1use crate::prelude::*;
  2use algebra::{Field, PairingEngine};
  3use core::fmt::Debug;
  4use r1cs_core::{ConstraintSystem, SynthesisError};
  5
  6pub mod bls12;
  7pub use self::bls12::bls12_377;
  8
  9pub trait PairingGadget<PairingE: PairingEngine, ConstraintF: Field> {
 10    type G1Gadget: GroupGadget<PairingE::G1Projective, ConstraintF>;
 11    type G2Gadget: GroupGadget<PairingE::G2Projective, ConstraintF>;
 12    type G1PreparedGadget: ToBytesGadget<ConstraintF> + Clone + Debug;
 13    type G2PreparedGadget: ToBytesGadget<ConstraintF> + Clone + Debug;
 14    type GTGadget: FieldGadget<PairingE::Fqk, ConstraintF> + Clone;
 15
 16    fn miller_loop<CS: ConstraintSystem<ConstraintF>>(
 17        cs: CS,
 18        p: &[Self::G1PreparedGadget],
 19        q: &[Self::G2PreparedGadget],
 20    ) -> Result<Self::GTGadget, SynthesisError>;
 21
 22    fn final_exponentiation<CS: ConstraintSystem<ConstraintF>>(
 23        cs: CS,
 24        p: &Self::GTGadget,
 25    ) -> Result<Self::GTGadget, SynthesisError>;
 26
 27    fn pairing<CS: ConstraintSystem<ConstraintF>>(
 28        mut cs: CS,
 29        p: Self::G1PreparedGadget,
 30        q: Self::G2PreparedGadget,
 31    ) -> Result<Self::GTGadget, SynthesisError> {
 32        let tmp = Self::miller_loop(cs.ns(|| "miller loop"), &[p], &[q])?;
 33        Self::final_exponentiation(cs.ns(|| "final_exp"), &tmp)
 34    }
 35
 36    /// Computes a product of pairings.
 37    #[must_use]
 38    fn product_of_pairings<CS: ConstraintSystem<ConstraintF>>(
 39        mut cs: CS,
 40        p: &[Self::G1PreparedGadget],
 41        q: &[Self::G2PreparedGadget],
 42    ) -> Result<Self::GTGadget, SynthesisError> {
 43        let miller_result = Self::miller_loop(&mut cs.ns(|| "Miller loop"), p, q)?;
 44        Self::final_exponentiation(&mut cs.ns(|| "Final Exp"), &miller_result)
 45    }
 46
 47    fn prepare_g1<CS: ConstraintSystem<ConstraintF>>(
 48        cs: CS,
 49        q: &Self::G1Gadget,
 50    ) -> Result<Self::G1PreparedGadget, SynthesisError>;
 51
 52    fn prepare_g2<CS: ConstraintSystem<ConstraintF>>(
 53        cs: CS,
 54        q: &Self::G2Gadget,
 55    ) -> Result<Self::G2PreparedGadget, SynthesisError>;
 56}
 57
 58#[cfg(test)]
 59mod test {
 60    use crate::{test_constraint_system::TestConstraintSystem, Vec};
 61    use algebra::{BitIterator, Field, One};
 62    use r1cs_core::ConstraintSystem;
 63
 64    #[test]
 65    fn bls12_377_gadget_bilinearity_test() {
 66        use algebra::{
 67            fields::{
 68                bls12_377::{fq::Fq, fr::Fr},
 69                PrimeField,
 70            },
 71            PairingEngine, ProjectiveCurve,
 72        };
 73
 74        use super::bls12_377::PairingGadget;
 75        use crate::{
 76            groups::bls12::bls12_377::{G1Gadget, G1PreparedGadget, G2Gadget, G2PreparedGadget},
 77            pairing::PairingGadget as _,
 78            prelude::*,
 79        };
 80        use algebra::curves::bls12_377::{Bls12_377, G1Projective, G2Projective};
 81        use core::ops::Mul;
 82
 83        let mut cs = TestConstraintSystem::<Fq>::new();
 84
 85        // let a: G1Projective = rand::random();
 86        // let b: G2Projective = rand::random();
 87        // let s: Fr = rand::random();
 88
 89        let a: G1Projective = G1Projective::prime_subgroup_generator();
