use ark_ec::mnt6::{
g2::{AteAdditionCoefficients, AteDoubleCoefficients},
G1Prepared, G2Prepared, MNT6Config,
};
use ark_ff::Field;
use ark_relations::r1cs::{Namespace, SynthesisError};
use crate::{
convert::ToBytesGadget,
fields::{fp::FpVar, fp3::Fp3Var, FieldVar},
groups::curves::short_weierstrass::ProjectiveVar,
pairing::mnt6::PairingVar,
prelude::*,
Vec,
};
use core::borrow::Borrow;
use educe::Educe;
pub type G1Var<P> = ProjectiveVar<<P as MNT6Config>::G1Config, FpVar<<P as MNT6Config>::Fp>>;
pub type G2Var<P> = ProjectiveVar<<P as MNT6Config>::G2Config, Fp3G<P>>;
#[derive(Educe)]
#[educe(Clone, Debug)]
pub struct G1PreparedVar<P: MNT6Config> {
#[doc(hidden)]
pub x: FpVar<P::Fp>,
#[doc(hidden)]
pub y: FpVar<P::Fp>,
#[doc(hidden)]
pub x_twist: Fp3Var<P::Fp3Config>,
#[doc(hidden)]
pub y_twist: Fp3Var<P::Fp3Config>,
}
impl<P: MNT6Config> G1PreparedVar<P> {
pub fn value(&self) -> Result<G1Prepared<P>, SynthesisError> {
let x = self.x.value()?;
let y = self.y.value()?;
let x_twist = self.x_twist.value()?;
let y_twist = self.y_twist.value()?;
Ok(G1Prepared {
x,
y,
x_twist,
y_twist,
})
}
#[tracing::instrument(target = "r1cs")]
pub fn from_group_var(q: &G1Var<P>) -> Result<Self, SynthesisError> {
let q = q.to_affine()?;
let zero = FpVar::<P::Fp>::zero();
let x_twist = Fp3Var::new(q.x.clone(), zero.clone(), zero.clone()) * P::TWIST;
let y_twist = Fp3Var::new(q.y.clone(), zero.clone(), zero) * P::TWIST;
let result = G1PreparedVar {
x: q.x,
y: q.y,
x_twist,
y_twist,
};
Ok(result)
}
}
impl<P: MNT6Config> AllocVar<G1Prepared<P>, P::Fp> for G1PreparedVar<P> {
#[tracing::instrument(target = "r1cs", skip(cs, f))]
fn new_variable<T: Borrow<G1Prepared<P>>>(
cs: impl Into<Namespace<P::Fp>>,
f: impl FnOnce() -> Result<T, SynthesisError>,
mode: AllocationMode,
) -> Result<Self, SynthesisError> {
let ns = cs.into();
let cs = ns.cs();
let g1_prep = f().map(|b| *b.borrow());
let x = FpVar::new_variable(ark_relations::ns!(cs, "x"), || g1_prep.map(|g| g.x), mode)?;
let y = FpVar::new_variable(ark_relations::ns!(cs, "y"), || g1_prep.map(|g| g.y), mode)?;
let x_twist = Fp3Var::new_variable(
ark_relations::ns!(cs, "x_twist"),
|| g1_prep.map(|g| g.x_twist),
mode,
)?;
let y_twist = Fp3Var::new_variable(
ark_relations::ns!(cs, "y_twist"),
|| g1_prep.map(|g| g.y_twist),
mode,
)?;
Ok(Self {
x,
y,
x_twist,
y_twist,
})
}
}
impl<P: MNT6Config> ToBytesGadget<P::Fp> for G1PreparedVar<P> {
#[inline]
#[tracing::instrument(target = "r1cs")]
fn to_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut x = self.x.to_bytes_le()?;
let mut y = self.y.to_bytes_le()?;
let mut x_twist = self.x_twist.to_bytes_le()?;
let mut y_twist = self.y_twist.to_bytes_le()?;
x.append(&mut y);
x.append(&mut x_twist);
x.append(&mut y_twist);
Ok(x)
}
#[tracing::instrument(target = "r1cs")]
fn to_non_unique_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut x = self.x.to_non_unique_bytes_le()?;
let mut y = self.y.to_non_unique_bytes_le()?;
let mut x_twist = self.x_twist.to_non_unique_bytes_le()?;
