.y = g.square() - (e_square.double() + e_square);
r.z = b * h;
match B::TWIST_TYPE {
TwistType::M => (i, j.double() + j, -h),
TwistType::D => (-h, j.double() + j, i),
}
}
#[allow(clippy::many_single_char_names)]
fn addition_step<B: Bls12Parameters>(r: &mut G2HomProjective<B>, q: &G2Affine<B>) -> CoeffTriplet<B::Fp2Params> {
let theta = r.y - (q.y * r.z);
let lambda = r.x - (q.x * r.z);
let c = theta.square();
let d = lambda.square();
let e = lambda * d;
let f = r.z * c;
let g = r.x * d;
let h = e + f - g.double();
r.x = lambda * h;
r.y = theta * (g - h) - (e * r.y);
r.z *= &e;
let j = theta * q.x - (lambda * q.y);
match B::TWIST_TYPE {
TwistType::M => (j, -theta, lambda),
TwistType::D => (lambda, -theta, j),
}
}