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use ark_ff::{BitIteratorBE, Field, Fp2};
use ark_serialize::*;
use ark_std::{vec::Vec, One};
use crate::{
bls12::{Bls12Config, TwistType},
models::short_weierstrass::SWCurveConfig,
short_weierstrass::{Affine, Projective},
AffineRepr, CurveGroup,
};
pub type G2Affine<P> = Affine<<P as Bls12Config>::G2Config>;
pub type G2Projective<P> = Projective<<P as Bls12Config>::G2Config>;
#[derive(Derivative, CanonicalSerialize, CanonicalDeserialize)]
#[derivative(
Clone(bound = "P: Bls12Config"),
Debug(bound = "P: Bls12Config"),
PartialEq(bound = "P: Bls12Config"),
Eq(bound = "P: Bls12Config")
)]
pub struct G2Prepared<P: Bls12Config> {
pub ell_coeffs: Vec<EllCoeff<P>>,
pub infinity: bool,
}
pub(crate) type EllCoeff<P> = (
Fp2<<P as Bls12Config>::Fp2Config>,
Fp2<<P as Bls12Config>::Fp2Config>,
Fp2<<P as Bls12Config>::Fp2Config>,
);
#[derive(Derivative)]
#[derivative(
Clone(bound = "P: Bls12Config"),
Copy(bound = "P: Bls12Config"),
Debug(bound = "P: Bls12Config")
)]
struct G2HomProjective<P: Bls12Config> {
x: Fp2<P::Fp2Config>,
y: Fp2<P::Fp2Config>,
z: Fp2<P::Fp2Config>,
}
impl<P: Bls12Config> Default for G2Prepared<P> {
fn default() -> Self {
Self::from(G2Affine::<P>::generator())
}
}
impl<P: Bls12Config> From<G2Affine<P>> for G2Prepared<P> {
fn from(q: G2Affine<P>) -> Self {
let two_inv = P::Fp::one().double().inverse().unwrap();
let zero = G2Prepared {
ell_coeffs: vec![],
infinity: true,
};
q.xy().map_or(zero, |(&q_x, &q_y)| {
let mut ell_coeffs = vec![];
let mut r = G2HomProjective::<P> {
x: q_x,
y: q_y,
z: Fp2::one(),
};
for i in BitIteratorBE::new(P::X).skip(1) {
ell_coeffs.push(r.double_in_place(&two_inv));
if i {
ell_coeffs.push(r.add_in_place(&q));
}
}
Self {
ell_coeffs,
infinity: false,
}
})
}
}
impl<P: Bls12Config> From<G2Projective<P>> for G2Prepared<P> {
fn from(q: G2Projective<P>) -> Self {
q.into_affine().into()
}
}
impl<'a, P: Bls12Config> From<&'a G2Affine<P>> for G2Prepared<P> {
fn from(other: &'a G2Affine<P>) -> Self {
(*other).into()
}
}
impl<'a, P: Bls12Config> From<&'a G2Projective<P>> for G2Prepared<P> {
fn from(q: &'a G2Projective<P>) -> Self {
q.into_affine().into()
}
}
impl<P: Bls12Config> G2Prepared<P> {
pub fn is_zero(&self) -> bool {
self.infinity
}
}
impl<P: Bls12Config> G2HomProjective<P> {
fn double_in_place(&mut self, two_inv: &P::Fp) -> EllCoeff<P> {
let mut a = self.x * &self.y;
a.mul_assign_by_fp(two_inv);
let b = self.y.square();
let c = self.z.square();
let e = P::G2Config::COEFF_B * &(c.double() + &c);
let f = e.double() + &e;
let mut g = b + &f;
g.mul_assign_by_fp(two_inv);
let h = (self.y + &self.z).square() - &(b + &c);
let i = e - &b;
let j = self.x.square();
let e_square = e.square();
self.x = a * &(b - &f);
self.y = g.square() - &(e_square.double() + &e_square);
self.z = b * &h;
match P::TWIST_TYPE {
TwistType::M => (i, j.double() + &j, -h),
TwistType::D => (-h, j.double() + &j, i),
}
}
fn add_in_place(&mut self, q: &G2Affine<P>) -> EllCoeff<P> {
let (&qx, &qy) = q.xy().unwrap();
let theta = self.y - &(qy * &self.z);
let lambda = self.x - &(qx * &self.z);
let c = theta.square();
let d = lambda.square();
let e = lambda * &d;
let f = self.z * &c;
let g = self.x * &d;
let h = e + &f - &g.double();
self.x = lambda * &h;
self.y = theta * &(g - &h) - &(e * &self.y);
self.z *= &e;
let j = theta * &qx - &(lambda * &qy);
match P::TWIST_TYPE {
TwistType::M => (j, -theta, lambda),
TwistType::D => (lambda, -theta, j),
}
}
}