let mut y_twist = self.y_twist.to_non_unique_bytes_le()?;
x.append(&mut y);
x.append(&mut x_twist);
x.append(&mut y_twist);
Ok(x)
}
}
type Fp3G<P> = Fp3Var<<P as MNT6Config>::Fp3Config>;
#[derive(Educe)]
#[educe(Clone, Debug)]
pub struct G2PreparedVar<P: MNT6Config> {
#[doc(hidden)]
pub x: Fp3Var<P::Fp3Config>,
#[doc(hidden)]
pub y: Fp3Var<P::Fp3Config>,
#[doc(hidden)]
pub x_over_twist: Fp3Var<P::Fp3Config>,
#[doc(hidden)]
pub y_over_twist: Fp3Var<P::Fp3Config>,
#[doc(hidden)]
pub double_coefficients: Vec<AteDoubleCoefficientsVar<P>>,
#[doc(hidden)]
pub addition_coefficients: Vec<AteAdditionCoefficientsVar<P>>,
}
impl<P: MNT6Config> AllocVar<G2Prepared<P>, P::Fp> for G2PreparedVar<P> {
#[tracing::instrument(target = "r1cs", skip(cs, f))]
fn new_variable<T: Borrow<G2Prepared<P>>>(
cs: impl Into<Namespace<P::Fp>>,
f: impl FnOnce() -> Result<T, SynthesisError>,
mode: AllocationMode,
) -> Result<Self, SynthesisError> {
let ns = cs.into();
let cs = ns.cs();
let g2_prep = f().map(|b| b.borrow().clone());
let g2 = g2_prep.as_ref().map_err(|e| *e);
let x = Fp3Var::new_variable(ark_relations::ns!(cs, "x"), || g2.map(|g| g.x), mode)?;
let y = Fp3Var::new_variable(ark_relations::ns!(cs, "y"), || g2.map(|g| g.y), mode)?;
let x_over_twist = Fp3Var::new_variable(
ark_relations::ns!(cs, "x_over_twist"),
|| g2.map(|g| g.x_over_twist),
mode,
)?;
let y_over_twist = Fp3Var::new_variable(
ark_relations::ns!(cs, "y_over_twist"),
|| g2.map(|g| g.y_over_twist),
mode,
)?;
let double_coefficients = Vec::new_variable(
ark_relations::ns!(cs, "double coeffs"),
|| g2.map(|g| g.double_coefficients.clone()),
mode,
)?;
let addition_coefficients = Vec::new_variable(
ark_relations::ns!(cs, "add coeffs"),
|| g2.map(|g| g.addition_coefficients.clone()),
mode,
)?;
Ok(Self {
x,
y,
x_over_twist,
y_over_twist,
double_coefficients,
addition_coefficients,
})
}
}
impl<P: MNT6Config> ToBytesGadget<P::Fp> for G2PreparedVar<P> {
#[inline]
#[tracing::instrument(target = "r1cs")]
fn to_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut x = self.x.to_bytes_le()?;
let mut y = self.y.to_bytes_le()?;
let mut x_over_twist = self.x_over_twist.to_bytes_le()?;
let mut y_over_twist = self.y_over_twist.to_bytes_le()?;
x.append(&mut y);
x.append(&mut x_over_twist);
x.append(&mut y_over_twist);
for coeff in self.double_coefficients.iter() {
x.extend_from_slice(&coeff.to_bytes_le()?);
}
for coeff in self.addition_coefficients.iter() {
x.extend_from_slice(&coeff.to_bytes_le()?);
}
Ok(x)
}
#[tracing::instrument(target = "r1cs")]
fn to_non_unique_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut x = self.x.to_non_unique_bytes_le()?;
let mut y = self.y.to_non_unique_bytes_le()?;
let mut x_over_twist = self.x_over_twist.to_non_unique_bytes_le()?;
let mut y_over_twist = self.y_over_twist.to_non_unique_bytes_le()?;
x.append(&mut y);
x.append(&mut x_over_twist);
x.append(&mut y_over_twist);
for coeff in self.double_coefficients.iter() {
x.extend_from_slice(&coeff.to_non_unique_bytes_le()?);
}
for coeff in self.addition_coefficients.iter() {
