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