Public API, reorganize tests, benchmarks and shootout.
This commit is contained in:
Sean Bowe
parent
b93e312eb0
commit
9e458130a6
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@ -10,7 +10,7 @@ repository = "https://github.com/zcash/bn"
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license = "MIT OR Apache-2.0"
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[[bench]]
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name = "fp"
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name = "api"
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[dependencies]
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rand = "0.3.14"
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20
README.md
20
README.md
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@ -23,7 +23,7 @@ extern crate bn;
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## API
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* `Scalar` is an element of F<sub>r</sub>
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* `Fr` is an element of F<sub>r</sub>
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* `G1` is a point on the BN curve E/Fq : y^2 = x^3 + b
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* `G2` is a point on the twisted BN curve E'/Fq2 : y^2 = x^3 + b/xi
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* `Gt` is a group element (written multiplicatively) obtained with the `pairing` function over `G1` and `G2`.
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@ -38,19 +38,19 @@ In a typical Diffie-Hellman key exchange, relying on ECDLP, a three-party key ex
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```rust
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// Generate private keys
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let alice_sk = Scalar::random(rng);
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let bob_sk = Scalar::random(rng);
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let carol_sk = Scalar::random(rng);
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let alice_sk = Fr::random(rng);
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let bob_sk = Fr::random(rng);
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let carol_sk = Fr::random(rng);
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// Generate public keys in G1 and G2
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let (alice_pk1, alice_pk2) = (G1::one() * &alice_sk, G2::one() * &alice_sk);
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let (bob_pk1, bob_pk2) = (G1::one() * &bob_sk, G2::one() * &bob_sk);
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let (carol_pk1, carol_pk2) = (G1::one() * &carol_sk, G2::one() * &carol_sk);
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let (alice_pk1, alice_pk2) = (G1::one() * alice_sk, G2::one() * alice_sk);
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let (bob_pk1, bob_pk2) = (G1::one() * bob_sk, G2::one() * bob_sk);
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let (carol_pk1, carol_pk2) = (G1::one() * carol_sk, G2::one() * carol_sk);
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// Each party computes the shared secret
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let alice_ss = pairing(&bob_pk1, &carol_pk2) ^ &alice_sk;
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let bob_ss = pairing(&carol_pk1, &alice_pk2) ^ &bob_sk;
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let carol_ss = pairing(&alice_pk1, &bob_pk2) ^ &carol_sk;
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let alice_ss = pairing(&bob_pk1, &carol_pk2).pow(alice_sk);
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let bob_ss = pairing(&carol_pk1, &alice_pk2).pow(bob_sk);
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let carol_ss = pairing(&alice_pk1, &bob_pk2).pow(carol_sk);
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assert!(alice_ss == bob_ss && bob_ss == carol_ss);
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```
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@ -1,5 +1,3 @@
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// TODO: later move all these benchmarks to within the code itself.
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#![feature(test)]
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extern crate test;
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extern crate rand;
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@ -78,148 +76,6 @@ fn fr_inverses(b: &mut test::Bencher) {
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});
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}
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#[bench]
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fn fq_addition(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] + v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq_subtraction(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] - v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq_multiplication(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] * v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq_inverses(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES].inverse()
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});
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}
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#[bench]
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fn fq2_multiplication(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] * v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq2_addition(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] + v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq2_subtraction(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES] - v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq2_inverses(b: &mut test::Bencher) {
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const SAMPLES: usize = 1000;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v1[ctr % SAMPLES].inverse()
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});
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}
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#[bench]
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fn g1_addition(b: &mut test::Bencher) {
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const SAMPLES: usize = 100;
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@ -327,3 +183,60 @@ fn g2_scalar_multiplication(b: &mut test::Bencher) {
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v1[ctr % SAMPLES] * v2[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq12_scalar_multiplication(b: &mut test::Bencher) {
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const SAMPLES: usize = 100;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect();
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let v3: Vec<_> = (0..SAMPLES).map(|i| pairing(v1[i], v2[i])).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v3[(ctr + SAMPLES/50) % SAMPLES] * v3[ctr % SAMPLES]
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});
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}
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#[bench]
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fn fq12_exponentiation(b: &mut test::Bencher) {
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const SAMPLES: usize = 100;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect();
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let v3: Vec<_> = (0..SAMPLES).map(|i| pairing(v1[i], v2[i])).collect();
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let v4: Vec<_> = (0..SAMPLES).map(|_| Fr::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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v3[ctr % SAMPLES].pow(v4[ctr % SAMPLES])
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});
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}
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#[bench]
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fn perform_pairing(b: &mut test::Bencher) {
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const SAMPLES: usize = 100;
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let rng = &mut rand::thread_rng();
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let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect();
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let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect();
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let mut ctr = 0;
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b.iter(|| {
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ctr += 1;
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pairing(v1[ctr % SAMPLES], v2[ctr % SAMPLES])
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});
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}
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@ -0,0 +1,34 @@
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// This is an example of three-party Diffie-Hellman key exchange
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// Requires two rounds
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extern crate bn;
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extern crate rand;
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use bn::*;
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fn main() {
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let rng = &mut rand::thread_rng();
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// Construct private keys
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let alice_sk = Fr::random(rng);
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let bob_sk = Fr::random(rng);
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let carol_sk = Fr::random(rng);
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// Construct public keys
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let alice_pk = G1::one() * alice_sk;
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let bob_pk = G1::one() * bob_sk;
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let carol_pk = G1::one() * carol_sk;
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// Round one:
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let alice_dh_1 = bob_pk * carol_sk;
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let bob_dh_1 = carol_pk * alice_sk;
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let carol_dh_1 = alice_pk * bob_sk;
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// Round two:
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let alice_dh_2 = alice_dh_1 * alice_sk;
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let bob_dh_2 = bob_dh_1 * bob_sk;
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let carol_dh_2 = carol_dh_1 * carol_sk;
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// All parties should arrive to the same shared secret
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assert!(alice_dh_2 == bob_dh_2 && bob_dh_2 == carol_dh_2);
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}
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@ -0,0 +1,24 @@
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extern crate bn;
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extern crate rand;
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use bn::{Fr, G1, G2, pairing};
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fn main() {
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let rng = &mut rand::thread_rng();
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// Generate private keys
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let alice_sk = Fr::random(rng);
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let bob_sk = Fr::random(rng);
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let carol_sk = Fr::random(rng);
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// Generate public keys in G1 and G2
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let (alice_pk1, alice_pk2) = (G1::one() * alice_sk, G2::one() * alice_sk);
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let (bob_pk1, bob_pk2) = (G1::one() * bob_sk, G2::one() * bob_sk);
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let (carol_pk1, carol_pk2) = (G1::one() * carol_sk, G2::one() * carol_sk);
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// Each party computes the shared secret
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let alice_ss = pairing(bob_pk1, carol_pk2).pow(alice_sk);
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let bob_ss = pairing(carol_pk1, alice_pk2).pow(bob_sk);
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let carol_ss = pairing(alice_pk1, bob_pk2).pow(carol_sk);
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assert!(alice_ss == bob_ss && bob_ss == carol_ss);
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}
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@ -1,34 +0,0 @@
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// This is an example of three-party Diffie-Hellman key exchange
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// Requires two rounds
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extern crate bn;
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extern crate rand;
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use bn::*;
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fn main() {
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let rng = &mut rand::thread_rng();
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// Construct private keys
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let alice_sk = Scalar::random(rng);
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let bob_sk = Scalar::random(rng);
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let carol_sk = Scalar::random(rng);
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// Construct public keys
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let alice_pk = G1::one() * &alice_sk;
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let bob_pk = G1::one() * &bob_sk;
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let carol_pk = G1::one() * &carol_sk;
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// Round one:
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let alice_dh_1 = &bob_pk * &carol_sk;
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let bob_dh_1 = &carol_pk * &alice_sk;
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let carol_dh_1 = &alice_pk * &bob_sk;
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// Round two:
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let alice_dh_2 = alice_dh_1 * &alice_sk;
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let bob_dh_2 = bob_dh_1 * &bob_sk;
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let carol_dh_2 = carol_dh_1 * &carol_sk;
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// All parties should arrive to the same shared secret
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assert!(alice_dh_2 == bob_dh_2 && bob_dh_2 == carol_dh_2);
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}
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@ -1,24 +0,0 @@
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extern crate bn;
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extern crate rand;
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use bn::{Field, Scalar, G1, G2, pairing};
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fn main() {
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let rng = &mut rand::thread_rng();
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// Generate private keys
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let alice_sk = Scalar::random(rng);
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let bob_sk = Scalar::random(rng);
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let carol_sk = Scalar::random(rng);
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// Generate public keys in G1 and G2
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let (alice_pk1, alice_pk2) = (G1::one() * &alice_sk, G2::one() * &alice_sk);
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let (bob_pk1, bob_pk2) = (G1::one() * &bob_sk, G2::one() * &bob_sk);
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let (carol_pk1, carol_pk2) = (G1::one() * &carol_sk, G2::one() * &carol_sk);
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// Each party computes the shared secret
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let alice_ss = pairing(&bob_pk1, &carol_pk2) ^ &alice_sk;
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let bob_ss = pairing(&carol_pk1, &alice_pk2) ^ &bob_sk;
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let carol_ss = pairing(&alice_pk1, &bob_pk2) ^ &carol_sk;
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assert!(alice_ss == bob_ss && bob_ss == carol_ss);
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}
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@ -1,167 +0,0 @@
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use rand::Rng;
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use num::{BigUint, Num};
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use std::ops::{Mul,Add,Sub,Neg};
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use std::cmp::{PartialEq, Eq};
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use std::convert::From;
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use std::fmt;
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use std::marker::PhantomData;
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use super::Field;
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pub trait PrimeFieldParams {
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fn modulus() -> BigUint;
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fn bits() -> usize;
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fn name() -> &'static str;
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}