x.extend_from_slice(&coeff.to_non_unique_bytes_le()?);
}
Ok(x)
}
}
impl<P: MNT6Config> G2PreparedVar<P> {
pub fn value(&self) -> Result<G2Prepared<P>, SynthesisError> {
let x = self.x.value()?;
let y = self.y.value()?;
let x_over_twist = self.x_over_twist.value()?;
let y_over_twist = self.y_over_twist.value()?;
let double_coefficients = self
.double_coefficients
.iter()
.map(|coeff| coeff.value())
.collect::<Result<Vec<_>, SynthesisError>>()?;
let addition_coefficients = self
.addition_coefficients
.iter()
.map(|coeff| coeff.value())
.collect::<Result<Vec<_>, SynthesisError>>()?;
Ok(G2Prepared {
x,
y,
x_over_twist,
y_over_twist,
double_coefficients,
addition_coefficients,
})
}
#[tracing::instrument(target = "r1cs")]
pub fn from_group_var(q: &G2Var<P>) -> Result<Self, SynthesisError> {
let q = q.to_affine()?;
let twist_inv = P::TWIST.inverse().unwrap();
let mut g2p = G2PreparedVar {
x: q.x.clone(),
y: q.y.clone(),
x_over_twist: &q.x * twist_inv,
y_over_twist: &q.y * twist_inv,
double_coefficients: vec![],
addition_coefficients: vec![],
};
let mut r = G2ProjectiveExtendedVar {
x: q.x.clone(),
y: q.y.clone(),
z: Fp3G::<P>::one(),
t: Fp3G::<P>::one(),
};
for bit in P::ATE_LOOP_COUNT.iter().skip(1) {
let (r2, coeff) = PairingVar::<P>::doubling_step_for_flipped_miller_loop(&r)?;
g2p.double_coefficients.push(coeff);
r = r2;
let add_coeff;
let r_temp;
match bit {
1 => {
(r_temp, add_coeff) =
PairingVar::<P>::mixed_addition_step_for_flipped_miller_loop(
&q.x, &q.y, &r,
)?;
},
-1 => {
(r_temp, add_coeff) =
PairingVar::<P>::mixed_addition_step_for_flipped_miller_loop(
&q.x,
&q.y.negate()?,
&r,
)?;
},
_ => continue,
}
g2p.addition_coefficients.push(add_coeff);
r = r_temp;
}
if P::ATE_IS_LOOP_COUNT_NEG {
let rz_inv = r.z.inverse()?;
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.negate()? * &rz3_inv;
let add_result = PairingVar::<P>::mixed_addition_step_for_flipped_miller_loop(
&minus_r_affine_x,
&minus_r_affine_y,
&r,
)?;
g2p.addition_coefficients.push(add_result.1);
}
Ok(g2p)
}
}
#[doc(hidden)]
#[derive(Educe)]
#[educe(Clone, Debug)]
pub struct AteDoubleCoefficientsVar<P: MNT6Config> {
pub c_h: Fp3Var<P::Fp3Config>,
pub c_4c: Fp3Var<P::Fp3Config>,
pub c_j: Fp3Var<P::Fp3Config>,
pub c_l: Fp3Var<P::Fp3Config>,
}
impl<P: MNT6Config> AllocVar<AteDoubleCoefficients<P>, P::Fp> for AteDoubleCoefficientsVar<P> {
#[tracing::instrument(target = "r1cs", skip(cs, f))]
fn new_variable<T: Borrow<AteDoubleCoefficients<P>>>(
cs: impl Into<Namespace<P::Fp>>,
f: impl FnOnce() -> Result<T, SynthesisError>,
mode: AllocationMode,
) -> Result<Self, SynthesisError> {
let ns = cs.into();
let cs = ns.cs();
let c_prep = f().map(|c| c.borrow().clone());
let c = c_prep.as_ref().map_err(|e| *e);
let c_h = Fp3Var::new_variable(ark_relations::ns!(cs, "c_h"), || c.map(|c| c.c_h), mode)?;
let c_4c =
Fp3Var::new_variable(ark_relations::ns!(cs, "c_4c"), || c.map(|c| c.c_4c), mode)?;
let c_j = Fp3Var::new_variable(ark_relations::ns!(cs, "c_j"), || c.map(|c| c.c_j), mode)?;
let c_l = Fp3Var::new_variable(ark_relations::ns!(cs, "c_l"), || c.map(|c| c.c_l), mode)?;
