ark_r1cs_std/pairing/mnt4/
mod.rsuse ark_relations::r1cs::SynthesisError;
use super::PairingVar as PG;
use crate::{
fields::{fp::FpVar, fp2::Fp2Var, fp4::Fp4Var, FieldVar},
groups::mnt4::{
AteAdditionCoefficientsVar, AteDoubleCoefficientsVar, G1PreparedVar, G1Var, G2PreparedVar,
G2ProjectiveExtendedVar, G2Var,
},
};
use ark_ec::mnt4::{MNT4Config, MNT4};
use core::marker::PhantomData;
pub struct PairingVar<P: MNT4Config>(PhantomData<P>);
type Fp2G<P> = Fp2Var<<P as MNT4Config>::Fp2Config>;
type Fp4G<P> = Fp4Var<<P as MNT4Config>::Fp4Config>;
pub type GTVar<P> = Fp4G<P>;
impl<P: MNT4Config> PairingVar<P> {
#[tracing::instrument(target = "r1cs", skip(r))]
pub(crate) fn doubling_step_for_flipped_miller_loop(
r: &G2ProjectiveExtendedVar<P>,
) -> Result<(G2ProjectiveExtendedVar<P>, AteDoubleCoefficientsVar<P>), SynthesisError> {
let a = r.t.square()?;
let b = r.x.square()?;
let c = r.y.square()?;
let d = c.square()?;
let e = (&r.x + &c).square()? - &b - &d;
let f = (b.double()? + &b) + &a * P::TWIST_COEFF_A;
let g = f.square()?;
let d_eight = d.double()?.double()?.double()?;
let e2 = e.double()?;
let x = &g - &e2.double()?;
let y = &f * (&e2 - &x) - &d_eight;
let z = (&r.y + &r.z).square()? - &c - &r.z.square()?;
let t = z.square()?;
let r2 = G2ProjectiveExtendedVar { x, y, z, t };
let c_h = (&r2.z + &r.t).square()? - &r2.t - &a;
let c_4c = c.double()?.double()?;
let c_j = (&f + &r.t).square()? - &g - &a;
let c_l = (&f + &r.x).square()? - &g - &b;
let coeff = AteDoubleCoefficientsVar {
c_h,
c_4c,
c_j,
c_l,
};
Ok((r2, coeff))
}
#[tracing::instrument(target = "r1cs", skip(r))]
pub(crate) fn mixed_addition_step_for_flipped_miller_loop(
x: &Fp2G<P>,
y: &Fp2G<P>,
r: &G2ProjectiveExtendedVar<P>,
) -> Result<(G2ProjectiveExtendedVar<P>, AteAdditionCoefficientsVar<P>), SynthesisError> {
let a = y.square()?;
let b = &r.t * x;
let d = ((&r.z + y).square()? - &a - &r.t) * &r.t;
let h = &b - &r.x;
let i = h.square()?;
let e = i.double()?.double()?;
let j = &h * &e;
let v = &r.x * &e;
let ry2 = r.y.double()?;
let l1 = &d - &ry2;
let x = l1.square()? - &j - &v.double()?;
let y = &l1 * &(&v - &x) - j * &ry2;
let z = (&r.z + &h).square()? - &r.t - &i;
let t = z.square()?;
let r2 = G2ProjectiveExtendedVar {
x,
y,
z: z.clone(),
t,
};
let coeff = AteAdditionCoefficientsVar { c_l1: l1, c_rz: z };
Ok((r2, coeff))
}
#[tracing::instrument(target = "r1cs", skip(p, q))]
pub(crate) fn ate_miller_loop(
p: &G1PreparedVar<P>,
q: &G2PreparedVar<P>,
) -> Result<Fp4G<P>, SynthesisError> {
let l1_coeff = Fp2G::<P>::new(p.x.clone(), FpVar::<P::Fp>::zero()) - &q.x_over_twist;
let mut f = Fp4G::<P>::one();
let mut add_idx: usize = 0;
let y_over_twist_neg = &q.y_over_twist.negate()?;
for (dbl_idx, bit) in P::ATE_LOOP_COUNT.iter().skip(1).enumerate() {
let dc = &q.double_coefficients[dbl_idx];
let g_rr_at_p = Fp4G::<P>::new(
&dc.c_l - &dc.c_4c - &dc.c_j * &p.x_twist,
&dc.c_h * &p.y_twist,
);
f = f.square()? * &g_rr_at_p;
let g_rq_at_p;