 90        let b: G2Projective = G2Projective::prime_subgroup_generator();
 91        let s: Fr = Fr::one() + &Fr::one();
 92
 93        let sa = a.mul(&s);
 94        let sb = b.mul(&s);
 95
 96        let a_g = G1Gadget::alloc(&mut cs.ns(|| "a"), || Ok(a)).unwrap();
 97        let b_g = G2Gadget::alloc(&mut cs.ns(|| "b"), || Ok(b)).unwrap();
 98        let sa_g = G1Gadget::alloc(&mut cs.ns(|| "sa"), || Ok(sa)).unwrap();
 99        let sb_g = G2Gadget::alloc(&mut cs.ns(|| "sb"), || Ok(sb)).unwrap();
100
101        let a_prep_g = G1PreparedGadget::from_affine(&mut cs.ns(|| "a_prep"), &a_g).unwrap();
102        let b_prep_g = G2PreparedGadget::from_affine(&mut cs.ns(|| "b_prep"), &b_g).unwrap();
103
104        let sa_prep_g = G1PreparedGadget::from_affine(&mut cs.ns(|| "sa_prep"), &sa_g).unwrap();
105        let sb_prep_g = G2PreparedGadget::from_affine(&mut cs.ns(|| "sb_prep"), &sb_g).unwrap();
106
107        let (ans1_g, ans1_n) = {
108            let ans_g =
109                PairingGadget::pairing(cs.ns(|| "pair(sa, b)"), sa_prep_g, b_prep_g.clone())
110                    .unwrap();
111            let ans_n = Bls12_377::pairing(sa, b);
112            (ans_g, ans_n)
113        };
114
115        let (ans2_g, ans2_n) = {
116            let ans_g =
117                PairingGadget::pairing(cs.ns(|| "pair(a, sb)"), a_prep_g.clone(), sb_prep_g)
118                    .unwrap();
119            let ans_n = Bls12_377::pairing(a, sb);
120            (ans_g, ans_n)
121        };
122
123        let (ans3_g, ans3_n) = {
124            let s_iter = BitIterator::new(s.into_repr())
125                .map(Boolean::constant)
126                .collect::<Vec<_>>();
127
128            let mut ans_g =
129                PairingGadget::pairing(cs.ns(|| "pair(a, b)"), a_prep_g, b_prep_g).unwrap();
130            let mut ans_n = Bls12_377::pairing(a, b);
131            ans_n = ans_n.pow(s.into_repr());
132            ans_g = ans_g.pow(cs.ns(|| "pow"), &s_iter).unwrap();
133
134            (ans_g, ans_n)
135        };
136
137        assert_eq!(ans1_n, ans2_n, "Failed ans1_native == ans2_native");
138        assert_eq!(ans2_n, ans3_n, "Failed ans2_native == ans3_native");
139        assert_eq!(
140            ans1_g.get_value(),
141            ans3_g.get_value(),
142            "Failed ans1 == ans3"
143        );
144        assert_eq!(
145            ans1_g.get_value(),
146            ans2_g.get_value(),
147            "Failed ans1 == ans2"
148        );
149        assert_eq!(
150            ans2_g.get_value(),
151            ans3_g.get_value(),
152            "Failed ans2 == ans3"
153        );
154
155        ans1_g
156            .enforce_equal(&mut cs.ns(|| "ans1 == ans2?"), &ans2_g)
157            .unwrap();
158        ans2_g
159            .enforce_equal(&mut cs.ns(|| "ans2 == ans3?"), &ans3_g)
160            .unwrap();
161
162        assert_eq!(ans1_g.get_value().unwrap(), ans1_n, "Failed native test 1");
163        assert_eq!(ans2_g.get_value().unwrap(), ans2_n, "Failed native test 2");
164        assert_eq!(ans3_g.get_value().unwrap(), ans3_n, "Failed native test 3");
165
166        if !cs.is_satisfied() {
167            println!("Unsatisfied: {:?}", cs.which_is_unsatisfied());
168        }
169
170        assert!(cs.is_satisfied(), "cs is not satisfied");
171    }
172}