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::{
 63        test_rng, BitIterator, Field, PairingEngine, PrimeField, ProjectiveCurve, UniformRand,
 64    };
 65    use r1cs_core::ConstraintSystem;
 66
 67    #[allow(dead_code)]
 68    pub(crate) fn bilinearity_test<
 69        E: PairingEngine,
 70        ConstraintF: Field,
 71        P: PairingGadget<E, ConstraintF>,
 72    >() {
 73        let mut cs = TestConstraintSystem::<ConstraintF>::new();
 74
 75        let mut rng = test_rng();
 76        let a = E::G1Projective::rand(&mut rng);
 77        let b = E::G2Projective::rand(&mut rng);
 78        let s = E::Fr::rand(&mut rng);
 79
 80        let mut sa = a;
 81        sa.mul_assign(s);
 82        let mut sb = b;
 83        sb.mul_assign(s);
 84
 85        let a_g = P::G1Gadget::alloc(&mut cs.ns(|| "a"), || Ok(a)).unwrap();
 86        let b_g = P::G2Gadget::alloc(&mut cs.ns(|| "b"), || Ok(b)).unwrap();
 87        let sa_g = P::G1Gadget::alloc(&mut cs.ns(|| "sa"), || Ok(sa)).unwrap();
 88        let sb_g = P::G2Gadget::alloc(&mut cs.ns(|| "sb"), || Ok(sb)).unwrap();
 89
 90        let a_prep_g = P::prepare_g1(&mut cs.ns(|| "a_prep"), &a_g).unwrap();
 91        let b_prep_g = P::prepare_g2(&mut cs.ns(|| "b_prep"), &b_g).unwrap();
 92
 93        let sa_prep_g = P::prepare_g1(&mut cs.ns(|| "sa_prep"), &sa_g).unwrap();
 94        let sb_prep_g = P::prepare_g2(&mut cs.ns(|| "sb_prep"), &sb_g).unwrap();
 95
 96        let (ans1_g, ans1_n) = {
 97            let ans_g = P::pairing(cs.ns(|| "pair(sa, b)"), sa_prep_g, b_prep_g.clone()).unwrap();
 98            let ans_n = E::pairing(sa, b);
 99            (ans_g, ans_n)
100        };
101
102        let (ans2_g, ans2_n) = {
103            let ans_g = P::pairing(cs.ns(|| "pair(a, sb)"), a_prep_g.clone(), sb_prep_g).unwrap();
104            let ans_n = E::pairing(a, sb);
105            (ans_g, ans_n)
106        };
107
108        let (ans3_g, ans3_n) = {
109            let s_iter = BitIterator::new(s.into_repr())
110                .map(Boolean::constant)
111                .collect::<Vec<_>>();
112
113            let mut ans_g = P::pairing(cs.ns(|| "pair(a, b)"), a_prep_g, b_prep_g).unwrap();
114            let mut ans_n = E::pairing(a, b);
115            ans_n = ans_n.pow(s.into_repr());
116            ans_g = ans_g.pow(cs.ns(|| "pow"), &s_iter).unwrap();
117
118            (ans_g, ans_n)
119        };
120
121        assert_eq!(ans1_n, ans2_n, "Failed ans1_native == ans2_native");
122        assert_eq!(ans2_n, ans3_n, "Failed ans2_native == ans3_native");
123        assert_eq!(
124            ans1_g.get_value(),
125            ans3_g.get_value(),
126            "Failed ans1 == ans3"
127        );
128        assert_eq!(
129            ans1_g.get_value(),
130            ans2_g.get_value(),
131            "Failed ans1 == ans2"
132        );
133        assert_eq!(
134            ans2_g.get_value(),
135            ans3_g.get_value(),
136            "Failed ans2 == ans3"
137        );
138
139        ans1_g
140            .enforce_equal(&mut cs.ns(|| "ans1 == ans2?"), &ans2_g)
141            .unwrap();
142        ans2_g
143            .enforce_equal(&mut cs.ns(|| "ans2 == ans3?"), &ans3_g)
144            .unwrap();
145
146        assert_eq!(ans1_g.get_value().unwrap(), ans1_n, "Failed native test 1");
147        assert_eq!(ans2_g.get_value().unwrap(), ans2_n, "Failed native test 2");
148        assert_eq!(ans3_g.get_value().unwrap(), ans3_n, "Failed native test 3");
149
150        if !cs.is_satisfied() {
151            println!("Unsatisfied: {:?}", cs.which_is_unsatisfied());
152        }
153
154        assert!(cs.is_satisfied(), "cs is not satisfied");
155    }
156}