1use r1cs_core::SynthesisError;
  2
  3use super::PairingVar as PG;
  4
  5use crate::{
  6    fields::{fp::FpVar, fp3::Fp3Var, fp6_2over3::Fp6Var, FieldVar},
  7    groups::mnt6::{
  8        AteAdditionCoefficientsVar, AteDoubleCoefficientsVar, G1PreparedVar, G1Var, G2PreparedVar,
  9        G2ProjectiveExtendedVar, G2Var,
 10    },
 11};
 12use algebra::{
 13    curves::mnt6::{MNT6Parameters, MNT6},
 14    fields::BitIterator,
 15};
 16use core::marker::PhantomData;
 17
 18pub struct PairingVar<P: MNT6Parameters>(PhantomData<P>);
 19
 20type Fp3G<P> = Fp3Var<<P as MNT6Parameters>::Fp3Params>;
 21type Fp6G<P> = Fp6Var<<P as MNT6Parameters>::Fp6Params>;
 22pub type GTVar<P> = Fp6G<P>;
 23
 24impl<P: MNT6Parameters> PairingVar<P> {
 25    pub(crate) fn doubling_step_for_flipped_miller_loop(
 26        r: &G2ProjectiveExtendedVar<P>,
 27    ) -> Result<(G2ProjectiveExtendedVar<P>, AteDoubleCoefficientsVar<P>), SynthesisError> {
 28        let a = r.t.square()?;
 29        let b = r.x.square()?;
 30        let c = r.y.square()?;
 31        let d = c.square()?;
 32        let e = (&r.x + &c).square()? - &b - &d;
 33        let f = b.double()? + &b + &(&a * P::TWIST_COEFF_A);
 34        let g = f.square()?;
 35
 36        let d_eight = d.double()?.double()?.double()?;
 37
 38        let e2 = e.double()?;
 39        let x = &g - e2.double()?;
 40        let y = &f * (e2 - &x) - d_eight;
 41        let z = (&r.y + &r.z).square()? - &c - &r.z.square()?;
 42        let t = z.square()?;
 43
 44        let r2 = G2ProjectiveExtendedVar { x, y, z, t };
 45        let coeff = AteDoubleCoefficientsVar {
 46            c_h: (&r2.z + &r.t).square()? - &r2.t - &a,
 47            c_4c: c.double()?.double()?,
 48            c_j: (&f + &r.t).square()? - &g - &a,
 49            c_l: (&f + &r.x).square()? - &g - &b,
 50        };
 51
 52        Ok((r2, coeff))
 53    }
 54
 55    pub(crate) fn mixed_addition_step_for_flipped_miller_loop(
 56        x: &Fp3G<P>,
 57        y: &Fp3G<P>,
 58        r: &G2ProjectiveExtendedVar<P>,
 59    ) -> Result<(G2ProjectiveExtendedVar<P>, AteAdditionCoefficientsVar<P>), SynthesisError> {
 60        let a = y.square()?;
 61        let b = &r.t * x;
 62        let d = ((&r.z + y).square()? - &a - &r.t) * &r.t;
 63        let h = &b - &r.x;
 64        let i = h.square()?;
 65        let e = i.double()?.double()?;
 66        let j = &h * &e;
 67        let v = &r.x * &e;
 68        let ry2 = r.y.double()?;
 69        let l1 = &d - &ry2;
 70
 71        let x = l1.square()? - &j - &v.double()?;
 72        let y = &l1 * &(&v - &x) - &j * ry2;
 73        let z = (&r.z + &h).square()? - &r.t - &i;
 74        let t = z.square()?;
 75
 76        let r2 = G2ProjectiveExtendedVar {
 77            x,
 78            y,
 79            z: z.clone(),
 80            t,
 81        };
 82        let coeff = AteAdditionCoefficientsVar { c_l1: l1, c_rz: z };
 83
 84        Ok((r2, coeff))
 85    }
 86
 87    pub fn ate_miller_loop(
 88        p: &G1PreparedVar<P>,
 89        q: &G2PreparedVar<P>,
 90    ) -> Result<Fp6G<P>, SynthesisError> {
 91        let zero = FpVar::<P::Fp>::zero();
 92        let l1_coeff = Fp3Var::new(p.x.clone(), zero.clone(), zero) - &q.x_over_twist;
 93
 94        let mut f = Fp6G::<P>::one();
 95
 96        let mut dbl_idx: usize = 0;
 97        let mut add_idx: usize = 0;
 98
 99        let mut found_one = false;
100
101        for bit in BitIterator::new(P::ATE_LOOP_COUNT) {
102            // code below gets executed for all bits (EXCEPT the MSB itself) of
103            // mnt6_param_p (skipping leading zeros) in MSB to LSB order
104            if !found_one && bit {
105                found_one = true;
106                continue;
107            } else if !found_one {
108                continue;