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pub struct Fp<P: PrimeFieldParams> {
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value: BigUint,
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_marker: PhantomData<P>
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}
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impl<P: PrimeFieldParams> fmt::Debug for Fp<P> {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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write!(f, "{}({})", P::name(), self.value)
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}
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}
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impl<P: PrimeFieldParams> Field for Fp<P> {
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fn zero() -> Self {
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use num::Zero;
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Fp {
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value: BigUint::zero(),
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_marker: PhantomData
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}
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}
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fn one() -> Self {
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use num::One;
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Fp {
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value: BigUint::one(),
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_marker: PhantomData
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}
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}
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fn random<R: Rng>(rng: &mut R) -> Self {
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use num::num_bigint::RandBigInt;
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use num::Zero;
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Fp {
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value: rng.gen_biguint_range(&BigUint::zero(), &P::modulus()),
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_marker: PhantomData
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}
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}
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fn inverse(&self) -> Self {
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if self.is_zero() {
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// TODO: this should likely bleed through the abstraction layers
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panic!("cannot get the multiplicative inverse of zero")
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} else {
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let mut res = Self::one();
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let mut found_one = false;
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let exp = Self::zero() - Self::one() - Self::one();
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|
||||
for i in (0..P::bits()).rev() {
|
||||
if found_one {
|
||||
res = res.squared();
|
||||
}
|
||||
|
||||
if exp.test_bit(i) {
|
||||
found_one = true;
|
||||
res = self * &res;
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
fn neg(&self) -> Self {
|
||||
use num::Zero;
|
||||
|
||||
Fp {
|
||||
value: if self.value.is_zero() {
|
||||
self.value.clone()
|
||||
} else {
|
||||
P::modulus() - &self.value
|
||||
},
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn mul(&self, other: &Self) -> Self {
|
||||
Fp {
|
||||
value: (&self.value * &other.value) % &P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn sub(&self, other: &Self) -> Self {
|
||||
if other.value > self.value {
|
||||
Fp {
|
||||
value: (&self.value + P::modulus()) - &other.value,
|
||||
_marker: PhantomData
|
||||
}
|
||||
} else {
|
||||
Fp {
|
||||
value: &self.value - &other.value,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fn add(&self, other: &Self) -> Self {
|
||||
let tmp = &self.value + &other.value;
|
||||
if tmp >= P::modulus() {
|
||||
Fp {
|
||||
value: tmp - P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
} else {
|
||||
Fp {
|
||||
value: tmp,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.value == other.value
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Fp<P> {
|
||||
pub fn test_bit(&self, bit: usize) -> bool {
|
||||
// TODO: This is a naive approach.
|
||||
use num::{One, Zero};
|
||||
|
||||
let mut b = BigUint::one();
|
||||
let two = &b + &b;
|
||||
for _ in 0..bit {
|
||||
b = &b + &b;
|
||||
}
|
||||
|
||||
(&self.value / b) % two != BigUint::zero()
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, P: PrimeFieldParams> From<&'a str> for Fp<P> {
|
||||
fn from(s: &'a str) -> Self {
|
||||
Fp {
|
||||
value: BigUint::from_str_radix(s, 10).unwrap() % P::modulus(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: PrimeFieldParams> Clone for Fp<P> {
|
||||
fn clone(&self) -> Self {
|
||||
Fp {
|
||||
value: self.value.clone(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
forward_ops_to_field_ops!(impl(P: PrimeFieldParams) Fp<P>);
|
||||
|
|
@ -1,294 +0,0 @@
|
|||
use ::Fr;
|
||||
use ::Fq2;
|
||||
use ::Fq6;
|
||||
use ::Fq12;
|
||||
use fields::fp::PrimeFieldParams;
|
||||
use fields::fp6::Fp6Params;
|
||||
use params::{FrParams,Fq6Params};
|
||||
use rand::Rng;
|
||||
use fields::Field;
|
||||
use std::ops::{Mul,Add,Sub,Neg};
|
||||
use std::cmp::{PartialEq, Eq};
|
||||
use std::marker::PhantomData;
|
||||
use std::fmt;
|
||||
|
||||
pub trait Fp12Params {
|
||||
fn non_residue() -> Fq2;
|
||||
fn name() -> &'static str;
|
||||
fn frobenius_coeffs_c1(n: usize) -> Fq2;
|
||||
}
|
||||
|
||||
pub struct Fp12<P: Fp12Params> {
|
||||
a: Fq6,
|
||||
b: Fq6,
|
||||
_marker: PhantomData<P>
|
||||
}
|
||||
|
||||
impl<P: Fp12Params> Fp12<P> {
|
||||
pub fn new(a: Fq6, b: Fq6) -> Self {
|
||||
Fp12 {
|
||||
a: a,
|
||||
b: b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn frobenius_map(&self, power: usize) -> Self {
|
||||
Fp12 {
|
||||
a: self.a.frobenius_map(power),
|
||||
b: &self.b.frobenius_map(power) * &P::frobenius_coeffs_c1(power % 12),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Fq12 {
|
||||
pub fn unitary_inverse(&self) -> Fq12 {
|
||||
Fp12 {
|
||||
a: self.a.clone(),
|
||||
b: -&self.b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn cyclotomic_exp(&self, exp: &Fr) -> Self {
|
||||
let mut res = Self::one();
|
||||
|
||||
let mut found_one = false;
|
||||
|
||||
for i in (0..FrParams::bits()).rev() {
|
||||
if found_one {
|
||||
res = res.cyclotomic_squared();
|
||||
}
|
||||
|
||||
if exp.test_bit(i) {
|
||||
found_one = true;
|
||||
res = self * &res;
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
pub fn cyclotomic_squared(&self) -> Self {
|
||||
let z0 = &self.a.a;
|
||||
let z4 = &self.a.b;
|
||||
let z3 = &self.a.c;
|
||||
let z2 = &self.b.a;
|
||||
let z1 = &self.b.b;
|
||||
let z5 = &self.b.c;
|
||||
|
||||
let tmp = z0 * z1;
|
||||
let t0 = (z0 + z1) * (z1 * Fq6Params::non_residue() + z0) - &tmp - &tmp * Fq6Params::non_residue();
|
||||
let t1 = &tmp + &tmp;
|
||||
|
||||
let tmp = z2 * z3;
|
||||
let t2 = (z2 + z3) * (z3 * Fq6Params::non_residue() + z2) - &tmp - &tmp * Fq6Params::non_residue();
|
||||
let t3 = &tmp + &tmp;
|
||||
|
||||
let tmp = z4 * z5;
|
||||
let t4 = (z4 + z5) * (z5 * Fq6Params::non_residue() + z4) - &tmp - &tmp * Fq6Params::non_residue();
|
||||
let t5 = &tmp + &tmp;
|
||||
|
||||
let z0 = &t0 - z0;
|
||||
let z0 = &z0 + &z0;
|
||||
let z0 = &z0 + &t0;
|
||||
|
||||
let z1 = &t1 + z1;
|
||||
let z1 = &z1 + &z1;
|
||||
let z1 = &z1 + &t1;
|
||||
|
||||
let tmp = &t5 * Fq6Params::non_residue();
|
||||
let z2 = &tmp + z2;
|
||||
let z2 = &z2 + &z2;
|
||||
let z2 = &z2 + &tmp;
|
||||
|
||||
let z3 = &t4 - z3;
|
||||
let z3 = &z3 + &z3;
|
||||
let z3 = &z3 + &t4;
|
||||
|
||||
let z4 = &t2 - z4;
|
||||
let z4 = &z4 + &z4;
|
||||
let z4 = &z4 + &t2;
|
||||
|
||||
let z5 = &t3 + z5;
|
||||
let z5 = &z5 + &z5;
|
||||
let z5 = &z5 + &t3;
|
||||
|
||||
Fp12 {
|
||||
a: Fq6::new(z0, z4, z3),
|
||||
b: Fq6::new(z2, z1, z5),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn mul_by_024(&self,
|
||||
ell_0: &Fq2,
|
||||
ell_vw: Fq2,
|
||||
ell_vv: Fq2) -> Fq12 {
|
||||
let z0 = &self.a.a;
|
||||
let z1 = &self.a.b;
|
||||
let z2 = &self.a.c;
|
||||
let z3 = &self.b.a;
|
||||
let z4 = &self.b.b;
|
||||
let z5 = &self.b.c;
|
||||
|
||||
let x0 = ell_0;
|
||||
let x2 = &ell_vv;
|
||||
let x4 = &ell_vw;
|
||||
|
||||
let d0 = z0 * x0;
|
||||
let d2 = z2 * x2;
|
||||
let d4 = z4 * x4;
|
||||
let t2 = z0 + z4;
|
||||
let t1 = z0 + z2;
|
||||
let s0 = z1 + z3 + z5;
|
||||
|
||||
let s1 = z1 * x2;
|
||||
let t3 = &s1 + &d4;
|
||||
let t4 = &t3 * Fq6Params::non_residue() + &d0;
|
||||
let z0 = t4;
|
||||
|
||||
let t3 = z5 * x4;
|
||||
let s1 = &s1 + &t3;
|
||||
let t3 = &t3 + &d2;
|
||||
let t4 = &t3 * Fq6Params::non_residue();
|
||||
let t3 = z1 * x0;
|
||||
let s1 = &s1 + &t3;
|
||||
let t4 = &t4 + &t3;
|
||||
let z1 = t4;
|
||||
|
||||
let t0 = x0 + x2;
|
||||
let t3 = &t1 * &t0 - &d0 - &d2;
|
||||
let t4 = z3 * x4;
|
||||
let s1 = &s1 + &t4;
|
||||
let t3 = &t3 + &t4;
|
||||
|
||||
let t0 = z2 + z4;
|
||||
let z2 = t3;
|
||||
|
||||
let t1 = x2 + x4;
|
||||
let t3 = &t0 * &t1 - &d2 - &d4;
|
||||
let t4 = &t3 * Fq6Params::non_residue();
|
||||
let t3 = z3 * x0;
|
||||
let s1 = &s1 + &t3;
|
||||
let t4 = &t4 + &t3;
|
||||
let z3 = t4;
|
||||
|
||||
let t3 = z5 * x2;
|
||||
let s1 = &s1 + &t3;
|
||||
let t4 = &t3 * Fq6Params::non_residue();
|
||||
let t0 = x0 + x4;
|
||||
let t3 = &t2 * &t0 - &d0 - &d4;
|
||||
let t4 = &t4 + &t3;
|
||||
let z4 = t4;
|
||||
|
||||
let t0 = x0 + x2 + x4;
|
||||
let t3 = &s0 * &t0 - &s1;
|
||||
let z5 = t3;
|
||||
|
||||
Fq12 {
|
||||
a: Fq6::new(z0, z1, z2),
|
||||
b: Fq6::new(z3, z4, z5),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp12Params> fmt::Debug for Fp12<P> {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{}({:?}, {:?})", P::name(), self.a, self.b)
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp12Params> Clone for Fp12<P> {
|
||||
fn clone(&self) -> Self {
|
||||
Fp12 {
|
||||
a: self.a.clone(),
|
||||
b: self.b.clone(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp12Params> Field for Fp12<P> {
|
||||
fn zero() -> Self {
|
||||
Fp12 {
|
||||
a: Fq6::zero(),
|
||||
b: Fq6::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn one() -> Self {
|
||||
Fp12 {
|
||||
a: Fq6::one(),
|
||||
b: Fq6::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn random<R: Rng>(rng: &mut R) -> Self {
|
||||
Fp12 {
|
||||
a: Fq6::random(rng),
|
||||
b: Fq6::random(rng),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn inverse(&self) -> Self {
|
||||
let t = (self.a.squared() - (self.b.squared().mul_by_nonresidue(&P::non_residue()))).inverse();
|
||||
|
||||
Fp12 {
|
||||
a: &self.a * &t,
|
||||
b: -(&self.b * &t),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn squared(&self) -> Self {
|
||||
let a = &self.a; let b = &self.b;
|
||||
let ab = &(a * b);
|
||||
|
||||
Fp12 {
|
||||
a: (b.mul_by_nonresidue(&P::non_residue()) + a) * (a + b) - ab - ab.mul_by_nonresidue(&P::non_residue()),
|
||||
b: ab + ab,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.a == other.a && self.b == other.b
|
||||
}
|
||||
fn neg(&self) -> Self {
|
||||
Fp12 {
|
||||
a: -(&self.a),
|
||||
b: -(&self.b),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn mul(&self, other: &Self) -> Self {
|
||||
let a_a = &(&self.a * &other.a);
|
||||
let b_b = &(&self.b * &other.b);
|
||||
|
||||
Fp12 {
|
||||
a: b_b.mul_by_nonresidue(&P::non_residue()) + a_a,
|
||||
b: (&self.a + &self.b) * (&other.a + &other.b) - a_a - b_b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn sub(&self, other: &Self) -> Self {
|
||||
Fp12 {
|
||||
a: &self.a - &other.a,
|
||||
b: &self.b - &other.b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn add(&self, other: &Self) -> Self {
|
||||
Fp12 {
|
||||
a: &self.a + &other.a,
|
||||
b: &self.b + &other.b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
forward_ops_to_field_ops!(impl(P: Fp12Params) Fp12<P>);
|
||||
|
|
@ -1,146 +0,0 @@
|
|||
use ::Fq;
|
||||
use rand::Rng;
|
||||
use fields::Field;
|
||||
use std::ops::{Mul,Add,Sub,Neg};
|
||||
use std::cmp::{PartialEq, Eq};
|
||||
use std::marker::PhantomData;
|
||||
use std::fmt;
|
||||
|
||||
pub trait Fp2Params {
|
||||
fn non_residue() -> Fq;
|
||||
fn name() -> &'static str;
|
||||
fn frobenius_coeffs_c1(usize) -> Fq;
|
||||
}
|
||||
|
||||
pub struct Fp2<P: Fp2Params> {
|
||||
a: Fq,
|
||||
b: Fq,
|
||||
_marker: PhantomData<P>
|
||||
}
|
||||
|
||||
impl<P: Fp2Params> Fp2<P> {
|
||||
pub fn new(a: Fq, b: Fq) -> Self {
|
||||
Fp2 {
|
||||
a: a,
|
||||
b: b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn frobenius_map(&self, power: usize) -> Self {
|
||||
Fp2 {
|
||||
a: self.a.clone(),
|
||||
b: &self.b * P::frobenius_coeffs_c1(power % 2),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp2Params> fmt::Debug for Fp2<P> {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{}({:?}, {:?})", P::name(), self.a, self.b)
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp2Params> Clone for Fp2<P> {
|
||||
fn clone(&self) -> Self {
|
||||
Fp2 {
|
||||
a: self.a.clone(),
|
||||
b: self.b.clone(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp2Params> Field for Fp2<P> {
|
||||
fn zero() -> Self {
|
||||
Fp2 {
|
||||
a: Fq::zero(),
|
||||
b: Fq::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn one() -> Self {
|
||||
Fp2 {
|
||||
a: Fq::one(),
|
||||
b: Fq::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn random<R: Rng>(rng: &mut R) -> Self {
|
||||
Fp2 {
|
||||
a: Fq::random(rng),
|
||||
b: Fq::random(rng),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn inverse(&self) -> Self {
|
||||
let t = (self.a.squared() - (self.b.squared() * P::non_residue())).inverse();
|
||||
|
||||
Fp2 {
|
||||
a: &self.a * &t,
|
||||
b: -(&self.b * &t),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn squared(&self) -> Self {
|
||||
let a = &self.a; let b = &self.b;
|
||||
let ab = &(a * b);
|
||||
|
||||
Fp2 {
|
||||
a: (b * P::non_residue() + a) * (a + b) - ab - ab * P::non_residue(),
|
||||
b: ab + ab,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.a == other.a && self.b == other.b
|
||||
}
|
||||
fn neg(&self) -> Self {
|
||||
Fp2 {
|
||||
a: -(&self.a),
|
||||
b: -(&self.b),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn mul(&self, other: &Self) -> Self {
|
||||
let a_a = &(&self.a * &other.a);
|
||||
let b_b = &(&self.b * &other.b);
|
||||
|
||||
Fp2 {
|
||||
a: b_b * P::non_residue() + a_a,
|
||||
b: (&self.a + &self.b) * (&other.a + &other.b) - a_a - b_b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn sub(&self, other: &Self) -> Self {
|
||||
Fp2 {
|
||||
a: &self.a - &other.a,
|
||||
b: &self.b - &other.b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
fn add(&self, other: &Self) -> Self {
|
||||
Fp2 {
|
||||
a: &self.a + &other.a,
|
||||
b: &self.b + &other.b,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, P: Fp2Params> Mul<&'a Fq> for &'b Fp2<P> {
|
||||
type Output = Fp2<P>;
|
||||
|
||||
fn mul(self, other: &Fq) -> Fp2<P> {
|
||||
Fp2 {
|
||||
a: &self.a * other,
|
||||
b: &self.b * other,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
forward_ops_to_field_ops!(impl(P: Fp2Params) Fp2<P>);
|
||||
|
|
@ -1,192 +0,0 @@
|
|||
use ::Fq2;
|
||||
use rand::Rng;
|
||||
use fields::Field;
|
||||
use std::ops::{Mul,Add,Sub,Neg};
|
||||
use std::cmp::{PartialEq, Eq};
|
||||
use std::marker::PhantomData;
|
||||
use std::fmt;
|
||||
|
||||
pub trait Fp6Params {
|
||||
fn non_residue() -> Fq2;
|
||||
fn name() -> &'static str;
|
||||
fn frobenius_coeffs_c1(usize) -> Fq2;
|
||||
fn frobenius_coeffs_c2(usize) -> Fq2;
|
||||
}
|
||||
|
||||
pub struct Fp6<P: Fp6Params> {
|
||||
pub a: Fq2,
|
||||
pub b: Fq2,
|
||||
pub c: Fq2,
|
||||
_marker: PhantomData<P>
|
||||
}
|
||||
|
||||
impl<P: Fp6Params> Fp6<P> {
|
||||
pub fn new(a: Fq2, b: Fq2, c: Fq2) -> Self {
|
||||
Fp6 {
|
||||
a: a,
|
||||
b: b,
|
||||
c: c,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
pub fn frobenius_map(&self, power: usize) -> Self {
|
||||
Fp6 {
|
||||
a: self.a.frobenius_map(power),
|
||||
b: self.b.frobenius_map(power) * P::frobenius_coeffs_c1(power % 6),
|
||||
c: self.c.frobenius_map(power) * P::frobenius_coeffs_c2(power % 6),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp6Params> fmt::Debug for Fp6<P> {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.a, self.b, self.c)
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp6Params> Clone for Fp6<P> {
|
||||
fn clone(&self) -> Self {
|
||||
Fp6 {
|
||||
a: self.a.clone(),
|
||||
b: self.b.clone(),
|
||||
c: self.c.clone(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp6Params> Field for Fp6<P> {
|
||||
fn zero() -> Self {
|
||||
Fp6 {
|
||||
a: Fq2::zero(),
|
||||
b: Fq2::zero(),
|
||||
c: Fq2::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn one() -> Self {
|
||||
Fp6 {
|
||||
a: Fq2::one(),
|
||||
b: Fq2::zero(),
|
||||
c: Fq2::zero(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn random<R: Rng>(rng: &mut R) -> Self {
|
||||
Fp6 {
|
||||
a: Fq2::random(rng),
|
||||
b: Fq2::random(rng),
|
||||
c: Fq2::random(rng),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn inverse(&self) -> Self {
|
||||
let c0 = self.a.squared() - &self.b * &self.c * P::non_residue();
|
||||
let c1 = self.c.squared() * P::non_residue() - &self.a * &self.b;
|
||||
let c2 = self.b.squared() - &self.a * &self.c;
|
||||
let t = ((&self.c * &c1 + &self.b * &c2) * P::non_residue() + &self.a * &c0).inverse();
|
||||
|
||||
Fp6 {
|
||||
a: &t * &c0,
|
||||
b: &t * &c1,
|
||||
c: &t * &c2,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.a == other.a && self.b == other.b && self.c == other.c
|
||||
}
|
||||
|
||||
fn neg(&self) -> Self {
|
||||
Fp6 {
|
||||
a: -(&self.a),
|
||||
b: -(&self.b),
|
||||
c: -(&self.c),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn mul(&self, other: &Self) -> Self {
|
||||
let a_a = &self.a * &other.a;
|
||||
let b_b = &self.b * &other.b;
|
||||
