Add 'pairing/' from commit '09b6e6f9212020f385218e5cf5287e381ccd312b'

git-subtree-dir: pairing
git-subtree-mainline: ad16ba6a35
git-subtree-split: 09b6e6f921

pairing/src/tests/engine.rs

@@ -0,0 +1,126 @@
+use rand::{Rand, SeedableRng, XorShiftRng};
+
+use {CurveAffine, CurveProjective, Engine, Field, PrimeField};
+
+pub fn engine_tests<E: Engine>() {
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+    for _ in 0..10 {
+        let a = E::G1::rand(&mut rng).into_affine();
+        let b = E::G2::rand(&mut rng).into_affine();
+
+        assert!(a.pairing_with(&b) == b.pairing_with(&a));
+        assert!(a.pairing_with(&b) == E::pairing(a, b));
+    }
+
+    for _ in 0..1000 {
+        let z1 = E::G1Affine::zero().prepare();
+        let z2 = E::G2Affine::zero().prepare();
+
+        let a = E::G1::rand(&mut rng).into_affine().prepare();
+        let b = E::G2::rand(&mut rng).into_affine().prepare();
+        let c = E::G1::rand(&mut rng).into_affine().prepare();
+        let d = E::G2::rand(&mut rng).into_affine().prepare();
+
+        assert_eq!(
+            E::Fqk::one(),
+            E::final_exponentiation(&E::miller_loop(&[(&z1, &b)])).unwrap()
+        );
+
+        assert_eq!(
+            E::Fqk::one(),
+            E::final_exponentiation(&E::miller_loop(&[(&a, &z2)])).unwrap()
+        );
+
+        assert_eq!(
+            E::final_exponentiation(&E::miller_loop(&[(&z1, &b), (&c, &d)])).unwrap(),
+            E::final_exponentiation(&E::miller_loop(&[(&a, &z2), (&c, &d)])).unwrap()
+        );
+
+        assert_eq!(
+            E::final_exponentiation(&E::miller_loop(&[(&a, &b), (&z1, &d)])).unwrap(),
+            E::final_exponentiation(&E::miller_loop(&[(&a, &b), (&c, &z2)])).unwrap()
+        );
+    }
+
+    random_bilinearity_tests::<E>();
+    random_miller_loop_tests::<E>();
+}
+
+fn random_miller_loop_tests<E: Engine>() {
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+    // Exercise the miller loop for a reduced pairing
+    for _ in 0..1000 {
+        let a = E::G1::rand(&mut rng);
+        let b = E::G2::rand(&mut rng);
+
+        let p2 = E::pairing(a, b);
+
+        let a = a.into_affine().prepare();
+        let b = b.into_affine().prepare();
+
+        let p1 = E::final_exponentiation(&E::miller_loop(&[(&a, &b)])).unwrap();
+
+        assert_eq!(p1, p2);
+    }
+
+    // Exercise a double miller loop
+    for _ in 0..1000 {
+        let a = E::G1::rand(&mut rng);
+        let b = E::G2::rand(&mut rng);
+        let c = E::G1::rand(&mut rng);
+        let d = E::G2::rand(&mut rng);
+
+        let ab = E::pairing(a, b);
+        let cd = E::pairing(c, d);
+
+        let mut abcd = ab;
+        abcd.mul_assign(&cd);
+
+        let a = a.into_affine().prepare();
+        let b = b.into_affine().prepare();
+        let c = c.into_affine().prepare();
+        let d = d.into_affine().prepare();
+
+        let abcd_with_double_loop =
+            E::final_exponentiation(&E::miller_loop(&[(&a, &b), (&c, &d)])).unwrap();
+
+        assert_eq!(abcd, abcd_with_double_loop);
+    }
+}
+
+fn random_bilinearity_tests<E: Engine>() {
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+    for _ in 0..1000 {
+        let a = E::G1::rand(&mut rng);
+        let b = E::G2::rand(&mut rng);
+
+        let c = E::Fr::rand(&mut rng);
+        let d = E::Fr::rand(&mut rng);
+
+        let mut ac = a;
+        ac.mul_assign(c);
+
+        let mut ad = a;
+        ad.mul_assign(d);
+
+        let mut bc = b;
+        bc.mul_assign(c);
+
+        let mut bd = b;
+        bd.mul_assign(d);
+
+        let acbd = E::pairing(ac, bd);
+        let adbc = E::pairing(ad, bc);
+
+        let mut cd = c;
+        cd.mul_assign(&d);
+
+        let abcd = E::pairing(a, b).pow(cd.into_repr());
+
+        assert_eq!(acbd, adbc);
+        assert_eq!(acbd, abcd);
+    }
+}