109            }
110
111            let dc = &q.double_coefficients[dbl_idx];
112            dbl_idx += 1;
113
114            let g_rr_at_p = Fp6Var::new(
115                &dc.c_l - &dc.c_4c - &dc.c_j * &p.x_twist,
116                &dc.c_h * &p.y_twist,
117            );
118
119            f = f.square()? * &g_rr_at_p;
120
121            if bit {
122                let ac = &q.addition_coefficients[add_idx];
123                add_idx += 1;
124
125                let g_rq_at_p = Fp6Var::new(
126                    &ac.c_rz * &p.y_twist,
127                    (&q.y_over_twist * &ac.c_rz + &(&l1_coeff * &ac.c_l1)).negate()?,
128                );
129                f *= &g_rq_at_p;
130            }
131        }
132
133        if P::ATE_IS_LOOP_COUNT_NEG {
134            let ac = &q.addition_coefficients[add_idx];
135
136            let g_rnegr_at_p = Fp6Var::new(
137                &ac.c_rz * &p.y_twist,
138                (&q.y_over_twist * &ac.c_rz + &(l1_coeff * &ac.c_l1)).negate()?,
139            );
140            f = (f * &g_rnegr_at_p).inverse()?;
141        }
142
143        Ok(f)
144    }
145
146    pub fn final_exponentiation(value: &Fp6G<P>) -> Result<GTVar<P>, SynthesisError> {
147        let value_inv = value.inverse()?;
148        let value_to_first_chunk = Self::final_exponentiation_first_chunk(value, &value_inv)?;
149        let value_inv_to_first_chunk = Self::final_exponentiation_first_chunk(&value_inv, value)?;
150        Self::final_exponentiation_last_chunk(&value_to_first_chunk, &value_inv_to_first_chunk)
151    }
152
153    fn final_exponentiation_first_chunk(
154        elt: &Fp6G<P>,
155        elt_inv: &Fp6G<P>,
156    ) -> Result<Fp6G<P>, SynthesisError> {
157        // (q^3-1)*(q+1)
158
159        // elt_q3 = elt^(q^3)
160        let elt_q3 = elt.unitary_inverse()?;
161        // elt_q3_over_elt = elt^(q^3-1)
162        let elt_q3_over_elt = elt_q3 * elt_inv;
163        // alpha = elt^((q^3-1) * q)
164        let alpha = elt_q3_over_elt.frobenius_map(1)?;
165        // beta = elt^((q^3-1)*(q+1)
166        Ok(alpha * &elt_q3_over_elt)
167    }
168
169    fn final_exponentiation_last_chunk(
170        elt: &Fp6G<P>,
171        elt_inv: &Fp6G<P>,
172    ) -> Result<Fp6G<P>, SynthesisError> {
173        let elt_q = elt.frobenius_map(1)?;
174
175        let w1_part = elt_q.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_1)?;
176        let w0_part = if P::FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG {
177            elt_inv.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0)?
178        } else {
179            elt.cyclotomic_exp(&P::FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0)?
180        };
181
182        Ok(w1_part * &w0_part)
183    }
184}
185
186impl<P: MNT6Parameters> PG<MNT6<P>, P::Fp> for PairingVar<P> {
187    type G1Var = G1Var<P>;
188    type G2Var = G2Var<P>;
189    type G1PreparedVar = G1PreparedVar<P>;
190    type G2PreparedVar = G2PreparedVar<P>;
191    type GTVar = GTVar<P>;
192
193    fn miller_loop(
194        ps: &[Self::G1PreparedVar],
195        qs: &[Self::G2PreparedVar],
196    ) -> Result<Self::GTVar, SynthesisError> {
197        let mut result = Fp6G::<P>::one();
198        for (p, q) in ps.iter().zip(qs) {
199            result *= Self::ate_miller_loop(p, q)?;
200        }
201
202        Ok(result)
203    }
204
205    fn final_exponentiation(r: &Self::GTVar) -> Result<Self::GTVar, SynthesisError> {
206        Self::final_exponentiation(r)
207    }
208
209    fn prepare_g1(p: &Self::G1Var) -> Result<Self::G1PreparedVar, SynthesisError> {
210        Self::G1PreparedVar::from_group_var(p)
211    }
212
213    fn prepare_g2(q: &Self::G2Var) -> Result<Self::G2PreparedVar, SynthesisError> {
214        Self::G2PreparedVar::from_group_var(q)
215    }
216}