ark-ec 0.3.0

A library for elliptic curves and pairings
Documentation 
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use crate::{
    mnt6::MNT6Parameters,
    models::mnt6::MNT6,
    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
    AffineCurve,
};
use ark_ff::{
    bytes::ToBytes,
    fields::{Field, Fp3},
};
use ark_std::{
    io::{Result as IoResult, Write},
    vec::Vec,
};
use num_traits::One;

pub type G2Affine<P> = GroupAffine<<P as MNT6Parameters>::G2Parameters>;
pub type G2Projective<P> = GroupProjective<<P as MNT6Parameters>::G2Parameters>;

#[derive(Derivative)]
#[derivative(
    Clone(bound = "P: MNT6Parameters"),
    Debug(bound = "P: MNT6Parameters"),
    PartialEq(bound = "P: MNT6Parameters"),
    Eq(bound = "P: MNT6Parameters")
)]
pub struct G2Prepared<P: MNT6Parameters> {
    pub x: Fp3<P::Fp3Params>,
    pub y: Fp3<P::Fp3Params>,
    pub x_over_twist: Fp3<P::Fp3Params>,
    pub y_over_twist: Fp3<P::Fp3Params>,
    pub double_coefficients: Vec<AteDoubleCoefficients<P>>,
    pub addition_coefficients: Vec<AteAdditionCoefficients<P>>,
}

impl<P: MNT6Parameters> Default for G2Prepared<P> {
    fn default() -> Self {
        Self::from(G2Affine::<P>::prime_subgroup_generator())
    }
}

impl<P: MNT6Parameters> ToBytes for G2Prepared<P> {
    fn write<W: Write>(&self, _writer: W) -> IoResult<()> {
        unimplemented!()
    }
}

impl<P: MNT6Parameters> From<G2Affine<P>> for G2Prepared<P> {
    fn from(g2: G2Affine<P>) -> Self {
        let twist_inv = P::TWIST.inverse().unwrap();

        let mut g2p = G2Prepared {
            x: g2.x,
            y: g2.y,
            x_over_twist: g2.x * &twist_inv,
            y_over_twist: g2.y * &twist_inv,
            double_coefficients: vec![],
            addition_coefficients: vec![],
        };

        let mut r = G2ProjectiveExtended {
            x: g2.x,
            y: g2.y,
            z: <Fp3<P::Fp3Params>>::one(),
            t: <Fp3<P::Fp3Params>>::one(),
        };

        for (idx, value) in P::ATE_LOOP_COUNT.iter().rev().enumerate() {
            let mut tmp = *value;
            let skip_extraneous_bits = 64 - value.leading_zeros();
            let mut v = Vec::with_capacity(16);
            for i in 0..64 {
                if idx == 0 && (i == 0 || i >= skip_extraneous_bits) {
                    continue;
                }
                v.push(tmp & 1 == 1);
                tmp >>= 1;
            }

            for bit in v.iter().rev() {
                let (r2, coeff) = MNT6::<P>::doubling_step_for_flipped_miller_loop(&r);
                g2p.double_coefficients.push(coeff);
                r = r2;

                if *bit {
                    let (r2, coeff) =
                        MNT6::<P>::mixed_addition_step_for_flipped_miller_loop(&g2.x, &g2.y, &r);
                    g2p.addition_coefficients.push(coeff);
                    r = r2;
                }

                tmp >>= 1;
            }
        }

        if P::ATE_IS_LOOP_COUNT_NEG {
            let rz_inv = r.z.inverse().unwrap();
            let rz2_inv = rz_inv.square();
            let rz3_inv = rz_inv * &rz2_inv;

            let minus_r_affine_x = r.x * &rz2_inv;
            let minus_r_affine_y = -r.y * &rz3_inv;

            let add_result = MNT6::<P>::mixed_addition_step_for_flipped_miller_loop(
                &minus_r_affine_x,
                &minus_r_affine_y,
                &r,
            );
            g2p.addition_coefficients.push(add_result.1);
        }

        g2p
    }
}

pub(super) struct G2ProjectiveExtended<P: MNT6Parameters> {
    pub(crate) x: Fp3<P::Fp3Params>,
    pub(crate) y: Fp3<P::Fp3Params>,
    pub(crate) z: Fp3<P::Fp3Params>,
    pub(crate) t: Fp3<P::Fp3Params>,
}

#[derive(Derivative)]
#[derivative(
    Clone(bound = "P: MNT6Parameters"),
    Debug(bound = "P: MNT6Parameters"),
    PartialEq(bound = "P: MNT6Parameters"),
    Eq(bound = "P: MNT6Parameters")
)]
pub struct AteDoubleCoefficients<P: MNT6Parameters> {
    pub c_h: Fp3<P::Fp3Params>,
    pub c_4c: Fp3<P::Fp3Params>,
    pub c_j: Fp3<P::Fp3Params>,
    pub c_l: Fp3<P::Fp3Params>,
}

#[derive(Derivative)]
#[derivative(
    Clone(bound = "P: MNT6Parameters"),
    Debug(bound = "P: MNT6Parameters"),
    PartialEq(bound = "P: MNT6Parameters"),
    Eq(bound = "P: MNT6Parameters")
)]
pub struct AteAdditionCoefficients<P: MNT6Parameters> {
    pub c_l1: Fp3<P::Fp3Params>,
    pub c_rz: Fp3<P::Fp3Params>,
}