if *bit == 1 {
let ac = &q.addition_coefficients[add_idx];
add_idx += 1;
g_rq_at_p = Fp4G::<P>::new(
&ac.c_rz * &p.y_twist,
(&q.y_over_twist * &ac.c_rz + &l1_coeff * &ac.c_l1).negate()?,
);
} else if *bit == -1 {
let ac = &q.addition_coefficients[add_idx];
add_idx += 1;
g_rq_at_p = Fp4G::<P>::new(
&ac.c_rz * &p.y_twist,
(y_over_twist_neg * &ac.c_rz + &l1_coeff * &ac.c_l1).negate()?,
);
} else {
continue;
}
f *= &g_rq_at_p;
}
if P::ATE_IS_LOOP_COUNT_NEG {
let ac = &q.addition_coefficients[add_idx];
let g_rnegr_at_p = Fp4G::<P>::new(
&ac.c_rz * &p.y_twist,
(&q.y_over_twist * &ac.c_rz + &l1_coeff * &ac.c_l1).negate()?,
);
f = (&f * &g_rnegr_at_p).inverse()?;
}
Ok(f)
}
#[tracing::instrument(target = "r1cs", skip(value))]
pub(crate) fn final_exponentiation(value: &Fp4G<P>) -> Result<GTVar<P>, SynthesisError> {
let value_inv = value.inverse()?;
let value_to_first_chunk = Self::final_exponentiation_first_chunk(value, &value_inv)?;
let value_inv_to_first_chunk = Self::final_exponentiation_first_chunk(&value_inv, value)?;
Self::final_exponentiation_last_chunk(&value_to_first_chunk, &value_inv_to_first_chunk)
}
#[tracing::instrument(target = "r1cs", skip(elt, elt_inv))]
fn final_exponentiation_first_chunk(
elt: &Fp4G<P>,
elt_inv: &Fp4G<P>,
) -> Result<Fp4G<P>, SynthesisError> {
let elt_q2 = elt.unitary_inverse()?;
Ok(elt_q2 * elt_inv)
}
#[tracing::instrument(target = "r1cs", skip(elt, elt_inv))]
fn final_exponentiation_last_chunk(
elt: &Fp4G<P>,
elt_inv: &Fp4G<P>,
) -> Result<Fp4G<P>, SynthesisError> {
let elt_clone = elt.clone();
let elt_inv_clone = elt_inv.clone();
let mut elt_q = elt.clone();
elt_q.frobenius_map_in_place(1)?;
let w1_part = elt_q.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_1)?;
let w0_part = if P::FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG {
elt_inv_clone.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0)?
} else {
elt_clone.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0)?
};
Ok(w1_part * &w0_part)
}
}
impl<P: MNT4Config> PG<MNT4<P>> for PairingVar<P> {
type G1Var = G1Var<P>;
type G2Var = G2Var<P>;
type G1PreparedVar = G1PreparedVar<P>;
type G2PreparedVar = G2PreparedVar<P>;
type GTVar = GTVar<P>;
#[tracing::instrument(target = "r1cs")]
fn miller_loop(
ps: &[Self::G1PreparedVar],
qs: &[Self::G2PreparedVar],
) -> Result<Self::GTVar, SynthesisError> {
let mut result = Fp4G::<P>::one();
for (p, q) in ps.iter().zip(qs) {
result *= Self::ate_miller_loop(p, q)?;
}
Ok(result)
}
#[tracing::instrument(target = "r1cs")]
fn final_exponentiation(r: &Self::GTVar) -> Result<Self::GTVar, SynthesisError> {
Self::final_exponentiation(r)
}
#[tracing::instrument(target = "r1cs")]
fn prepare_g1(p: &Self::G1Var) -> Result<Self::G1PreparedVar, SynthesisError> {
Self::G1PreparedVar::from_group_var(p)
}
#[tracing::instrument(target = "r1cs")]
fn prepare_g2(q: &Self::G2Var) -> Result<Self::G2PreparedVar, SynthesisError> {
Self::G2PreparedVar::from_group_var(q)
}
}