let c_c = &self.c * &other.c;
|
||||
|
||||
Fp6 {
|
||||
a: ((&self.b + &self.c) * (&other.b + &other.c) - &b_b - &c_c) * P::non_residue() + &a_a,
|
||||
b: (&self.a + &self.b) * (&other.a + &other.b) - &a_a - &b_b + &c_c * P::non_residue(),
|
||||
c: (&self.a + &self.c) * (&other.a + &other.c) - &a_a + &b_b - &c_c,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn squared(&self) -> Self {
|
||||
let a = &self.a;
|
||||
let b = &self.b;
|
||||
let c = &self.c;
|
||||
|
||||
let s0 = a.squared();
|
||||
let ab = a * b;
|
||||
let s1 = &ab + &ab;
|
||||
let s2 = (a - b + c).squared();
|
||||
let bc = b * c;
|
||||
let s3 = &bc + &bc;
|
||||
let s4 = c.squared();
|
||||
|
||||
Fp6 {
|
||||
a: &s0 + &s3 * P::non_residue(),
|
||||
b: &s1 + &s4 * P::non_residue(),
|
||||
c: &s1 + &s2 + &s3 - &s0 - &s4,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn sub(&self, other: &Self) -> Self {
|
||||
Fp6 {
|
||||
a: &self.a - &other.a,
|
||||
b: &self.b - &other.b,
|
||||
c: &self.c - &other.c,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
|
||||
fn add(&self, other: &Self) -> Self {
|
||||
Fp6 {
|
||||
a: &self.a + &other.a,
|
||||
b: &self.b + &other.b,
|
||||
c: &self.c + &other.c,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: Fp6Params> Fp6<P> {
|
||||
pub fn mul_by_nonresidue(&self, other: &Fq2) -> Fp6<P> {
|
||||
Fp6 {
|
||||
a: &self.c * other,
|
||||
b: self.a.clone(),
|
||||
c: self.b.clone(),
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, P: Fp6Params> Mul<&'a Fq2> for &'b Fp6<P> {
|
||||
type Output = Fp6<P>;
|
||||
|
||||
fn mul(self, other: &Fq2) -> Fp6<P> {
|
||||
Fp6 {
|
||||
a: &self.a * other,
|
||||
b: &self.b * other,
|
||||
c: &self.c * other,
|
||||
_marker: PhantomData
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
forward_ops_to_field_ops!(impl(P: Fp6Params) Fp6<P>);
|
||||
|
|
@ -1,107 +0,0 @@
|
|||
macro_rules! forward_val_val_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident) => {
|
||||
impl<$($t: $p),*> $imp<$res> for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: $res) -> $res {
|
||||
$imp::$method(&self, &other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_ref_val_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident) => {
|
||||
impl<'a, $($t: $p),*> $imp<$res> for &'a $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: $res) -> $res {
|
||||
$imp::$method(self, &other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_val_ref_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident) => {
|
||||
impl<'a, $($t: $p),*> $imp<&'a $res> for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: &$res) -> $res {
|
||||
$imp::$method(&self, other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_all_binop_to_ref_ref {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident) => {
|
||||
forward_val_val_binop!(impl($($t: $p),*) $imp for $res, $method);
|
||||
forward_ref_val_binop!(impl($($t: $p),*) $imp for $res, $method);
|
||||
forward_val_ref_binop!(impl($($t: $p),*) $imp for $res, $method);
|
||||
};
|
||||
}
|
||||
|
||||
macro_rules! forward_ops_to_field_ops {
|
||||
(impl($($t:ident: $p:ident),*) $res:ty) => {
|
||||
impl<'a, 'b, $($t: $p),*> Add<&'a $res> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn add(self, other: &'a $res) -> $res {
|
||||
Field::add(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, $($t: $p),*> Sub<&'a $res> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn sub(self, other: &'a $res) -> $res {
|
||||
Field::sub(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, $($t: $p),*> Mul<&'a $res> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn mul(self, other: &'a $res) -> $res {
|
||||
Field::mul(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, $($t: $p),*> Neg for &'a $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn neg(self) -> $res {
|
||||
Field::neg(self)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> Neg for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn neg(self) -> $res {
|
||||
Field::neg(&self)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> PartialEq for $res {
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
Field::eq(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> Eq for $res {}
|
||||
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Add for $res, add);
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Sub for $res, sub);
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Mul for $res, mul);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,54 +0,0 @@
|
|||
#[macro_use]
|
||||
mod macros;
|
||||
|
||||
pub mod fp;
|
||||
pub mod fp2;
|
||||
pub mod fp6;
|
||||
pub mod fp12;
|
||||
|
||||
#[cfg(test)]
|
||||
pub mod tests;
|
||||
|
||||
use rand::Rng;
|
||||
use self::fp::{Fp, PrimeFieldParams};
|
||||
use std::fmt::Debug;
|
||||
|
||||
pub trait Field: Sized + Clone + Debug {
|
||||
fn zero() -> Self;
|
||||
fn one() -> Self;
|
||||
fn random<R: Rng>(rng: &mut R) -> Self;
|
||||
fn is_zero(&self) -> bool {
|
||||
self.eq(&Self::zero())
|
||||
}
|
||||
fn inverse(&self) -> Self;
|
||||
fn squared(&self) -> Self {
|
||||
self.mul(self)
|
||||
}
|
||||
fn pow<P: PrimeFieldParams>(&self, exp: &Fp<P>) -> Self {
|
||||
let mut res = Self::one();
|
||||
|
||||
let mut found_one = false;
|
||||
|
||||
for i in (0..P::bits()).rev() {
|
||||
if found_one {
|
||||
res = res.squared();
|
||||
}
|
||||
|
||||
if exp.test_bit(i) {
|
||||
found_one = true;
|
||||
res = self.mul(&res);
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
fn eq(&self, other: &Self) -> bool;
|
||||
fn ne(&self, other: &Self) -> bool {
|
||||
!self.eq(other)
|
||||
}
|
||||
|
||||
fn neg(&self) -> Self;
|
||||
fn mul(&self, other: &Self) -> Self;
|
||||
fn sub(&self, other: &Self) -> Self;
|
||||
fn add(&self, other: &Self) -> Self;
|
||||
}
|
||||
|
|
@ -1,203 +0,0 @@
|
|||
use rand::{Rng,SeedableRng,StdRng};
|
||||
use fields::Field;
|
||||
|
||||
mod large_field {
|
||||
use fields::fp::*;
|
||||
use num::{BigUint, Num};
|
||||
|
||||
struct Large;
|
||||
|
||||
impl PrimeFieldParams for Large {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10).unwrap()
|
||||
}
|
||||
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Large" }
|
||||
}
|
||||
|
||||
type Ft = Fp<Large>;
|
||||
|
||||
#[test]
|
||||
fn bit_testing() {
|
||||
let a = Ft::from("13");
|
||||
assert!(a.test_bit(0) == true);
|
||||
assert!(a.test_bit(1) == false);
|
||||
assert!(a.test_bit(2) == true);
|
||||
assert!(a.test_bit(3) == true);
|
||||
|
||||
let expected: Vec<bool> = [1,1,0,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,1]
|
||||
.iter().map(|a| *a == 1).rev().collect();
|
||||
|
||||
let a = Ft::from("453624211");
|
||||
|
||||
for (i, b) in expected.into_iter().enumerate() {
|
||||
assert!(a.test_bit(i) == b);
|
||||
}
|
||||
|
||||
let expected: Vec<bool> = [1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,1,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,1,0,1,1,0,0]
|
||||
.iter().map(|a| *a == 1).rev().collect();
|
||||
let a = Ft::from("13888242871869275222244405745257275088696211157297823662689037894645226208556");
|
||||
|
||||
for (i, b) in expected.into_iter().enumerate() {
|
||||
assert!(a.test_bit(i) == b);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
mod small_field {
|
||||
use fields::fp::*;
|
||||
use fields::Field;
|
||||
use num::{BigUint, Num};
|
||||
|
||||
struct Small;
|
||||
|
||||
impl PrimeFieldParams for Small {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("13", 10).unwrap()
|
||||
}
|
||||
|
||||
fn bits() -> usize { 6 }
|
||||
fn name() -> &'static str { "Small" }
|
||||
}
|
||||
|
||||
type Ft = Fp<Small>;
|
||||
|
||||
#[test]
|
||||
fn field_ops() {
|
||||
fn test_field_operation<C: Fn(&Ft, &Ft) -> Ft>(a: u64, b: u64, f: C, expected: u64) {
|
||||
let af = Ft::from(format!("{}", a).as_ref());
|
||||
let bf = Ft::from(format!("{}", b).as_ref());
|
||||
let expectedf = Ft::from(format!("{}", expected).as_ref());
|
||||
|
||||
let res = f(&af, &bf);
|
||||
|
||||
if res != expectedf {
|
||||
panic!("res={:?} != expectedf={:?} (a={}, b={}, expected={})", res, expectedf, a, b, expected);
|
||||
}
|
||||
}
|
||||
|
||||
const MODULO: u64 = 13;
|
||||
|
||||
for a in 0..13u64 {
|
||||
for b in 0..13u64 {
|
||||
test_field_operation(a, b, |a,b| {a * b}, (a*b)%MODULO);
|
||||
test_field_operation(a, b, |a,b| {a + b}, (a+b)%MODULO);
|
||||
test_field_operation(a, b, |a,b| {a - b}, {
|
||||
let mut tmp = (a as i64) - (b as i64);
|
||||
if tmp < 0 {
|
||||
tmp += MODULO as i64;
|
||||
}
|
||||
|
||||
tmp as u64
|
||||
});
|
||||
test_field_operation(a, b, |a,b| {a.pow(b)}, (a.pow(b as u32))%MODULO);
|
||||
}
|
||||
test_field_operation(a, 0, |a,_| {-a}, if a == 0 { 0 } else { MODULO - a });
|
||||
if a > 0 {
|
||||
test_field_operation(a, 0, |a,_| {&a.inverse() * a}, 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
fn can_invert<F: Field>() {
|
||||
let mut a = F::one();
|
||||
for _ in 0..1000 {
|
||||
assert!(a.ne(&F::zero()));
|
||||
|
||||
let inv = a.inverse();
|
||||
|
||||
assert!(a.mul(&inv).eq(&F::one()));
|
||||
|
||||
a = a.add(&F::one());
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
fn rand_element_squaring<F: Field, R: Rng>(rng: &mut R) {
|
||||
for _ in 0..100 {
|
||||
let a = F::random(rng);
|
||||
|
||||
let mul = a.mul(&a);
|
||||
let sq = a.squared();
|
||||
|
||||
assert!(sq.eq(&mul));
|
||||
}
|
||||
|
||||
let mut cur = F::zero();
|
||||
for _ in 0..100 {
|
||||
let mul = cur.mul(&cur);
|
||||
let sq = cur.squared();
|
||||
|
||||
assert!(sq.eq(&mul));
|
||||
|
||||
cur = cur.add(&F::one());
|
||||
}
|
||||
}
|
||||
|
||||
fn rand_element_addition_and_negation<F: Field, R: Rng>(rng: &mut R) {
|
||||
for _ in 0..10 {
|
||||
let mut a = F::random(rng);
|
||||
let r = F::random(rng);
|
||||
let mut b = a.add(&r);
|
||||
|
||||
for _ in 0..10 {
|
||||
let r = F::random(rng);
|
||||
a = a.add(&r);
|
||||
b = b.add(&r);
|
||||
|
||||
let r = F::random(rng);
|
||||
a = a.sub(&r);
|
||||
b = b.sub(&r);
|
||||
|
||||
let r = F::random(rng);
|
||||
a = a.add(&r);
|
||||
b = b.add(&r);
|
||||
}
|
||||
|
||||
b = b.sub(&r);
|
||||
assert!(a.eq(&b));
|
||||
}
|
||||
}
|
||||
|
||||
fn rand_element_inverse<F: Field, R: Rng>(rng: &mut R) {
|
||||
for _ in 0..100 {
|
||||
let mut n = F::random(rng);
|
||||
n = n.inverse().mul(&n);
|
||||
assert!(n.eq(&F::one()));
|
||||
}
|
||||
for _ in 0..100 {
|
||||
let a = F::random(rng);
|
||||
let b = F::random(rng);
|
||||
assert!(a.mul(&b).mul(&a.inverse()).eq(&b));
|
||||
}
|
||||
}
|
||||
|
||||
fn rand_element_multiplication<F: Field, R: Rng>(rng: &mut R) {
|
||||
// If field is not associative under multiplication, 1/8 of all triplets a, b, c
|
||||
// will fail the test (a*b)*c = a*(b*c).
|
||||
|
||||
for _ in 0..250 {
|
||||
let a = F::random(rng);
|
||||
let b = F::random(rng);
|
||||
let c = F::random(rng);
|
||||
|
||||
assert!(a.mul(&b).mul(&c).eq(&b.mul(&c).mul(&a)));
|
||||
}
|
||||
}
|
||||
|
||||
pub fn field_trials<F: Field>() {
|
||||
can_invert::<F>();
|
||||
|
||||
let seed: [usize; 4] = [103245, 191922, 1293, 192103];
|
||||
let mut rng = StdRng::from_seed(&seed);
|
||||
|
||||
rand_element_squaring::<F, StdRng>(&mut rng);
|
||||
rand_element_addition_and_negation::<F, StdRng>(&mut rng);
|
||||
rand_element_multiplication::<F, StdRng>(&mut rng);
|
||||
rand_element_inverse::<F, StdRng>(&mut rng);
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -1,32 +0,0 @@
|
|||
use ::Fq12;
|
||||
use ::Scalar;
|
||||
use std::ops::{BitXor,Mul};
|
||||
use fields::Field;
|
||||
|
||||
#[derive(Debug,Eq,PartialEq)]
|
||||
pub struct Gt(Fq12);
|
||||
|
||||
impl Gt {
|
||||
pub fn new(a: Fq12) -> Gt {
|
||||
return Gt(a);
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b> Mul<&'a Gt> for &'b Gt {
|
||||
type Output = Gt;
|
||||
|
||||
fn mul(self, other: &Gt) -> Gt {
|
||||
Gt(&self.0 * &other.0)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b> BitXor<&'a Scalar> for &'b Gt {
|
||||
type Output = Gt;
|
||||
|
||||
fn bitxor(self, other: &Scalar) -> Gt {
|
||||
Gt(self.0.pow(other))
|
||||
}
|
||||
}
|
||||
|
||||
forward_all_binop_to_ref_ref!(impl() Mul for Gt, mul, Gt);
|
||||
forward_all_binop_to_ref_ref!(impl() BitXor for Gt, bitxor, Scalar);
|
||||
|
|
@ -1,107 +0,0 @@
|
|||
macro_rules! forward_val_val_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
|
||||
impl<$($t: $p),*> $imp<$rhs> for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: $rhs) -> $res {
|
||||
$imp::$method(&self, &other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_ref_val_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
|
||||
impl<'a, $($t: $p),*> $imp<$rhs> for &'a $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: $rhs) -> $res {
|
||||
$imp::$method(self, &other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_val_ref_binop {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
|
||||
impl<'a, $($t: $p),*> $imp<&'a $rhs> for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn $method(self, other: &$rhs) -> $res {
|
||||
$imp::$method(&self, other)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
macro_rules! forward_all_binop_to_ref_ref {
|
||||
(impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
|
||||
forward_val_val_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
|
||||
forward_ref_val_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
|
||||
forward_val_ref_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
|
||||
};
|
||||
}
|
||||
|
||||
macro_rules! forward_ops_to_group_ops {
|
||||
(impl($($t:ident: $p:ident),*) $res:ty) => {
|
||||
impl<'a, 'b, $($t: $p),*> Add<&'a $res> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn add(self, other: &'a $res) -> $res {
|
||||
Jacobian::add(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, $($t: $p),*> Mul<&'a Fr> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn mul(self, other: &'a Fr) -> $res {
|
||||
Jacobian::mul(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, 'b, $($t: $p),*> Sub<&'a $res> for &'b $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn sub(self, other: &'a $res) -> $res {
|
||||
Jacobian::sub(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<'a, $($t: $p),*> Neg for &'a $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn neg(self) -> $res {
|
||||
Jacobian::neg(self)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> Neg for $res {
|
||||
type Output = $res;
|
||||
|
||||
#[inline]
|
||||
fn neg(self) -> $res {
|
||||
Jacobian::neg(&self)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> PartialEq for $res {
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
Jacobian::eq(self, other)
|
||||
}
|
||||
}
|
||||
|
||||
impl<$($t: $p),*> Eq for $res {}
|
||||
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Add for $res, add, $res);
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Sub for $res, sub, $res);
|
||||
forward_all_binop_to_ref_ref!(impl($($t: $p),*) Mul for $res, mul, Fr);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,355 +0,0 @@
|
|||
use fields::Field;
|
||||
use fields::fp::{PrimeFieldParams, Fp};
|
||||
use params::G2Params;
|
||||
use super::{Fr,Fq,Fq2};
|
||||
use rand::Rng;
|
||||
use std::ops::{Add,Mul,Sub,Neg};
|
||||
use std::fmt;
|
||||
|
||||
#[cfg(test)]
|
||||
pub mod tests;
|
||||
|
||||
#[macro_use]
|
||||
mod macros;
|
||||
|
||||
mod gt;
|
||||
pub use self::gt::Gt;
|
||||
|
||||
pub trait GroupParams: Sized {
|
||||
type Base: Field;
|
||||
|
||||
fn zero() -> Jacobian<Self>;
|
||||
fn one() -> Jacobian<Self>;
|
||||
fn coeff_b() -> Self::Base;
|
||||
fn name() -> &'static str;
|
||||
}
|
||||
|
||||
pub struct Jacobian<P: GroupParams> {
|
||||
x: P::Base,
|
||||
y: P::Base,
|
||||
z: P::Base
|
||||
}
|
||||
|
||||
impl<P: GroupParams> fmt::Debug for Jacobian<P> {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.x, self.y, self.z)
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: GroupParams> Clone for Jacobian<P> {
|
||||
fn clone(&self) -> Self {
|
||||
Jacobian {
|
||||
x: self.x.clone(),
|
||||
y: self.y.clone(),
|
||||
z: self.z.clone()
|
||||
}
|
||||
}
|
||||
}
|
||||
pub enum Affine<P: GroupParams> {
|
||||
Zero,
|
||||
Point{x: P::Base, y: P::Base}
|
||||
}
|
||||
|
||||
impl<P: GroupParams> Clone for Affine<P> {
|
||||
fn clone(&self) -> Self {
|
||||
match *self {
|
||||
Affine::Zero => Affine::Zero,
|
||||
Affine::Point{ref x, ref y} => Affine::Point{x: x.clone(), y: y.clone()}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[derive(PartialEq, Eq)]
|
||||
pub struct EllCoeffs {
|
||||
pub ell_0: Fq2,
|
||||
pub ell_vw: Fq2,
|
||||
pub ell_vv: Fq2
|
||||
}
|
||||
|
||||
impl<P: GroupParams> Affine<P> {
|
||||
pub fn get_x(&self) -> P::Base {
|
||||
match *self {
|
||||
Affine::Zero => P::Base::zero(),
|
||||
Affine::Point{ref x, ref y} => x.clone()
|
||||
}
|
||||
}
|
||||
|
||||
pub fn get_y(&self) -> P::Base {
|
||||
match *self {
|
||||
Affine::Zero => P::Base::one(),
|
||||
Affine::Point{ref x, ref y} => y.clone()
|
||||
}
|
||||
}
|
||||
|
||||
pub fn to_jacobian(&self) -> Jacobian<P> {
|
||||
match *self {
|
||||
Affine::Zero => P::zero(),
|
||||
Affine::Point{ref x, ref y} => Jacobian {
|
||||
x: x.clone(),
|
||||
y: y.clone(),
|
||||
z: P::Base::one()
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
pub fn neg(&self) -> Self {
|
||||
match *self {
|
||||
Affine::Zero => Affine::Zero,
|
||||
Affine::Point{ref x, ref y} => Affine::Point{x: x.clone(), y: y.neg()}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Jacobian<G2Params> {
|
||||
pub fn mul_by_q(&self) -> Jacobian<G2Params> {
|
||||
Jacobian {
|
||||
x: G2Params::twist_mul_by_q_x() * self.x.frobenius_map(1),
|
||||
y: G2Params::twist_mul_by_q_y() * self.y.frobenius_map(1),
|
||||
z: self.z.frobenius_map(1)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Affine<G2Params> {
|
||||
pub fn mul_by_q(&self) -> Affine<G2Params> {
|
||||
self.to_jacobian().mul_by_q().to_affine()
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: GroupParams> Jacobian<P> {
|
||||
pub fn new(x: P::Base, y: P::Base, z: P::Base) -> Option<Self> {
|
||||
let tmp = Jacobian {
|
||||
x: x,
|
||||
y: y,
|
||||