Ok(Self {
c_h,
c_4c,
c_j,
c_l,
})
}
}
impl<P: MNT6Config> ToBytesGadget<P::Fp> for AteDoubleCoefficientsVar<P> {
#[inline]
#[tracing::instrument(target = "r1cs")]
fn to_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut c_h = self.c_h.to_bytes_le()?;
let mut c_4c = self.c_4c.to_bytes_le()?;
let mut c_j = self.c_j.to_bytes_le()?;
let mut c_l = self.c_l.to_bytes_le()?;
c_h.append(&mut c_4c);
c_h.append(&mut c_j);
c_h.append(&mut c_l);
Ok(c_h)
}
#[tracing::instrument(target = "r1cs")]
fn to_non_unique_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut c_h = self.c_h.to_non_unique_bytes_le()?;
let mut c_4c = self.c_4c.to_non_unique_bytes_le()?;
let mut c_j = self.c_j.to_non_unique_bytes_le()?;
let mut c_l = self.c_l.to_non_unique_bytes_le()?;
c_h.append(&mut c_4c);
c_h.append(&mut c_j);
c_h.append(&mut c_l);
Ok(c_h)
}
}
impl<P: MNT6Config> AteDoubleCoefficientsVar<P> {
pub fn value(&self) -> Result<AteDoubleCoefficients<P>, SynthesisError> {
let c_h = self.c_h.value()?;
let c_4c = self.c_4c.value()?;
let c_j = self.c_j.value()?;
let c_l = self.c_l.value()?;
Ok(AteDoubleCoefficients {
c_h,
c_4c,
c_j,
c_l,
})
}
}
#[doc(hidden)]
#[derive(Educe)]
#[educe(Clone, Debug)]
pub struct AteAdditionCoefficientsVar<P: MNT6Config> {
pub c_l1: Fp3Var<P::Fp3Config>,
pub c_rz: Fp3Var<P::Fp3Config>,
}
impl<P: MNT6Config> AllocVar<AteAdditionCoefficients<P>, P::Fp> for AteAdditionCoefficientsVar<P> {
#[tracing::instrument(target = "r1cs", skip(cs, f))]
fn new_variable<T: Borrow<AteAdditionCoefficients<P>>>(
cs: impl Into<Namespace<P::Fp>>,
f: impl FnOnce() -> Result<T, SynthesisError>,
mode: AllocationMode,
) -> Result<Self, SynthesisError> {
let ns = cs.into();
let cs = ns.cs();
let c_prep = f().map(|c| c.borrow().clone());
let c = c_prep.as_ref().map_err(|e| *e);
let c_l1 =
Fp3Var::new_variable(ark_relations::ns!(cs, "c_l1"), || c.map(|c| c.c_l1), mode)?;
let c_rz =
Fp3Var::new_variable(ark_relations::ns!(cs, "c_rz"), || c.map(|c| c.c_rz), mode)?;
Ok(Self { c_l1, c_rz })
}
}
impl<P: MNT6Config> ToBytesGadget<P::Fp> for AteAdditionCoefficientsVar<P> {
#[inline]
#[tracing::instrument(target = "r1cs")]
fn to_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut c_l1 = self.c_l1.to_bytes_le()?;
let mut c_rz = self.c_rz.to_bytes_le()?;
c_l1.append(&mut c_rz);
Ok(c_l1)
}
#[tracing::instrument(target = "r1cs")]
fn to_non_unique_bytes_le(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
let mut c_l1 = self.c_l1.to_non_unique_bytes_le()?;
let mut c_rz = self.c_rz.to_non_unique_bytes_le()?;
c_l1.append(&mut c_rz);
Ok(c_l1)
}
}
impl<P: MNT6Config> AteAdditionCoefficientsVar<P> {
pub fn value(&self) -> Result<AteAdditionCoefficients<P>, SynthesisError> {
let c_l1 = self.c_l1.value()?;
let c_rz = self.c_rz.value()?;
Ok(AteAdditionCoefficients { c_l1, c_rz })
}
}
#[doc(hidden)]
pub struct G2ProjectiveExtendedVar<P: MNT6Config> {
pub x: Fp3Var<P::Fp3Config>,
pub y: Fp3Var<P::Fp3Config>,
pub z: Fp3Var<P::Fp3Config>,
pub t: Fp3Var<P::Fp3Config>,
}