z: z
|
||||
};
|
||||
|
||||
if tmp.is_well_formed() {
|
||||
Some(tmp)
|
||||
} else {
|
||||
None
|
||||
}
|
||||
}
|
||||
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self {
|
||||
Self::one() * &Fr::random(rng)
|
||||
}
|
||||
|
||||
pub fn is_well_formed(&self) -> bool {
|
||||
if self.is_zero() {
|
||||
true
|
||||
} else {
|
||||
let x2 = self.x.squared();
|
||||
let y2 = self.y.squared();
|
||||
let z2 = self.z.squared();
|
||||
|
||||
let x3 = self.x.mul(&x2);
|
||||
let z3 = self.z.mul(&z2);
|
||||
let z6 = z3.squared();
|
||||
|
||||
(y2.eq(&z6.mul(&P::coeff_b()).add(&x3)))
|
||||
}
|
||||
}
|
||||
|
||||
pub fn to_affine(&self) -> Affine<P> {
|
||||
if self.is_zero() {
|
||||
Affine::Zero
|
||||
} else {
|
||||
let z_inv = self.z.inverse();
|
||||
let z2_inv = z_inv.squared();
|
||||
let z3_inv = z2_inv.mul(&z_inv);
|
||||
|
||||
Affine::Point {
|
||||
x: self.x.mul(&z2_inv),
|
||||
y: self.y.mul(&z3_inv)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
pub fn zero() -> Self {
|
||||
P::zero()
|
||||
}
|
||||
|
||||
pub fn one() -> Self {
|
||||
P::one()
|
||||
}
|
||||
|
||||
pub fn add(&self, other: &Self) -> Self {
|
||||
if self.is_zero() {
|
||||
return other.clone()
|
||||
}
|
||||
|
||||
if other.is_zero() {
|
||||
return self.clone()
|
||||
}
|
||||
|
||||
let z1_squared = self.z.squared();
|
||||
let z2_squared = other.z.squared();
|
||||
let u1 = self.x.mul(&z2_squared);
|
||||
let u2 = other.x.mul(&z1_squared);
|
||||
let z1_cubed = self.z.mul(&z1_squared);
|
||||
let z2_cubed = other.z.mul(&z2_squared);
|
||||
let s1 = self.y.mul(&z2_cubed);
|
||||
let s2 = other.y.mul(&z1_cubed);
|
||||
|
||||
if u1.eq(&u2) && s1.eq(&s2) {
|
||||
self.double()
|
||||
} else {
|
||||
let h = u2.sub(&u1);
|
||||
let s2_minus_s1 = s2.sub(&s1);
|
||||
let i = h.add(&h).squared();
|
||||
let j = h.mul(&i);
|
||||
let r = s2_minus_s1.add(&s2_minus_s1);
|
||||
let v = u1.mul(&i);
|
||||
let s1_j = s1.mul(&j);
|
||||
let x3 = r.squared().sub(&j).sub(&v.add(&v));
|
||||
let y3 = r.mul(&v.sub(&x3)).sub(&s1_j.add(&s1_j));
|
||||
|
||||
Jacobian {
|
||||
x: x3,
|
||||
y: y3,
|
||||
z: self.z.add(&other.z).squared().sub(&z1_squared).sub(&z2_squared).mul(&h)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
pub fn double(&self) -> Self {
|
||||
let a = self.x.squared();
|
||||
let b = self.y.squared();
|
||||
let c = b.squared();
|
||||
let mut d = self.x.add(&b).squared().sub(&a).sub(&c);
|
||||
d = d.add(&d);
|
||||
let e = a.add(&a).add(&a);
|
||||
let f = e.squared();
|
||||
let x3 = f.sub(&d.add(&d));
|
||||
let mut eight_c = c.add(&c);
|
||||
eight_c = eight_c.add(&eight_c);
|
||||
eight_c = eight_c.add(&eight_c);
|
||||
let y3 = e.mul(&d.sub(&x3)).sub(&eight_c);
|
||||
let y1z1 = self.y.mul(&self.z);
|
||||
let z3 = y1z1.add(&y1z1);
|
||||
|
||||
Jacobian {
|
||||
x: x3,
|
||||
y: y3,
|
||||
z: z3
|
||||
}
|
||||
}
|
||||
|
||||
pub fn eq(&self, other: &Self) -> bool {
|
||||
if self.is_zero() {
|
||||
return other.is_zero()
|
||||
}
|
||||
|
||||
if other.is_zero() {
|
||||
return false;
|
||||
}
|
||||
|
||||
let z1_squared = self.z.squared();
|
||||
let z2_squared = other.z.squared();
|
||||
|
||||
if self.x.mul(&z2_squared).ne(&other.x.mul(&z1_squared)) {
|
||||
return false;
|
||||
}
|
||||
|
||||
let z1_cubed = self.z.mul(&z1_squared);
|
||||
let z2_cubed = other.z.mul(&z2_squared);
|
||||
|
||||
if self.y.mul(&z2_cubed).ne(&other.y.mul(&z1_cubed)) {
|
||||
return false;
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
pub fn neg(&self) -> Self {
|
||||
Jacobian {
|
||||
x: self.x.clone(),
|
||||
y: self.y.neg(),
|
||||
z: self.z.clone()
|
||||
}
|
||||
}
|
||||
|
||||
#[inline]
|
||||
pub fn is_zero(&self) -> bool {
|
||||
self.z.is_zero()
|
||||
}
|
||||
|
||||
pub fn mul<S: PrimeFieldParams>(&self, other: &Fp<S>) -> Jacobian<P> {
|
||||
let mut result = Jacobian::<P>::zero();
|
||||
let mut found_one = false;
|
||||
for i in (0..S::bits()).rev() {
|
||||
if found_one {
|
||||
result = result.double();
|
||||
}
|
||||
|
||||
if other.test_bit(i) {
|
||||
found_one = true;
|
||||
result = &result + self;
|
||||
}
|
||||
}
|
||||
|
||||
result
|
||||
}
|
||||
|
||||
#[inline]
|
||||
pub fn sub(&self, other: &Self) -> Jacobian<P> {
|
||||
self.add(&other.neg())
|
||||
}
|
||||
}
|
||||
|
||||
impl Jacobian<G2Params> {
|
||||
pub fn mixed_addition_step_for_flipped_miller_loop(&mut self, base: &Affine<G2Params>) -> EllCoeffs {
|
||||
let d = &self.x - &self.z * &base.get_x();
|
||||
let e = &self.y - &self.z * &base.get_y();
|
||||
let f = d.squared();
|
||||
let g = e.squared();
|
||||
let h = &d * &f;
|
||||
let i = &self.x * &f;
|
||||
let j = &self.z * &g + &h - (&i + &i);
|
||||
|
||||
self.x = &d * &j;
|
||||
self.y = &e * (&i - &j) - &h * &self.y;
|
||||
self.z = &self.z * &h;
|
||||
|
||||
EllCoeffs {
|
||||
ell_0: G2Params::twist() * (&e * &base.get_x() - &d * &base.get_y()),
|
||||
ell_vv: e.neg(),
|
||||
ell_vw: d
|
||||
}
|
||||
}
|
||||
|
||||
pub fn doubling_step_for_flipped_miller_loop(&mut self, two_inv: &Fq) -> EllCoeffs {
|
||||
let a = &(&self.x * &self.y) * two_inv;
|
||||
let b = self.y.squared();
|
||||
let c = self.z.squared();
|
||||
let d = &c + &c + &c;
|
||||
let e = G2Params::coeff_b() * &d;
|
||||
let f = &e + &e + &e;
|
||||
let g = &(&b + &f) * two_inv;
|
||||
let h = (&self.y + &self.z).squared() - (&b + &c);
|
||||
let i = &e - &b;
|
||||
let j = self.x.squared();
|
||||
let e_sq = e.squared();
|
||||
|
||||
self.x = &a * (&b - &f);
|
||||
self.y = g.squared() - (&e_sq + &e_sq + &e_sq);
|
||||
self.z = &b * &h;
|
||||
|
||||
EllCoeffs {
|
||||
ell_0: G2Params::twist() * &i,
|
||||
ell_vw: h.neg(),
|
||||
ell_vv: &j + &j + &j
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
forward_ops_to_group_ops!(impl(P: GroupParams) Jacobian<P>);
|
||||
|
||||
impl<P: GroupParams> PartialEq for Affine<P> {
|
||||
fn eq(&self, other: &Self) -> bool {
|
||||
self.to_jacobian() == other.to_jacobian()
|
||||
}
|
||||
}
|
||||
|
||||
impl<P: GroupParams> Eq for Affine<P> { }
|
||||
|
|
@ -1,76 +0,0 @@
|
|||
use super::*;
|
||||
use ::Fr;
|
||||
use fields::Field;
|
||||
|
||||
use rand::Rng;
|
||||
|
||||
pub fn group_trials<P: GroupParams>() {
|
||||
fn test_doubling<P: GroupParams>() {
|
||||
type G<P> = Jacobian<P>;
|
||||
|
||||
let one = G::<P>::one();
|
||||
let two = one.add(&one);
|
||||
let three = two.add(&one);
|
||||
let four = three.add(&one);
|
||||
|
||||
assert_eq!(one.double(), two);
|
||||
assert_eq!(two.double(), four);
|
||||
}
|
||||
|
||||
fn random_test_addition<P: GroupParams, R: Rng>(rng: &mut R) {
|
||||
type G<P> = Jacobian<P>;
|
||||
|
||||
for _ in 0..50 {
|
||||
let r1 = &G::<P>::random(rng);
|
||||
let r2 = &G::<P>::random(rng);
|
||||
let r3 = &G::<P>::random(rng);
|
||||
|
||||
let s1 = (r1 + r2) + r3;
|
||||
let s2 = (r2 + r3) + r1;
|
||||
|
||||
assert_eq!(s1, s2);
|
||||
}
|
||||
}
|
||||
|
||||
fn random_test_doubling<P: GroupParams, R: Rng>(rng: &mut R) {
|
||||
type G<P> = Jacobian<P>;
|
||||
|
||||
for _ in 0..50 {
|
||||
let r1 = &G::<P>::random(rng);
|
||||
let r2 = &G::<P>::random(rng);
|
||||
|
||||
let a = (r1 + r2) + r1;
|
||||
let b = r1.double() + r2;
|
||||
|
||||
assert!(a.eq(&b));
|
||||
}
|
||||
}
|
||||
|
||||
fn random_test_dh<P: GroupParams, R: Rng>(rng: &mut R) {
|
||||
type G<P> = Jacobian<P>;
|
||||
|
||||
for _ in 0..50 {
|
||||
let alice_sk = Fr::random(rng);
|
||||
let bob_sk = Fr::random(rng);
|
||||
|
||||
let alice_pk = G::<P>::one() * &alice_sk;
|
||||
let bob_pk = G::<P>::one() * &bob_sk;
|
||||
|
||||
let alice_shared = &bob_pk * &alice_sk;
|
||||
let bob_shared = &alice_pk * &bob_sk;
|
||||
|
||||
assert_eq!(alice_shared, bob_shared);
|
||||
}
|
||||
}
|
||||
|
||||
test_doubling::<P>();
|
||||
|
||||
use rand::{SeedableRng,StdRng};
|
||||
let seed: [usize; 4] = [103245, 191922, 1293, 192103];
|
||||
let mut rng = StdRng::from_seed(&seed);
|
||||
|
||||
random_test_addition::<P, _>(&mut rng);
|
||||
random_test_doubling::<P, _>(&mut rng);
|
||||
random_test_dh::<P, _>(&mut rng);
|
||||
}
|
||||
|
||||
406
oldsrc/lib.rs
406
oldsrc/lib.rs
|
|
@ -1,406 +0,0 @@
|
|||
extern crate num;
|
||||
extern crate rand;
|
||||
|
||||
mod fields;
|
||||
mod params;
|
||||
|
||||
mod groups;
|
||||
|
||||
pub use groups::Gt;
|
||||
pub use fields::fp::Fp;
|
||||
pub use fields::fp2::Fp2;
|
||||
pub use fields::fp6::Fp6;
|
||||
pub use fields::fp12::Fp12;
|
||||
pub use params::{FrParams,FqParams,Fq2Params,G1Params,G2Params,Fq6Params,Fq12Params,ate_loop_count,final_exponent_z};
|
||||
pub use fields::Field;
|
||||
pub use groups::{Jacobian};
|
||||
use groups::{EllCoeffs,Affine};
|
||||
use fields::fp::PrimeFieldParams;
|
||||
|
||||
pub type Fr = Fp<FrParams>;
|
||||
pub type Fq = Fp<FqParams>;
|
||||
pub type Fq2 = Fp2<Fq2Params>;
|
||||
pub type Fq6 = Fp6<Fq6Params>;
|
||||
pub type Fq12 = Fp12<Fq12Params>;
|
||||
|
||||
pub type Scalar = Fr;
|
||||
pub type G1 = Jacobian<G1Params>;
|
||||
pub type G2 = Jacobian<G2Params>;
|
||||
|
||||
#[derive(PartialEq,Eq)]
|
||||
struct G2Precomp {
|
||||
q: Affine<G2Params>,
|
||||
coeffs: Vec<EllCoeffs>
|
||||
}
|
||||
|
||||
impl G2Precomp {
|
||||
fn new(from: &G2) -> G2Precomp {
|
||||
let g2 = from.to_affine();
|
||||
|
||||
let mut r = g2.to_jacobian();
|
||||
|
||||
let mut result = G2Precomp {
|
||||
q: g2.clone(),
|
||||
coeffs: Vec::new()
|
||||
};
|
||||
|
||||
let two_inv = Fq::from("2").inverse();
|
||||
|
||||
let mut found_one = false;
|
||||
let ate = ate_loop_count();
|
||||
for i in (0..FrParams::bits()).rev() {
|
||||
let bit = ate.test_bit(i);
|
||||
|
||||
if !found_one {
|
||||
found_one = bit;
|
||||
continue;
|
||||
}
|
||||
|
||||
result.coeffs.push(r.doubling_step_for_flipped_miller_loop(&two_inv));
|
||||
|
||||
if bit {
|
||||
result.coeffs.push(r.mixed_addition_step_for_flipped_miller_loop(&g2));
|
||||
}
|
||||
}
|
||||
|
||||
let q1 = g2.mul_by_q();
|
||||
let q2 = q1.mul_by_q().neg();
|
||||
|
||||
result.coeffs.push(r.mixed_addition_step_for_flipped_miller_loop(&q1));
|
||||
result.coeffs.push(r.mixed_addition_step_for_flipped_miller_loop(&q2));
|
||||
|
||||
result
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_prepared_g2() {
|
||||
let g2 = G2::one() * Fr::from("20390255904278144451778773028944684152769293537511418234311120800877067946");
|
||||
|
||||
let g2_p = G2Precomp::new(&g2);
|
||||
|
||||
let expected_g2_p = G2Precomp {
|
||||
q: G2::new(
|
||||
Fq2::new(
|
||||
Fq::from("13936578204263895229092967414825041569724079982537616431212348844388899776640"),
|
||||
Fq::from("6372636725635053773371996212293600406870925440022386078671828127711809436031")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("19293035970010898452454381709939058714495082898872914526540420247178075881697"),
|
||||
Fq::from("13822349107533275437553410197128434338071760794202849712402800746887549494974"),
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("1"),
|
||||
Fq::from("0"),
|
||||
)
|
||||
).unwrap().to_affine(),
|
||||
coeffs: vec![
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("2627043964130257285960335798481049684473505235282434252362906013168360965985"), Fq::from("14787221188041042838526170263203159226721816513593198738527261794343476005673")), ell_vw: Fq2::new(Fq::from("5190413803656753539584048070636432748402456516849818272297235294934300653772"), Fq::from("16131787528611999569385991096257681501249100726189947900572474295515353427218")), ell_vv: Fq2::new(Fq::from("11284217811624345285836951206193951701052480344824103057273798441033858118424"), Fq::from("6392116536365389562188363539617434898082427085812013656312597845585909267447")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("827617134098165717451808940080463277390770457691666780560712143809003953598"), Fq::from("6776229088211374446530917353066321938640163548858035832637439231634790575465")), ell_vw: Fq2::new(Fq::from("987776078024262725561041258416387561158070255475504730561661362421251696401"), Fq::from("15312963471998242334683179861466148222641884112991952428739813077336923189144")), ell_vv: Fq2::new(Fq::from("2813988028633040066320201189843971639620433430176492766961373503539074898364"), Fq::from("17055167212030988864288747645634552775658830115224987200613220012554982651578")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17093477194591041266397380404112224367919571835678040889250664706433487493043"), Fq::from("8643160753646550179100165428401120938543691942215161396502118430923535820500")), ell_vw: Fq2::new(Fq::from("10933962898922943120024964690690003920835888964592980369975615298196656183772"), Fq::from("10054435552662455933652209211749007190981947542684285471884164039871580864235")), ell_vv: Fq2::new(Fq::from("1475406195060586931258578851599932495282912871465827155842007043242102046659"), Fq::from("5049830924161187876168845800328902567850325970867534538120475909389784841990")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("10434276065336457961840942984114655645641355797054067910262735814196303889171"), Fq::from("13878009844584745291193244072670264656592436467816383615606044714978763054890")), ell_vw: Fq2::new(Fq::from("20993505060568459085534388708128029516059470166174503494622391683433030357130"), Fq::from("10192769806017258272908841309051731389378033999625803563624881649401237928876")), ell_vv: Fq2::new(Fq::from("17377091829483421118284926147077357677507183290871250621761583281560333718550"), Fq::from("18297780639039540893260206902113850213293978821982237672423968999898103045256")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("5064242330961655837810472366173802140673816516016739528934082190598759216129"), Fq::from("20172028727708469864987113767379594545870343866584998839699240724281670882460")), ell_vw: Fq2::new(Fq::from("2996734698689069564052128450078797792056313730363946953355442668966438200951"), Fq::from("9910941594900797404370917094355311738210439203708671856236954583027355115302")), ell_vv: Fq2::new(Fq::from("6899792008443933570863502403567742315007264221354931185809349393350618040985"), Fq::from("18692424201235977456836009406318755884773471215777102117879530727096807383696")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9406196439119227017197200697795682187217614676635965071601916278141238949664"), Fq::from("1156397052245190909533108891675012415349316096091404012699655652677336827483")), ell_vw: Fq2::new(Fq::from("9249275523859165912800910211783530541095037634552893633043938333737241478198"), Fq::from("13674086724537885208439774394455021050268654286498757861381516198880504360984")), ell_vv: Fq2::new(Fq::from("5760486636714317173624828119078349011897522431614835257025421978626292083787"), Fq::from("19195594701877562770296730558597966521343920474874926443609709880727520577918")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("12166638768862632131967787101186130559865354321458713212316891357299196109517"), Fq::from("1517854601414954363921968422436855204960697222979994177630673862982254831193")), ell_vw: Fq2::new(Fq::from("13366104107979832799705928625277388583673352228059815944738106504080223007902"), Fq::from("21648874073566751720910466086303831459661520354253552089758049591613143727506")), ell_vv: Fq2::new(Fq::from("3488776451414334656597670851583995239177248056342375163461521452312663358741"), Fq::from("20333414955874213710027365371143864644434939642550352414403887754960702108637")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("20468104499950674906991599591024893438007901046236752159815194628487603192867"), Fq::from("19069685413250623899891139234721987960230148622397590130148098858949057649761")), ell_vw: Fq2::new(Fq::from("2458162095258922865086779772179745380154704066745856173311580123496018896409"), Fq::from("14594824564551859025266692529845827840804005950672166057231487026855067744741")), ell_vv: Fq2::new(Fq::from("9689655654286496198845571066967567466951511863880400774464590553022163229348"), Fq::from("10870127206120874488753221889350215535903993427218589071224774335669836789433")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("15334990572515495832170458963151379997993357347608954164027751164770129172212"), Fq::from("13576640273125978757652414940234881692674718901710647917847939367156260249620")), ell_vw: Fq2::new(Fq::from("17441399177222030197667035179458353890777336233312342937564354849059149975908"), Fq::from("17007488955907409465543686050546106251553784366237996525801373957978511005278")), ell_vv: Fq2::new(Fq::from("11907792503811346855438657769533223907267837220830333730410940125854558637383"), Fq::from("19490060942462197243379937108210110931787757078893580540054690416131017931738")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17315779415820661602591970083599829709759601467527578787441772726289774228451"), Fq::from("12080802446892182171725856453369856169039939341293608060423916935382017714476")), ell_vw: Fq2::new(Fq::from("12912774602739952889552025090054804346758888115608888766725054474682313950190"), Fq::from("18204955971588024842905918028829132053489100674596042021111813303048407250440")), ell_vv: Fq2::new(Fq::from("15721987682182104464109212111163313043868345920774975073102123159159010623181"), Fq::from("12041652399509652544977783565303273845883245418094457529808044120827920548972")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19999070717670362479390656255660288732744476951677182489244240784338456791622"), Fq::from("3906002755238658676658974095984902840159437088441472633765497396881255783772")), ell_vw: Fq2::new(Fq::from("4998301920940599524538129746790252820575786197710804708434384224972978627969"), Fq::from("13740819604543965458992763357705315276969968429480411530007322182403523242226")), ell_vv: Fq2::new(Fq::from("12357083524385039711813704948190809675818592911528835736620903716727226601953"), Fq::from("13949012942996636079549854439740332990496218971788334041233648192605019948979")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19805154539184543843735550309592886829271314363908537964547876413114433734624"), Fq::from("16481416862400234230001935040590314552205484054708993091993487440981092053599")), ell_vw: Fq2::new(Fq::from("2850933690997557614680452825756662353227291804228932023648526608593113870536"), Fq::from("4786423507519240726599235257249783193682886531662683554713943115802063984530")), ell_vv: Fq2::new(Fq::from("1023533030117941985730558522296044345509721849960856436490999820443312747347"), Fq::from("16431548648882316869128893343209930754508425074299553782883149795599907406302")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17203075478724975791441470425150871365957382183648220405350599958349478966969"), Fq::from("19566853320706390536799238411444563555185156853468371794865496424286288424312")), ell_vw: Fq2::new(Fq::from("15310908404682220539815850064952575682898427316407655213706791187971849703724"), Fq::from("16518878079785062271298378680376701241016697782308466806532677867880353948389")), ell_vv: Fq2::new(Fq::from("14461573034674366293217641735721285869692106578982161360427147953320122006893"), Fq::from("6682535969691272372531048932989583075363217464304983455197465867679730319705")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("20895553497690200905762157235991552162755238828234592755315911339400881373107"), Fq::from("11947919061415103173593352950044808416347417810515010536678086292686107222044")), ell_vw: Fq2::new(Fq::from("6277981470671734560229149673222400771590408919719217743512900463425397921908"), Fq::from("857212248193599195410711267373529614085739023676782457331058533755337294689")), ell_vv: Fq2::new(Fq::from("13885916052404740835214284721162700704805447448922857617672445286139626987191"), Fq::from("19585389042100086858633036225209396447924441966778662250950999864988284098182")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("12748401205319976481200663793287165427761341490879316890008250070038707706903"), Fq::from("9347025175062646190962067344106887221752685406563421042329129538495481178145")), ell_vw: Fq2::new(Fq::from("12819473645128401077507234830331609583133696659610406468927174080626676619197"), Fq::from("9039389340404634934394726812078086316924048399159604642340339967187032834011")), ell_vv: Fq2::new(Fq::from("3576972655652865483567741810151575278761470911419381093571973994483543095285"), Fq::from("15017468236028111406921228193688973260631093975412858847563400987354453569177")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("15407570760857043664675198351546637734249070940748070513828892036078049928562"), Fq::from("16864837887933576789187120028615006826049916557295792205508706545038103706967")), ell_vw: Fq2::new(Fq::from("10721360465919602144653520112889689786555051462198759164582568961994647563952"), Fq::from("15294101887395462362997873520785213441488786364828649600395509678143054744021")), ell_vv: Fq2::new(Fq::from("338877711237691732068166553384070140091720428235937017002925264628733553275"), Fq::from("8565770517833678396194963042166078986348581926120249815567974171840711179000")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17302401852599488824262121640328139426135883695023154134865582322858078206108"), Fq::from("17762524466294762819341377108361075499043287383142581974755577861093917129883")), ell_vw: Fq2::new(Fq::from("13015933066581331586057031655765394156438563571733887223640331819027233831808"), Fq::from("758435331870656231667722761984400968773108978847112431665229252181053186864")), ell_vv: Fq2::new(Fq::from("1969703955244816291771524536928710541897907643982046151796341732075930805350"), Fq::from("7031491051442716548063495812915693048061021502544985435130728834982309403017")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("3256431897334799395000264533777543923057110731812322608781781329228902421476"), Fq::from("12181683857561584905762347955319259913388176042023651776593530168946356566719")), ell_vw: Fq2::new(Fq::from("796109596241493969908761241268545233387446802589790513588935996990189190052"), Fq::from("1881011435205668659920588004752042238985141500261993259857887774967416952583")), ell_vv: Fq2::new(Fq::from("8939978626202472531630769965940628317376245215184468794030552730424109408120"), Fq::from("6876296539554825957959953448623382464100292373640362636397165101276891176372")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9977776755404508431321449793657366203354342168643747704006143818738023991417"), Fq::from("17287266532802977377832339048078093713694407321084566908200498605546793435820")), ell_vw: Fq2::new(Fq::from("13828304001931491210449888619926027655755205497065268858009259221646932328015"), Fq::from("15160507616608365341639459841002920786281000303114113782821091199951204875277")), ell_vv: Fq2::new(Fq::from("11161349646944933007552237093278324942110971730799870343491465916610232191523"), Fq::from("1406353163795290818414111649956135144227974028417320470897284179379367096127")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7051926909684750402992796647032741235565177570654429988875094870973533133596"), Fq::from("20900584116079647608136401104271956963096697793208792824067775068966626057321")), ell_vw: Fq2::new(Fq::from("16845876804097000415961425779514720605919619149076212452284059758659650969766"), Fq::from("20806461795944565303534619813753388058736049320841472653130287521152836019826")), ell_vv: Fq2::new(Fq::from("14700937697004489523945953560825193972493636932341330040072362595384517591325"), Fq::from("17137955424118909932502168320776219042080643724609838664247554484115994974522")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("11997142079850902731018491830701934107296522353910410046841604519639199995406"), Fq::from("7846127392296015970710836702134527490160588060582987110380879354952036676012")), ell_vw: Fq2::new(Fq::from("17663414534578185845724108244425572237371794484114570058559740097895281553299"), Fq::from("5029140669755495687983399191536061323171057684732073778423303267496666431971")), ell_vv: Fq2::new(Fq::from("18428442704115060890708987869503078260482829714024061977805185634781850796860"), Fq::from("10997089106320530533400287751108615584976629751702164406696900094998369084403")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("13049677819639682137107272322562642308503411465986079606334189062279441432203"), Fq::from("8874624972677935217588093490885486721673594121072678233714072789659128555367")), ell_vw: Fq2::new(Fq::from("17057994029556488440657870420250293132874472170733557198308184169150330844407"), Fq::from("21633949388482190843211557537195287403106536528012825991981214057356654097223")), ell_vv: Fq2::new(Fq::from("6897044784874980042628318562068623805084522888972873438474139199226581764756"), Fq::from("2692625602037608101594849144393949134766066123857076012132350588113519149572")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9195356099870032305655798667367006686897880523242566329014149856866611060003"), Fq::from("8052880750949660720559492348565167987253311417692073778040482170195175946428")), ell_vw: Fq2::new(Fq::from("14126308928695836758114496610102001680995565158909643521688860213965125059872"), Fq::from("671075569038912473223544948981506373517307914345286644404839238190008163502")), ell_vv: Fq2::new(Fq::from("16828103633974871724641544770525140436938333764966095252502003672344759889143"), Fq::from("11294529501746593948507624028584472676389760897716457892342249916318954501723")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("21124500310722447577044753724306337899524073055454053171030128408285122310058"), Fq::from("6266274689105996173186441194758121417834460925587732781640173398761521329055")), ell_vw: Fq2::new(Fq::from("21576331134605070996263178912402854747994495442070419140713471256922277734125"), Fq::from("10074747339717657657921727946300324710951646905879034242434327125816600264379")), ell_vv: Fq2::new(Fq::from("21765519811276677250031796638148457542841530645055777846258335421409598000534"), Fq::from("21113224637771003677145667454854210585751245642107143223999187554888833454243")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("3972300323627467772646468544189830113523911494046612234673787196935654523692"), Fq::from("4678843490808368914310764558657240771944434980659329233409943752329617161210")), ell_vw: Fq2::new(Fq::from("17273599953138772488805612764323870175561796764345770950040891840763740358904"), Fq::from("20415406312940209525918367703821373463952436739154646433333601347381723237136")), ell_vv: Fq2::new(Fq::from("9160987523541118769404859219229455872777126347530590315596894278463599930633"), Fq::from("9054614112960826755739076858442558227570393423663838494067070216861352843202")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9994954547022379603539679290217274617475455164007187108524364097751858323148"), Fq::from("20207771379440433457553782484784849880846158790602128386495229840158065235194")), ell_vw: Fq2::new(Fq::from("4256518944443059194982602310083745017699415852751800911480635583088649250060"), Fq::from("15878038811235111024146051545935959211923223574364333740058604258589674044428")), ell_vv: Fq2::new(Fq::from("15953919860849853924955813198899405295748673040941543212644580663271517228860"), Fq::from("19594437991878043589671466710739298733201896072505590020656735731744884281871")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("1333543700232406379832215757617068657339748039338978081735192495239856176346"), Fq::from("13583045269132775344737980756385257860562307101313068058661941588822340692712")), ell_vw: Fq2::new(Fq::from("11316045827391404343818336116749364562466461792138476673985290066961360847098"), Fq::from("6683447190424452097068562814518005185732181765401062334661636064120276671717")), ell_vv: Fq2::new(Fq::from("21483741541431414142042872578822487244163622589552506298253453995156009765340"), Fq::from("16502358172728062550923345759488126380665850742066670591562640787191536290296")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("4727679401549029925466046980042210063407620223804057104870816459356196798234"), Fq::from("4245208253099058296636688301996648265313738760450861302514451065904449375848")), ell_vw: Fq2::new(Fq::from("19589426516750929424306774984752060788246605243046082989256140076730177865962"), Fq::from("19202599366770569221216501935740579180019961851730854119509268985533547631061")), ell_vv: Fq2::new(Fq::from("18329650333197074546830734977650617140322812110454751288122555715911145072440"), Fq::from("18685828888894718887886440900247948352873037333999376257561751598045361934940")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("15348453159719894937627693446890053385899104841918429189733580400902437025934"), Fq::from("7501190780205720975723852235835733848687299193764526538831345783610137314719")), ell_vw: Fq2::new(Fq::from("12341649147852680664345690534373468938440543264264387581538764313149640739302"), Fq::from("140543540021318882234026314588789476198722270107997413913717074968501481488")), ell_vv: Fq2::new(Fq::from("5960374673747504135132782820167542238733653290730217772559545641742563125282"), Fq::from("14507139191276441762644240084427079430815677404266073216544260783868466836469")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("1463974716527100203803811366059855506152810619047460592789012516365557382809"), Fq::from("12894560712946121716686238503640546420854178898471895472462918225441749701869")), ell_vw: Fq2::new(Fq::from("10508120321944855490271402587060090544503473558782513226881398929302598320386"), Fq::from("20659878091446285231719184399846880718538938504006216923931157918871132219202")), ell_vv: Fq2::new(Fq::from("9314687360620406591930278900314522432964075856747694070384017245464130048974"), Fq::from("17694675150016443475335083504221747995503842086249559620223686305992007745569")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14196539467892272085884829545587228956041818801561947743113049357924737022135"), Fq::from("11319357657686312684765696405805456576475636756706867678717962076341276658626")), ell_vw: Fq2::new(Fq::from("2758949814978246411081695103954624266457693267107844100147125044169545866221"), Fq::from("9492100316900274072027501035053797502489796059345864111677781413985743864383")), ell_vv: Fq2::new(Fq::from("4704107896591496617393915690357581449785399000813194972371050438639491862314"), Fq::from("11531365345870313813093010071065540963321572589131340821665512078366854738990")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("18802465664727774773666122120775907428094487475952383150269507875840089541246"), Fq::from("1731637922302665944958348222164323910730404298281499149800917211427254836819")), ell_vw: Fq2::new(Fq::from("9297609456558817283944780415839637083190742770917810313181849518385379162642"), Fq::from("16377246183633200781091121197835476043913744319877154056563766308564474143489")), ell_vv: Fq2::new(Fq::from("9542461764772800142773586971354345045722377861760780709590923740133551871717"), Fq::from("21640615613954317564353959148225302612886621120325752435425437529806262143694")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19906049876176293236988182778475214525096978055900789654464603831282713330781"), Fq::from("20362580925091945825523087376754169675844247448742703441518744743887060798158")), ell_vw: Fq2::new(Fq::from("12267599301269062964822189844562856172284191535014283588478875529832316401461"), Fq::from("16669825137620567269982790548542800570592942517936126877686519256685036586668")), ell_vv: Fq2::new(Fq::from("8883573260261802165780406246211290131940260376316892224137508921505842308805"), Fq::from("19231108274886583687672953546761020040720197580241947146286750565108059707992")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("634182853515641884871095612114627494589971356340786857463490962898713112220"), Fq::from("11430884471074068345749191262196070058384500365559620896062382995797164195815")), ell_vw: Fq2::new(Fq::from("10550902705393315932525976596381459439846414130661652807183357995272197708172"), Fq::from("3961587743443277010160905820636488892023891053433292002931434257476626412826")), ell_vv: Fq2::new(Fq::from("12451440882697904111698352784988882971851697245540249016187908252126835129000"), Fq::from("11782592623486603129029758483031965320434451423371375539247662743178943477576")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("1404156345033137762434737426689373534725204733157905834242027185649572912742"), Fq::from("19570890322851668915358612375948367153948206621537633922343603465980161569078")), ell_vw: Fq2::new(Fq::from("8686503710040621382075118769097735385052600877432244428197116763766844918162"), Fq::from("17223447941612107204326938316335236704702567123017447936901253775530936851086")), ell_vv: Fq2::new(Fq::from("18767158861904777443587157807982315566545548385817262926280782765269843879565"), Fq::from("21334543677892438295079840326280352051766440588072368601899791201007143326750")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("20453014818098756686381445228623803935714316636974320420742351477862354368007"), Fq::from("11004429848286161246832723709453157691786114066215975460914111961981461575367")), ell_vw: Fq2::new(Fq::from("14444837779919119651023367195508370508399423510380962187645910198528103345317"), Fq::from("4021193867366929691652413553892868612329317391162172266658368471326882495507")), ell_vv: Fq2::new(Fq::from("21098047915839588616030399663527845846589272989005835932893550785408588982098"), Fq::from("16796487305049888740077005894512139332211008298712590271618863352993144873711")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8799932768264091269394526725962837485495458036153083882004277055769655900574"), Fq::from("18596145973176446599121174893654309094121045316907408604913712044917019537350")), ell_vw: Fq2::new(Fq::from("5727901458562943136998396728651681550262281371313580881804977990767435431080"), Fq::from("16665276274186006945492338822028666786935953718794303569570538737692828117635")), ell_vv: Fq2::new(Fq::from("10910280368195212990489805322100030141483989387720003214110076576431959738476"), Fq::from("9606982070265587786427675480691869167035030735018706315315080889814741903522")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14453637744147393731588213406970287317078500183808667567110703622821377404467"), Fq::from("2399421543794348043991999124897133983828094348779941685913680103324762089779")), ell_vw: Fq2::new(Fq::from("9949473626857777965864312230577133154733097780222892008806269288857107115742"), Fq::from("3174442934451895428948522429276679446276043250911620596846605340399481680631")), ell_vv: Fq2::new(Fq::from("10773554875563236900680111254025179423521083612506388720894431016952344645908"), Fq::from("1791500946161395076321848651097476041018873800532919907790655022966446958329")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("13228018442560564090007964181563674306630092611719086476342149061864561185280"), Fq::from("12610285327624889222715450538150491139050620893563766277510163987972586901233")), ell_vw: Fq2::new(Fq::from("17479662858773093405375538474745376030990506794065246603293683266124925174043"), Fq::from("2084404960859519365733972471606438409123459865402210971655148862692485946826")), ell_vv: Fq2::new(Fq::from("9675635536108496330861750800277390856149950003475979013330722219857375990089"), Fq::from("17889926389980731198337394126857435112726851886206769936779651682292365620935")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19205463777127243508919644186723680978776945615422050305472500178064412123473"), Fq::from("10530028762478985738084339660443655112791893212694172883230610760959423970096")), ell_vw: Fq2::new(Fq::from("16515559472874148379011472911124765449097459867226728232468301906190158644000"), Fq::from("17379548905015313648731271429222704537289418711815257252434537403381161039222")), ell_vv: Fq2::new(Fq::from("13018298656134311744614296809909600459918460239498208291306800551968894517759"), Fq::from("16285303269049929546880902543736204779249639088136468614535789316688521663976")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9506592875949693201584225006409064359870098448027454395748349563972724759341"), Fq::from("1756212124305090096775291444252901778765176938185769777272403090820692916832")), ell_vw: Fq2::new(Fq::from("8608069305722185875126845710591577689851258364137915830961192516727536204958"), Fq::from("7879742654857051185278955345176850926952262018841407228150061698899939295057")), ell_vv: Fq2::new(Fq::from("2311752966405194522531977544398652994349075269275918521122768201037004674541"), Fq::from("8056192790171072186146581305753657840809572079825584316343698126369167589177")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("16894171323623324294071017663897158494527746239981369238071300334653959886935"), Fq::from("21839557351524624846710837291698003965911117746801809883425361529677608757736")), ell_vw: Fq2::new(Fq::from("7921995242367245298209685641602469741817826911044923939882608549077724733892"), Fq::from("16195366803093832645900011617380218833645406154510352140817411408898365560241")), ell_vv: Fq2::new(Fq::from("12718951609280728995721445896408716663776093135974310357265585518411722037823"), Fq::from("14775730569800772809191320148533632897226925930462946258120395650683306784222")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("18324740767049924394294219212760164185884801967765967078427354810675386933254"), Fq::from("18510525798971302215942990229348890627301667188256739950256532108744423958467")), ell_vw: Fq2::new(Fq::from("392130232730851920199052091589353916248087256056205523658797958171832234380"), Fq::from("21095230708713942590602820178155041621291598326436725983218983799781802054278")), ell_vv: Fq2::new(Fq::from("3496296009938486548567151348321691013571513425434397040346440937975425900960"), Fq::from("5982055369526470853931810147684497423036063399292908540001447206525852512531")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19247021831371751344058078378442480867649167715937305884736113857856820190448"), Fq::from("3844115161163747856814522390569661892955450798273343821401275758096863392646")), ell_vw: Fq2::new(Fq::from("6827864046826742026186179073427918229064686953470940699125130948982461542396"), Fq::from("17615043663229174389408922909891358248158892597678816385681324344031892930590")), ell_vv: Fq2::new(Fq::from("17143020152984715373298117189870583206488981021188881359521310100992509008220"), Fq::from("2174519777022093979454116656397980458948553322768446892932246705483799164016")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7787149350876246869417695770873628344850130125888658086308716316049428077539"), Fq::from("3645376584593179034263104864050174094110419584940335745722492256564582048708")), ell_vw: Fq2::new(Fq::from("11834206166934740935662681278907472701573638397628522018255718023777042308993"), Fq::from("11564024956967266505944728035150285591786947709753433733529805379472238406883")), ell_vv: Fq2::new(Fq::from("15009525058621581543328262019401183048318643177731888421709672368574056014500"), Fq::from("13573139489477783981960389988307434036015536834494019264597795654229345703051")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("16059660214342726778635842789601639915164060169646706775268999439826160969051"), Fq::from("3592864998692836817549974752747753891215991801035643051485066473571282986623")), ell_vw: Fq2::new(Fq::from("16014086539360826224382965134738311010906671679277894939278016943520015391650"), Fq::from("8080101227643664909861133876167034094240488311720250596061359317310944652491")), ell_vv: Fq2::new(Fq::from("3252331663236937425057834000082561720577180169369353108561319513563871033743"), Fq::from("11096433584385810520286571872297862049422429286608206525566845219548956753724")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19106172305007554707393707438702629275907204152148571359255256006833275609105"), Fq::from("19930525972818199875851038877132322547334829658949554806801108404941414101103")), ell_vw: Fq2::new(Fq::from("6679449617056144648556013688092503718528081567224358397706944806960707450866"), Fq::from("11834339054115289581728384446510154030614495257639549098914576992681792644317")), ell_vv: Fq2::new(Fq::from("1103971970080878735020200145931068396548255816344141900100578642050167835756"), Fq::from("17442014287618549059909689032626628911431121434337187918457502534017974292771")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("13076805492928497748141329405065621544173515733010216253264862326898999186011"), Fq::from("19346998537378535293491878821381642632408077348855336790184043880601230192418")), ell_vw: Fq2::new(Fq::from("2545953185107430710067715026283426197979102699516436299879612082830465064387"), Fq::from("658480144944520773976742499043453183928200527625254756411898212059863027220")), ell_vv: Fq2::new(Fq::from("10599092041977168661053673645861514974472253862403262653806335823439984547520"), Fq::from("17162893574285047796735108280435654463748265136801600105571927738662909784323")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7085319511141515608176313666085289847826695130590757892136226409211984372940"), Fq::from("4640142023499829801003091193578633557246618475866500623404375352964089302137")), ell_vw: Fq2::new(Fq::from("1378711095367589966539356394028311641404402942969200900226036867512926984525"), Fq::from("20227188036459114276006891788262806649925222994898646338447622388573680807347")), ell_vv: Fq2::new(Fq::from("10909351851886459521617902618958119972478357132140936115187854789408351897716"), Fq::from("4270359828288113001419972416654771076387260764523167288282363565700959902034")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("10664974041382313497332907041293813168318012018754207087217051246266695094381"), Fq::from("7224602128989495563505314962160716046811485526332201590284671097356858321790")), ell_vw: Fq2::new(Fq::from("3934655983500232748821065857705540333423053242147172231346384664554964864345"), Fq::from("11454752219285395886386371667205283572988335397450041936477253847740701967591")), ell_vv: Fq2::new(Fq::from("8613140983903038954690786727135433848146709090100659195246608245554768285578"), Fq::from("11683437859485859733100235618517710813205908191940301821880216475492534630964")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9260311336006363265451970156091146121161647548618044834929651955256342089015"), Fq::from("13937163080647677520680042908210664749449075029135461146729576039103333691760")), ell_vw: Fq2::new(Fq::from("17902331142943185999552054453100857674678810044830315483268693319046882556841"), Fq::from("1544882902322119030227919062381439448920928851067359863906156836436873153173")), ell_vv: Fq2::new(Fq::from("16995331248700240765237826468302734126993772776070338276810983166039248498016"), Fq::from("14969634758504522458179971123440531767135906355134596040598769037804654587702")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("9691457346326988270440356562380914538881384898220972529069554878570918299675"), Fq::from("4212749851190062070411861546581519573149862920541429109749681953529770836138")), ell_vw: Fq2::new(Fq::from("10890917529063563080488636605724946896609903254351684402546841801646043334166"), Fq::from("17064796604657821037034221187126605208939910043822292844975397354283757360178")), ell_vv: Fq2::new(Fq::from("10053764157025690527213061522668163518874554311426109722786780729745637570153"), Fq::from("12784239716790558610229592219566905741360808124013978959238298462172061891010")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("18178610037180803777372696468852749823139836169202607246443680867419301660001"), Fq::from("2203553150397509140176760042861998991151797164185565920046676990283238338489")), ell_vw: Fq2::new(Fq::from("20994248737185978263276750124680792452522185817020429107744966692073225126536"), Fq::from("6349838002511478763817816496894821255234760390494115897123421446389963162622")), ell_vv: Fq2::new(Fq::from("1263928993764270656816573911502202456032289420152723320064785370753332332564"), Fq::from("3046827108505433561924898780283267608115953987844810798949064271834105292424")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8956928906602747002792065663685826131559810003765184492377190892700326559543"), Fq::from("9256558483224710959389211180674778886236784676421453067453985103303008910100")), ell_vw: Fq2::new(Fq::from("19258483215045500292709619645410473292886118206783068420253408398264757067719"), Fq::from("4451865829956913287893327659699467549695832858717473490066802599791690802339")), ell_vv: Fq2::new(Fq::from("2764660330371796211645912465865514165647712230266940655139955982219479135487"), Fq::from("13240152986607724183470740198192310673584785226612774164092563912390438227662")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("681767682327814473892054649470454096768283412403007527891528077929769397010"), Fq::from("7668193584311505399758378551993462119934308304509766677185196010163712481402")), ell_vw: Fq2::new(Fq::from("5655243760535315520783349710797795360471266639432050916814563868068635911845"), Fq::from("6563255051651012450772847952915771842363624186837705815170827122750163703821")), ell_vv: Fq2::new(Fq::from("649940975249127008407571724305690292046357719924151085455652491670338045916"), Fq::from("21579311737676937819033214124612551530127167774002946532496743344036322675381")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("21175778737847401044104466077056088822729568143966863788586142950892805137666"), Fq::from("5595589116740977138584720715075423123216685509908153451278598090500673116809")), ell_vw: Fq2::new(Fq::from("10584200644032922607821101570277578933623023426596682657073390742969073652895"), Fq::from("12837953697025504547863231066503572653998301486985427806275987315834659812986")), ell_vv: Fq2::new(Fq::from("8117107548208718171682922744254403704391859020172151233388364110731129041045"), Fq::from("13049999463955485268550904857465746325902043660001708636685369259450564610454")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8364961604780202742303921161081604160922838515374423608219736048018999860853"), Fq::from("2351019119583633406807532653396626109486234484023597064733508979159842183382")), ell_vw: Fq2::new(Fq::from("21028432880575926523752559333294402827459370060933557257525967464997077946986"), Fq::from("8046872296156140750811104526560806223677002170113323621491280498583760192616")), ell_vv: Fq2::new(Fq::from("12898024833491487058567514428449740829256150305937499595589780150928565842102"), Fq::from("4285065448422006185829060466560686578745712460867295748911655362509144300948")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8072232359889306936722303478835558056241116613774315547062190240728474923834"), Fq::from("11177008054227634237663439894104913366867843529726469624208391026893438331544")), ell_vw: Fq2::new(Fq::from("6809080759521318546573252139200749353665236974149238674422052122591837770337"), Fq::from("17038522274461048605370004543286094433565235245947661777349160189041706387246")), ell_vv: Fq2::new(Fq::from("14024834693814357899802394991122512208020612837103453479716792821268632856005"), Fq::from("12162253519201182595066522680875457472054933146636012038079782236991342232964")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7517621744472550238729147112582763290619696603888340562320661653468259785459"), Fq::from("5775958628431902009928696648706206677051589697801230225207961079701351805991")), ell_vw: Fq2::new(Fq::from("17101537508347637393046612945060881733341630882242907674489426818282232192765"), Fq::from("11439924192045730134857855444951867487673481853061712676505751821713592417848")), ell_vv: Fq2::new(Fq::from("16524831954193049226680237913906512849861747525312574297009556588583016003485"), Fq::from("17961833510100001957206410577764797351002903290115563676683242640020206248673")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("16912575460065719860154998920476780598787708817030774617128864437198545819929"), Fq::from("18523390726102623209642393197047309169880798198922216024709291880134883505164")), ell_vw: Fq2::new(Fq::from("8711744315121016096444521009902336544777137803294883395587631628756743226403"), Fq::from("384665796631718061484470820770858149414181395445222225443039170963661807931")), ell_vv: Fq2::new(Fq::from("15774538322747462731385931838340979144243491164741595437453112329195248618714"), Fq::from("11632275451601229685994821619837954138410931366643826111939350416539675376582")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("4193777370819241345875098285464776579390947200963349948619027946434227330979"), Fq::from("509866391215626792725431227507051906680902316754753085884521978793646270092")), ell_vw: Fq2::new(Fq::from("6037175194865804429042789680410737585033925490367655507316663717551980954540"), Fq::from("18041663784750649636833746105782119188697038394822653258671508993118228507622")), ell_vv: Fq2::new(Fq::from("5823434994217288412340362524966578492063846889148854293277163714066988854109"), Fq::from("5672396008289604057966364197930061596003079754530820851713923211431895221182")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("4038166397773785982077422827894979131906966567246129821324959462204170431412"), Fq::from("18437550501813119699199412531646289403507307693226141098858673836744295275291")), ell_vw: Fq2::new(Fq::from("14284923653983275338299458156785711701885868498245540450770121796221847779083"), Fq::from("12602897944901625024952695280664364105484904418233840369524699062991946110320")), ell_vv: Fq2::new(Fq::from("5486498814295375008109094800710678785628460899485721363575459728835468025031"), Fq::from("16200691130190012476008796365701719097160136918178762563260333528187553865070")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("12314546787967340174315157919495563500551846522430770700093005979883034971431"), Fq::from("3526449836226747514409509674529965207620312182683788709671366453353950282439")), ell_vw: Fq2::new(Fq::from("5093273668274685698542824313074411944254604209522407110762874543698544425100"), Fq::from("14413934995969972893982204347979972725062293812449032149868616703831967954701")), ell_vv: Fq2::new(Fq::from("5926816361020227072352913556957354039762675747717706660663155084741002986207"), Fq::from("11598493987133778453993847174276604684683441101397418085992950965674684594056")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14605016886275487293555440005295724730930746064070181829857167303747503806723"), Fq::from("125488028578519699988648864181559879827394253209756997049515479109363959656")), ell_vw: Fq2::new(Fq::from("13618798589781916917754240943924749450694915714095829562214241999969133303075"), Fq::from("7919521676249934186275057369006254600339974917319129664598969307290994883444")), ell_vv: Fq2::new(Fq::from("13618646464444173552701873510284352084626546810748938598145778229202447557390"), Fq::from("9476574581262975213029808591741428214940842553330900266594833123385626035464")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("20330569420634759863618802200434379756882301920599312733161738334139846403423"), Fq::from("16941424680188140264426604507849243567044731815188670894126312258606055646954")), ell_vw: Fq2::new(Fq::from("4276245652046353558826181153633997046897244969830610112857888938076187872093"), Fq::from("5218134511825218024578456539758678791071455837562669069391138178014247652283")), ell_vv: Fq2::new(Fq::from("5074559277335429630740829563679793620243538875458585401599810469948320707914"), Fq::from("8399181532479234777915440768158248538072911084393374644710065479068982458679")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("228456190514225889641604150077307010131630607092226273786181288134202785827"), Fq::from("6829691501727142726895142554058769478742020003540473851444113314854839779896")), ell_vw: Fq2::new(Fq::from("7239124420778199901449006013253700083679198792863456824897986348225520969318"), Fq::from("9612815502366829000381428453387330590336692138445456863004983078118510731327")), ell_vv: Fq2::new(Fq::from("3032095333965417803301146592958869325973325547652138997619203744855910423626"), Fq::from("9140900126707960555227810341717821370276432039323462635381934661102939064717")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("15183121839690585327918066578070528787848569635478652970262274682157344344126"), Fq::from("17032257654469593612895387885450704824985120918227803531218149228038247116993")), ell_vw: Fq2::new(Fq::from("4449946720064992614521464039848704811573349967863291193814384877976473528180"), Fq::from("16213473115750238158840972181958630393893069174331658126086552358850995045944")), ell_vv: Fq2::new(Fq::from("14820364816206160787218030695278797219740217739100995460398841348849807343630"), Fq::from("13391831978082769659226335015618034703517552702532093599836056107584855920091")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19376350172596821938106071755601309991977917109030961898807003698880067029751"), Fq::from("8432677549750770318577385075581043130355856390772751886981628666318547719067")), ell_vw: Fq2::new(Fq::from("19907801542387995008974808935818119635245812040205527769417146511798917761987"), Fq::from("5161102563798536355551540455475021097419898845343559944869423371507274303876")), ell_vv: Fq2::new(Fq::from("8934093116311670296805867189709376457342708648536176030347455800639124491789"), Fq::from("2703243001408501823489300103176986467031566088207792046257025791153593204110")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14246576411085900561418149065736187542613160942023368670593924207716148262147"), Fq::from("3894319734417282749436553474309402307762162253367446669496582090013706055610")), ell_vw: Fq2::new(Fq::from("8375748526029577467798965722696242475050467009610481042928314348040697238273"), Fq::from("5150547143250446746041060583106242553976637956855972603954741388536316657102")), ell_vv: Fq2::new(Fq::from("15907790590424017252473639606980913201030067954178224590289142061847439584806"), Fq::from("11159987404206640511954116561264499629862056981304725791275082386203982274572")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8534750176510034607784585561677263909151653570221826711790070724427621935471"), Fq::from("7817152482056867378682253092041139659293041868731996264204246731388352069129")), ell_vw: Fq2::new(Fq::from("16961113237531514134058762308816541864350643273034658785830240248900850618232"), Fq::from("1179078000730113993104369721112852911420394064162245727296751799866128074554")), ell_vv: Fq2::new(Fq::from("20457374714339105220680185601375259716132143552962630535477097129353077443649"), Fq::from("4422525926709336878773825319073188719230418589270084994878618648788354576429")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7627847586963893527076371866753343482026765205726665650559945926181618692545"), Fq::from("11854660093187915385325641424610609952992715573834872602540776698350931163771")), ell_vw: Fq2::new(Fq::from("12061802008303461437760636908585485318885385024493098952040511326354153801540"), Fq::from("2483328707802038203960641185873859652602098605879879702928670691083351376828")), ell_vv: Fq2::new(Fq::from("3179938981834043637934998748622377818001614400201120097155888429286598162788"), Fq::from("3387712903817602592588061982323804658595985412237324988504760476608661908669")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("18935668687475417752670528265758371887227072908926123795139093572891409166177"), Fq::from("7137948322161355685471108734802366001522057971184080351365620151904917529667")), ell_vw: Fq2::new(Fq::from("4339156032094542567838794153972725732752104151129467898887880650450609600794"), Fq::from("12048671216064877807276853910375839173096391682288251978695349073893797560105")), ell_vv: Fq2::new(Fq::from("1950772803812480571427275248471639178971170644950730072787717123474197730954"), Fq::from("9181624035531055165333621510604231877029437698520448252367489746796255738472")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("11063654615400954717295218153285806614049542407631184476400061600226642090639"), Fq::from("10322234663627758865726091502227262577963762851829427143908452375568424940506")), ell_vw: Fq2::new(Fq::from("5088512375045637070831200431021199523774202712519349524231646029565850243137"), Fq::from("13830164350727008423053294968318643994288249825064419288902919319598527803018")), ell_vv: Fq2::new(Fq::from("5664114633031170805308124108402506179037402200165762737765348606356467981435"), Fq::from("6420500289322096738785425211380588437700105870048213919996474830908364662080")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("12089017351045163205876906516764262596252750496306969979802152087250767442655"), Fq::from("10210558808216547366164047615754858102665922901025755697993978799086515582216")), ell_vw: Fq2::new(Fq::from("5805411494371431706302702029555168082350433630263841912576207114214821637903"), Fq::from("13417649473832328299363309530328161775713579734460687495589323668315481789186")), ell_vv: Fq2::new(Fq::from("7100161023424716303226449735068569399024504614273633218656928626719841360262"), Fq::from("4608780226874321006375565633722017610093139802788639970961143211665122970425")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7402656885283645637844399867437832414708002274719716809314550750025200002816"), Fq::from("3359755418859898733774484791668766343777859472186478368952701397946858170923")), ell_vw: Fq2::new(Fq::from("13972633490402551449646647488711159435500678729477306484155919447807727623768"), Fq::from("7493072689132118410451346570771015894599566093753023472904593233187191189290")), ell_vv: Fq2::new(Fq::from("10553632499535499938294059057022861371325444554911689769145218759723376859522"), Fq::from("15031724096959569889887883166930429112400023614133986918505200177949730145621")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("19614666780105423133718014776333000423285968913902974939878172716992608453809"), Fq::from("11603995082765755677014543451017101337084691386341657702599446172204728703168")), ell_vw: Fq2::new(Fq::from("3640285626277218751703647194759635465446306209869384174139659856814138047153"), Fq::from("19852827152161121673942769427296662914445783006570890136096053338872958018957")), ell_vv: Fq2::new(Fq::from("15133277841235179795557173122463348349264603847086033764926472096701308210280"), Fq::from("11477545358800195084620539652687203979589770655971679975137907269158992047904")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14110112013826130627308137057440352762673176006101512326319632538666268095190"), Fq::from("11939502323738533476551128890683182628994629048369580067812328846012456410750")), ell_vw: Fq2::new(Fq::from("4903570904021379863440412383519324112841733022665060696302943089410552325193"), Fq::from("14266803156893138980425811506240396635009593456307449490727186191181005152878")), ell_vv: Fq2::new(Fq::from("14881072700587137091207448172180518390500891251946414292329369965686915854422"), Fq::from("15926908436628594399583920130944357569706863129497064862365363758969852348774")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("12558706151877569296451844961986237406953575964353502214928234165049347203902"), Fq::from("20986351119648698768747274174278231882270962658108929786748672594878002377020")), ell_vw: Fq2::new(Fq::from("19049669232824485247328064933680299726722169816787419902393190195363675139966"), Fq::from("9038064204016446065702766858179381867420605337773795708435102200352238225734")), ell_vv: Fq2::new(Fq::from("20935836360010341957040867041308346409399314465762274744792154001186771274330"), Fq::from("10203406114258970224185400536984459120400171034941205452745624846762632193745")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("5273485321155899320017031787320374433252287213043632779466667239152835002841"), Fq::from("3053056741460414900892697870729818263336633719763669407853703091660209931803")), ell_vw: Fq2::new(Fq::from("14340825980720147789753139378133767339849529468405152905403690972933175947523"), Fq::from("10774533501875920615470512566140848784460524907884011188458749902565676606519")), ell_vv: Fq2::new(Fq::from("3964278893337662256819152335242286127722672026565541866237058714197501521533"), Fq::from("18022244127367262334687067361628890804799640514175862613915842388966614841200")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("16332502873726000727943290608233946425803707374189230473690022986938005644703"), Fq::from("1567962947294031055122165158764344785171646063465144808831306664719326769256")), ell_vw: Fq2::new(Fq::from("20252166217271346908492216031557669988560255907738941815783926955730505937199"), Fq::from("17117796187826532609679851805915085724672631310980423533710032156677468384570")), ell_vv: Fq2::new(Fq::from("17447467886258986370787137061379217598255780655216428459333948972673151012677"), Fq::from("5126879980313476901131854669269919146638602687291477011061931179530480305128")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("6088970897125028663727223015788851329277811231049906821835210021445230531470"), Fq::from("8269042454443245208032034843063473106607747629991910601236499943382389383909")), ell_vw: Fq2::new(Fq::from("9390988514296458582044517134794855627538985266829573142624063333360969055582"), Fq::from("14809192622791971819542419564616657251564340618078775692251491022692953050806")), ell_vv: Fq2::new(Fq::from("12392403118986217155446218801253632414719473065843423820454574775060624572223"), Fq::from("17315648550786131512187415565477299679361071890287921321719420341945848525344")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8509704393616883918389461491307625357351608849562781376448108143686881397874"), Fq::from("20273788844812669168701278525056990767412251703786041383351127813548056060175")), ell_vw: Fq2::new(Fq::from("13587733380957601917144020513037833512715927912961534242274129611676082179670"), Fq::from("18219007782547538891755131684432302965729501555658190323551992733355994409648")), ell_vv: Fq2::new(Fq::from("15212235563035911012497734239429958536448576200220918241945992532007455729638"), Fq::from("15868967159924843704138451124239001351258676891119605450618238262537266256000")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("566642944339341838872659990670775497018813579200118662738575067585620262683"), Fq::from("80633561422247315402489148783136836267866433112423246780090434639448081501")), ell_vw: Fq2::new(Fq::from("16776314135335488452712466347201660236874408701359052824185479604688604443386"), Fq::from("9397286871750513195379912820117368990110423949006393550333044521067916303673")), ell_vv: Fq2::new(Fq::from("11213241389292792759942014406027965770431479614859139543821417488303149467800"), Fq::from("13968940593285273772185768016764839518710968380183853737025067101492115101555")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("6582524148524166281651049223972241418275829952930531957133089376081226599310"), Fq::from("12912796945237135113112612780707994091197804899944634993937602107108817617069")), ell_vw: Fq2::new(Fq::from("5915143763477343907746278070838860419057837978194254349309930636588762054019"), Fq::from("16829580672314341143130263740133292836202318062773617917928807522786048686905")), ell_vv: Fq2::new(Fq::from("6048262046277135430490078693604752857941808479983722633615831914037376701617"), Fq::from("11339265196645696685132629437938382050130007247287625382019491127986659567508")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("16221040390720130701106818492787718054167551387591190581820867019772199748452"), Fq::from("13816650124538024294513769170531808824213976236314395631188393480750356347832")), ell_vw: Fq2::new(Fq::from("17884725815671017389514271919761437310258619463085199936932965564030171526767"), Fq::from("18248973796984942533601080062907385035195180110558182226420098600644022965345")), ell_vv: Fq2::new(Fq::from("3137416660392142651716799414483848222789075294982695366740419822188364577896"), Fq::from("9694367271685190541749430052152010428005565838702388077250686840743397580564")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("6357610272973630149840225505274539351850867930627803566656124705077309138236"), Fq::from("6532064867969562545750502093085673423036025281166230602025667552530979558092")), ell_vw: Fq2::new(Fq::from("16786670094068652274677750111730144379312178408732829954083928254919389983983"), Fq::from("6341529030893580474995202784328098673009525246309131907462803539077246776781")), ell_vv: Fq2::new(Fq::from("1974498926273096258802796702119259182018579009158122203612017565775578915815"), Fq::from("16202371700345289299248140495735793174324620209466889736695203996551421837181")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("7645596703863049949671625140189098533219782764649960681401839437305310089346"), Fq::from("19662686877039093771787921401379726144714150453645437909640334762978238819386")), ell_vw: Fq2::new(Fq::from("19675517233991845002128733409028273554556593365253876728982552859262257722391"), Fq::from("17810553502824017140555114404262914434390762266054795883352268646885364159410")), ell_vv: Fq2::new(Fq::from("18665072545928024509881282829034535118797458683193169885406548536617293330990"), Fq::from("19411595053923298782146703680748498557982136082135126508584153240357549362078")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14470514611309746071605255274946119202484366658141275541087020842175954067559"), Fq::from("2594897518684998941907190849745518961756699273476562463311001408776339658780")), ell_vw: Fq2::new(Fq::from("935873152179726234311073616163680460286310013909076125956427156452613025181"), Fq::from("1833293684395168387765260233178732135932817355166697645828433012629591012612")), ell_vv: Fq2::new(Fq::from("15506344864201849985196152671178663605696906693236430756412539843011256851197"), Fq::from("21249626787247514663459670711353542343321937134901366527096486234949436840608")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14844298589371811580114643149994926627935566419885127313767249060440840193460"), Fq::from("21865492910219121705480174226763323783866193080747061232287801827306146286946")), ell_vw: Fq2::new(Fq::from("17151100973274235243640792655189642956800303990602164052684336481398298289411"), Fq::from("14392190221562986523826107157981466944764379735735544220135185056395768909930")), ell_vv: Fq2::new(Fq::from("4350255565215767538405433120041486620343663937357318680211203103336875636557"), Fq::from("9926081950735179732148156026738993553156731124330466866635273595752973758855")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("13218761129163938072615510267349114476398845757988353548581904005855607494827"), Fq::from("5599121822325202341068442750237639791575579072233857524815548719976323285948")), ell_vw: Fq2::new(Fq::from("15971120376538832228790474763995956330325241100841265267806125625593561200292"), Fq::from("12523288625433720594713119420870235433458343202664663107083051275205911332632")), ell_vv: Fq2::new(Fq::from("16334648365696506264242655102949242813244449705193389318653840069223698505218"), Fq::from("5656148484258838154513173637616383061988381726003070282394323376702835298685")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17813738829828434290335491956960173922453516626523775773406434062574864455163"), Fq::from("20602369742562270094694203910247000789225384961205618501257582838246099644397")), ell_vw: Fq2::new(Fq::from("19878549521928480892919729627745688905048802531306612605469432942519616386562"), Fq::from("5017457857497268504225948371697060380418757800650743056471872023476645133890")), ell_vv: Fq2::new(Fq::from("11253669115821132651967277438747600032147012598164512191026558281212405907059"), Fq::from("17527101633359473938082679669763197242520773041737623688955597341205608093817")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("4215545173967763533303120784928042872427929334572670490629936371429427871071"), Fq::from("12294795716682648009432653500746413304750644076589949908249345884220200424705")), ell_vw: Fq2::new(Fq::from("18825720171660950734491494575282684507875213824417353005009465489701558195915"), Fq::from("16705960611772713893529695679517111622754789317070946155202186944060021844706")), ell_vv: Fq2::new(Fq::from("727717707174551758531261221179545916153780087179478433501944451338651779512"), Fq::from("8112271980906996458859937804680221894935591766524365848766530295751121904748")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("10233024162783159141952008177866660607852287510058437429941412641351833243474"), Fq::from("9594838646894429694778293318641489517645344438331800828882574864439372872574")), ell_vw: Fq2::new(Fq::from("16645682756797429615195184700295338945089747965333104334845226609564841400023"), Fq::from("4162352035394629024812623559649906911351409190415492302470361657064711946691")), ell_vv: Fq2::new(Fq::from("6032119528092518381867266123093895943802103316999621961287699634448441322294"), Fq::from("16978590002913514123461500015923670605519520926487110857783653291799516315656")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8218196524386055233961282665657821183883422738571989211183480610420112668380"), Fq::from("10415506866745570162620028320970394286106067432626512901854031549920339603997")), ell_vw: Fq2::new(Fq::from("5210044150482547744429104832217210823770891140961861953610847155896342519957"), Fq::from("7249576834325689075837879557249227252903732278842727723303356548006299693332")), ell_vv: Fq2::new(Fq::from("10566250213397026997176223676662431109660830193211672199901829008963029461821"), Fq::from("10109726446308488117042758961222375921166426648339199001670753736584698407831")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("14958658301977599538003236672511296104101995894564376511283101560012949683335"), Fq::from("3048608469033125363311089547916169290720115268350540694596412955569118898494")), ell_vw: Fq2::new(Fq::from("574489666015527527356241753990038643397861257676315289742492198353125347063"), Fq::from("20135743140323312729475654806927894483883158119600963784497647679670289292384")), ell_vv: Fq2::new(Fq::from("429037282750459454100296565403648201904295120071497517313998879109362521423"), Fq::from("15853233349247701874380259741343021520320591334343875702627292292088300425145")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("18700030680590279184945769912899822403041358764323477965514340815228877402331"), Fq::from("10683998632701796443517414309938660369292269662497518738662465524924019738910")), ell_vw: Fq2::new(Fq::from("1310694906110452150099267122613851606459600617516350757492763828252192371857"), Fq::from("4783076385012654125132398886450190041207227400254467276271580769333335151361")), ell_vv: Fq2::new(Fq::from("19588709046778297839342456362815786766378666302331732601204786295010565114246"), Fq::from("15768094978512846661820502043664035262466161785979259300748269497441797675546")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("13060364876687824737412369705619641318084803694180161837383771909738942399322"), Fq::from("18217552047682533290011237332328856250732338018560605204821714348687071938690")), ell_vw: Fq2::new(Fq::from("12869661643727171099080271622741099816758098286424339832028838960253051261267"), Fq::from("9771005613420764951919925720405408601257471427085946188171574196917272408972")), ell_vv: Fq2::new(Fq::from("50909581144623642750375885935872654509592339539711209410079054797052409354"), Fq::from("18926528403466649263993967111065644144239906211315737390219036362821972145669")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("20549804669307980165961565026567668900175984309510667407934326603524068980568"), Fq::from("2860891967505015044048360806986650576604923893849408592665407858213623973073")), ell_vw: Fq2::new(Fq::from("15425380359872501526721873883293811604657689327716748473720120299487795555723"), Fq::from("19476618728903347368164774764554105623361814261939990815870207909384053172994")), ell_vv: Fq2::new(Fq::from("1391900673866549134877070137078952075347059393013450066057338968238992587955"), Fq::from("4196316861965319041187484774757427170509633759722370813890904092023663955821")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("17275387403896977778123657295201685204905269368879700703438840824610915049467"), Fq::from("19208898840130004899976179132541534722147305748950927170013798354273078356439")), ell_vw: Fq2::new(Fq::from("2806476769978795611970161315323438770892084130100332531802098991493644141407"), Fq::from("12027685137795878129532114449809592645364590672303716160923491816560315933093")), ell_vv: Fq2::new(Fq::from("8236588507133996535585623995380369531792969451558421380293164596516832310024"), Fq::from("7194816002224802847462171990762514812770222507636791853795854276216118633532")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("8988630595018387496849477785798469553390006328427704582362113137927154840355"), Fq::from("2295777524525303845671711839319946449143831320846022233249545363172788331149")), ell_vw: Fq2::new(Fq::from("19856063720990800344827304970869772811632532243020577718537161398914360273978"), Fq::from("19822454791015240925652351664190735476954892251509376470361602440577337517739")), ell_vv: Fq2::new(Fq::from("16437024240432855113321845721989731630224984534156413407578941758236945886728"), Fq::from("10915573623321985107029933965796058231484519510670830600808943167010577314334")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("21286975582879196598650077668567283554136994229408922053641846042051746388886"), Fq::from("5421529658065143080970166226046014500038127295988164061860891929414040927615")), ell_vw: Fq2::new(Fq::from("5555485154537896512520569992616892769357525491868135294451583184259218193278"), Fq::from("4831809465565304340310880868620257258305484211486308136368207144444325564275")), ell_vv: Fq2::new(Fq::from("2583089702666220608189326901976548985583885001543445628170288810575076369034"), Fq::from("7097788099664798415333498763272677734135137637990913349021964143797057593727")) },
|
||||
EllCoeffs { ell_0: Fq2::new(Fq::from("21356455346146359274071336488740257199607341582407258426849457339859865454145"), Fq::from("19512280220246743343068375192508909480135195681362473260894831078332945004959")), ell_vw: Fq2::new(Fq::from("15435677241338788169971902812985017500898533325271813422525238374746874853456"), Fq::from("6382067580057986766020919077216175344977116334133202456947134195629074647989")), ell_vv: Fq2::new(Fq::from("1150360546643207487285835972411275438312694180812115547021545502055712764110"), Fq::from("2194960903427600986795419731825236689333014397679688012527722471213485607323")) }
|
||||
]
|
||||
};
|
||||
|
||||
assert!(expected_g2_p.eq(&g2_p));
|
||||
assert!(expected_g2_p.coeffs.len() == 102);
|
||||
}
|
||||
|
||||
fn miller_loop(p: &Affine<G1Params>, q: &G2Precomp) -> Fq12 {
|
||||
let mut f = Fq12::one();
|
||||
|
||||
let mut idx = 0;
|
||||
|
||||
let mut found_one = false;
|
||||
let ate = ate_loop_count();
|
||||
|
||||
for i in (0..FrParams::bits()).rev() {
|
||||
let bit = ate.test_bit(i);
|
||||
|
||||
if !found_one {
|
||||
found_one = bit;
|
||||
continue;
|
||||
}
|
||||
|
||||
let c = &q.coeffs[idx];
|
||||
idx += 1;
|
||||
f = f.squared().mul_by_024(&c.ell_0, &c.ell_vw * &p.get_y(), &c.ell_vv * &p.get_x());
|
||||
|
||||
if bit {
|
||||
let c = &q.coeffs[idx];
|
||||
idx += 1;
|
||||
f = f.mul_by_024(&c.ell_0, &c.ell_vw * &p.get_y(), &c.ell_vv * &p.get_x());
|
||||
}
|
||||
}
|
||||
|
||||
let c = &q.coeffs[idx];
|
||||
idx += 1;
|
||||
f = f.mul_by_024(&c.ell_0, &c.ell_vw * &p.get_y(), &c.ell_vv * &p.get_x());
|
||||
|
||||
let c = &q.coeffs[idx];
|
||||
//idx += 1;
|
||||
f = f.mul_by_024(&c.ell_0, &c.ell_vw * &p.get_y(), &c.ell_vv * &p.get_x());
|
||||
|
||||
f
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_miller_loop() {
|
||||
let g1 = G1::one() * Fr::from("18097487326282793650237947474982649264364522469319914492172746413872781676");
|
||||
let g2 = G2::one() * Fr::from("20390255904278144451778773028944684152769293537511418234311120800877067946");
|
||||
|
||||
let g1_pre = g1.to_affine();
|
||||
let g2_pre = G2Precomp::new(&g2);
|
||||
|
||||
let gt = miller_loop(&g1_pre, &g2_pre);
|
||||
|
||||
assert_eq!(gt,
|
||||
Fq12::new(Fq6::new(
|
||||
Fq2::new(Fq::from("14551901853310307118181117653102171756020286507151693083446930124375536995872"), Fq::from("9312135802322424742640599513015426415694425842442244572104764725304978020017")),
|
||||
Fq2::new(Fq::from("2008578374540014049115224515107136454624926345291695498760935593377832328658"), Fq::from("19401931167387470703307774451905975977586101231060812348184567722817888018105")),
|
||||
Fq2::new(Fq::from("15835061253582829097893482726334173316772697321004871665993836763948321578465"), Fq::from("2434436628082562384254182545550914004674636606111293955202388712261962820365"))
|
||||
),
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from("2874440054453559166574356420729655370224872280550180463983603224123901706537"), Fq::from("21199736323249863378180814900160978651989782296293186487853700340281870105680")),
|
||||
Fq2::new(Fq::from("19165582755854282767090326095669835261356341739532443976394958023142879015770"), Fq::from("1381947898997178910398427566832118260186305708991760706544743699683050330259")),
|
||||
Fq2::new(Fq::from("282285618133171001983721596014922591835675934808772882476123488581876545578"), Fq::from("9533292755262567365755835323107174518472361243562718718917822947506880920117"))
|
||||
)
|
||||
)
|
||||
);
|
||||
}
|
||||
|
||||
pub fn final_exponentiation_first_chunk(elt: &Fq12) -> Fq12 {
|
||||
let a = elt.unitary_inverse();
|
||||
let b = elt.inverse();
|
||||
let c = a * b;
|
||||
let d = c.frobenius_map(2);
|
||||
|
||||
d * c
|
||||
}
|
||||
|
||||
pub fn exp_by_neg_z(elt: &Fq12) -> Fq12 {
|
||||
elt.cyclotomic_exp(&final_exponent_z()).unitary_inverse()
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_cyclotomic_exp() {
|
||||
let orig = Fq12::new(
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from("2259924035228092997691937637688451143058635253053054071159756458902878894295"), Fq::from("13145690032701362144460254305183927872683620413225364127064863863535255135244")),
|
||||
Fq2::new(Fq::from("9910063591662383599552477067956819406417086889312288278252482503717089428441"), Fq::from("537414042055419261990282459138081732565514913399498746664966841152381183961")),
|
||||
Fq2::new(Fq::from("15311812409497308894370893420777496684951030254049554818293571309705780605004"), Fq::from("13657107176064455789881282546557276003626320193974643644160350907227082365810"))
|
||||
),
|
||||
Fq6::new(Fq2::new(Fq::from("4913017949003742946864670837361832856526234260447029873580022776602534856819"), Fq::from("7834351480852267338070670220119081676575418514182895774094743209915633114041")),
|
||||
Fq2::new(Fq::from("12837298223308203788092748646758194441270207338661891973231184407371206766993"), Fq::from("12756474445699147370503225379431475413909971718057034061593007812727141391799")),
|
||||
Fq2::new(Fq::from("9473802207170192255373153510655867502408045964296373712891954747252332944018"), Fq::from("4583089109360519374075173304035813179013579459429335467869926761027310749713"))
|
||||
)
|
||||
);
|
||||
|
||||
let expected = Fq12::new(
|
||||
Fq6::new(
|
||||
Fp2::new(Fq::from("14722956046055152398903846391223329501345567382234608299399030576415080188350"), Fq::from("14280703280777926697010730619606819467080027543707671882210769811674790473417")),
|
||||
Fp2::new(Fq::from("19969875076083990244184003223190771301761436396530543002586073549972410735411"), Fq::from("10717335566913889643303549252432531178405520196706173198634734518494041323243")),
|
||||
Fp2::new(Fq::from("6063612626166484870786832843320782567259894784043383626084549455432890717937"), Fq::from("17089783040131779205038789608891431427943860868115199598200376195935079808729"))
|
||||
),
|
||||
Fq6::new(
|
||||
Fp2::new(Fq::from("10029863438921507421569931792104023129735006154272482043027653425575205672906"), Fq::from("6406252222753462799887280578845937185621081001436094637606245493619821542775")),
|
||||
Fp2::new(Fq::from("1048245462913506652602966692378792381004227332967846949234978073448561848050"), Fq::from("1444281375189053827455518242624554285012408033699861764136810522738182087554")),
|
||||
Fp2::new(Fq::from("8839610992666735109106629514135300820412539620261852250193684883379364789120"), Fq::from("11347360242067273846784836674906058940820632082713814508736182487171407730718"))
|
||||
)
|
||||
);
|
||||
|
||||
let e = exp_by_neg_z(&orig);
|
||||
|
||||
assert_eq!(e, expected);
|
||||
}
|
||||
|
||||
pub fn final_exponentiation_last_chunk(elt: &Fq12) -> Fq12 {
|
||||
let a = exp_by_neg_z(elt);
|
||||
let b = a.cyclotomic_squared();
|
||||
let c = b.cyclotomic_squared();
|
||||
let d = c.mul(&b);
|
||||
|
||||
let e = exp_by_neg_z(&d);
|
||||
let f = e.cyclotomic_squared();
|
||||
let g = exp_by_neg_z(&f);
|
||||
let h = d.unitary_inverse();
|
||||
let i = g.unitary_inverse();
|
||||
|
||||
let j = i.mul(&e);
|
||||
let k = j.mul(&h);
|
||||
let l = k.mul(&b);
|
||||
let m = k.mul(&e);
|
||||
let n = m.mul(elt);
|
||||
|
||||
let o = l.frobenius_map(1);
|
||||
let p = o.mul(&n);
|
||||
|
||||
let q = k.frobenius_map(2);
|
||||
let r = q.mul(&p);
|
||||
|
||||
let s = elt.unitary_inverse();
|
||||
let t = s.mul(&l);
|
||||
let u = t.frobenius_map(3);
|
||||
let v = u.mul(&r);
|
||||
|
||||
v
|
||||
}
|
||||
|
||||
pub fn final_exponentiation(elt: &Fq12) -> Fq12 {
|
||||
final_exponentiation_last_chunk(&final_exponentiation_first_chunk(elt))
|
||||
}
|
||||
|
||||
pub fn pairing(p: &G1, q: &G2) -> Gt {
|
||||
let p = p.to_affine();
|
||||
let q = G2Precomp::new(q);
|
||||
|
||||
Gt::new(final_exponentiation(&miller_loop(&p, &q)))
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_reduced_pairing() {
|
||||
let g1 = G1::one() * Fr::from("18097487326282793650237947474982649264364522469319914492172746413872781676");
|
||||
let g2 = G2::one() * Fr::from("20390255904278144451778773028944684152769293537511418234311120800877067946");
|
||||
|
||||
let gt = pairing(&g1, &g2);
|
||||
|
||||
let expected = Gt::new(Fq12::new(
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from("7520311483001723614143802378045727372643587653754534704390832890681688842501"), Fq::from("20265650864814324826731498061022229653175757397078253377158157137251452249882")),
|
||||
Fq2::new(Fq::from("11942254371042183455193243679791334797733902728447312943687767053513298221130"), Fq::from("759657045325139626991751731924144629256296901790485373000297868065176843620")),
|
||||
Fq2::new(Fq::from("16045761475400271697821392803010234478356356448940805056528536884493606035236"), Fq::from("4715626119252431692316067698189337228571577552724976915822652894333558784086"))
|
||||
),
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from("14901948363362882981706797068611719724999331551064314004234728272909570402962"), Fq::from("11093203747077241090565767003969726435272313921345853819385060670210834379103")),
|
||||
Fq2::new(Fq::from("17897835398184801202802503586172351707502775171934235751219763553166796820753"), Fq::from("1344517825169318161285758374052722008806261739116142912817807653057880346554")),
|
||||
Fq2::new(Fq::from("11123896897251094532909582772961906225000817992624500900708432321664085800838"), Fq::from("17453370448280081813275586256976217762629631160552329276585874071364454854650"))
|
||||
)
|
||||
));
|
||||
|
||||
assert_eq!(expected, gt);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_binlinearity() {
|
||||
use rand::{SeedableRng,StdRng};
|
||||
let seed: [usize; 4] = [103245, 191922, 1293, 192103];
|
||||
let mut rng = StdRng::from_seed(&seed);
|
||||
|
||||
for _ in 0..50 {
|
||||
let p = G1::random(&mut rng);
|
||||
let q = G2::random(&mut rng);
|
||||
let s = Fr::random(&mut rng);
|
||||
let sp = &p * &s;
|
||||
let sq = &q * &s;
|
||||
|
||||
let a = pairing(&p, &q) ^ &s;
|
||||
let b = pairing(&sp, &q);
|
||||
let c = pairing(&p, &sq);
|
||||
|
||||
assert_eq!(a, b);
|
||||
assert_eq!(b, c);
|
||||
|
||||
let t = Fr::zero().sub(&Fr::one());
|
||||
|
||||
assert!(a != Gt::new(Fq12::one()));
|
||||
assert_eq!((&a ^ t) * &a, Gt::new(Fq12::one()));
|
||||
}
|
||||
}
|
||||
432
oldsrc/params.rs
432
oldsrc/params.rs
|
|
@ -1,432 +0,0 @@
|
|||
use num::{Num,BigUint};
|
||||
use fields::Field;
|
||||
use fields::fp::PrimeFieldParams;
|
||||
use fields::fp2::Fp2Params;
|
||||
use fields::fp6::Fp6Params;
|
||||
use fields::fp12::Fp12Params;
|
||||
use super::{Fr,Fq,Fq2};
|
||||
use groups::*;
|
||||
|
||||
pub struct FrParams;
|
||||
|
||||
impl PrimeFieldParams for FrParams {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10).unwrap()
|
||||
}
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Fr" }
|
||||
}
|
||||
|
||||
pub struct FqParams;
|
||||
|
||||
impl PrimeFieldParams for FqParams {
|
||||
fn modulus() -> BigUint {
|
||||
BigUint::from_str_radix("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10).unwrap()
|
||||
}
|
||||
fn bits() -> usize { 254 }
|
||||
fn name() -> &'static str { "Fq" }
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fr() {
|
||||
use fields;
|
||||
|
||||
fields::tests::field_trials::<Fr>();
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq() {
|
||||
use fields;
|
||||
|
||||
fields::tests::field_trials::<Fq>();
|
||||
}
|
||||
|
||||
pub struct G1Params;
|
||||
|
||||
impl GroupParams for G1Params {
|
||||
type Base = Fq;
|
||||
|
||||
fn name() -> &'static str {
|
||||
"G1"
|
||||
}
|
||||
fn zero() -> Jacobian<Self> {
|
||||
Jacobian::new(Fq::zero(), Fq::one(), Fq::zero()).unwrap()
|
||||
}
|
||||
fn one() -> Jacobian<Self> {
|
||||
Jacobian::new(Fq::from("1"), Fq::from("2"), Fq::one()).unwrap()
|
||||
}
|
||||
fn coeff_b() -> Self::Base {
|
||||
Fq::from("3")
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_g1() {
|
||||
use groups;
|
||||
use ::G1;
|
||||
|
||||
groups::tests::group_trials::<G1Params>();
|
||||
|
||||
assert_eq!(G1::zero(), G1::one() + (G1::zero() - G1::one()));
|
||||
assert_eq!(G1::zero(), G1::one() * Fr::from("21888242871839275222246405745257275088548364400416034343698204186575808495616") + G1::one());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn g1_test_vector() {
|
||||
use ::G1;
|
||||
let a = G1::one() * Fr::from("19797905000333868150253315089095386158892526856493194078073564469188852136946");
|
||||
let b = G1::one() * Fr::from("2730506433347642574983433139433778984782882168213690554721050571242082865799");
|
||||
let e = &a + &b;
|
||||
|
||||
let expect = G1::new(
|
||||
Fq::from("18450621724990678172567114131642278789161361170999664461184794604011563728206"),
|
||||
Fq::from("21329688341674583036384007811166435666174342925504675855816423131698588368496"),
|
||||
Fq::one()
|
||||
).unwrap();
|
||||
|
||||
assert_eq!(expect, e);
|
||||
}
|
||||
|
||||
pub struct Fq2Params;
|
||||
|
||||
impl Fp2Params for Fq2Params {
|
||||
fn non_residue() -> Fq {
|
||||
Fq::from("21888242871839275222246405745257275088696311157297823662689037894645226208582")
|
||||
}
|
||||
fn name() -> &'static str {
|
||||
"Fq2"
|
||||
}
|
||||
fn frobenius_coeffs_c1(n: usize) -> Fq {
|
||||
match n {
|
||||
0 => Fq::from("1"),
|
||||
1 => Fq::from("21888242871839275222246405745257275088696311157297823662689037894645226208582"),
|
||||
_ => panic!()
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2() {
|
||||
use fields;
|
||||
|
||||
fields::tests::field_trials::<Fq2>();
|
||||
}
|
||||
|
||||
pub struct G2Params;
|
||||
|
||||
impl G2Params {
|
||||
pub fn twist() -> Fq2 {
|
||||
Fq2::new(Fq::from("9"), Fq::from("1"))
|
||||
}
|
||||
pub fn twist_mul_by_q_x() -> Fq2 {
|
||||
Fq2::new(Fq::from("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
|
||||
Fq::from("10307601595873709700152284273816112264069230130616436755625194854815875713954"))
|
||||
}
|
||||
pub fn twist_mul_by_q_y() -> Fq2 {
|
||||
Fq2::new(Fq::from("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
|
||||
Fq::from("3505843767911556378687030309984248845540243509899259641013678093033130930403"))
|
||||
}
|
||||
}
|
||||
|
||||
impl GroupParams for G2Params {
|
||||
type Base = Fq2;
|
||||
|
||||
fn name() -> &'static str {
|
||||
"G2"
|
||||
}
|
||||
fn zero() -> Jacobian<Self> {
|
||||
Jacobian::new(Fq2::zero(), Fq2::one(), Fq2::zero()).unwrap()
|
||||
}
|
||||
fn one() -> Jacobian<Self> {
|
||||
Jacobian::new(
|
||||
Fq2::new(
|
||||
Fq::from("10857046999023057135944570762232829481370756359578518086990519993285655852781"),
|
||||
Fq::from("11559732032986387107991004021392285783925812861821192530917403151452391805634")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("8495653923123431417604973247489272438418190587263600148770280649306958101930"),
|
||||
Fq::from("4082367875863433681332203403145435568316851327593401208105741076214120093531")
|
||||
),
|
||||
Fq2::one()
|
||||
).unwrap()
|
||||
}
|
||||
fn coeff_b() -> Self::Base {
|
||||
&G2Params::twist().inverse() * &Fq::from("3")
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_g2() {
|
||||
use groups;
|
||||
use ::G2;
|
||||
|
||||
groups::tests::group_trials::<G2Params>();
|
||||
|
||||
assert_eq!(G2::zero(), G2::one() + (G2::zero() - G2::one()));
|
||||
assert_eq!(G2::zero(), G2::one() * Fr::from("21888242871839275222246405745257275088548364400416034343698204186575808495616") + G2::one());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn g2_test_vector() {
|
||||
use ::G2;
|
||||
let a = G2::one() * Fr::from("19797905000333868150253315089095386158892526856493194078073564469188852136946");
|
||||
let b = G2::one() * Fr::from("2730506433347642574983433139433778984782882168213690554721050571242082865799");
|
||||
let e = &a + &b;
|
||||
|
||||
let expect = G2::new(
|
||||
Fq2::new(
|
||||
Fq::from("10805137482603266627116066166226222153808813611856467496561473491230213987197"),
|
||||
Fq::from("11018998371825437935082073888099464993330606622517843684670450190973893289235")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("371699491666579792038680273553261511891341995868329474144713691525212078012"),
|
||||
Fq::from("2123259504314265904107110265140842273706723557882599408954283209162529085097")
|
||||
),
|
||||
Fq2::one()
|
||||
).unwrap();
|
||||
|
||||
assert_eq!(expect, e);
|
||||
}
|
||||
|
||||
pub struct Fq6Params;
|
||||
|
||||
impl Fp6Params for Fq6Params {
|
||||
fn non_residue() -> Fq2 {
|
||||
Fq2::new(Fq::from("9"), Fq::from("1"))
|
||||
}
|
||||
fn name() -> &'static str {
|
||||
"Fq6"
|
||||
}
|
||||
fn frobenius_coeffs_c1(n: usize) -> Fq2 {
|
||||
match n {
|
||||
0 => Fq2::new(
|
||||
Fq::from("1"),
|
||||
Fq::from("0")
|
||||
),
|
||||
1 => Fq2::new(
|
||||
Fq::from("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
|
||||
Fq::from("10307601595873709700152284273816112264069230130616436755625194854815875713954")
|
||||
),
|
||||
2 => Fq2::new(
|
||||
Fq::from("21888242871839275220042445260109153167277707414472061641714758635765020556616"),
|
||||
Fq::from("0")
|
||||
),
|
||||
3 => Fq2::new(
|
||||
Fq::from("3772000881919853776433695186713858239009073593817195771773381919316419345261"),
|
||||
Fq::from("2236595495967245188281701248203181795121068902605861227855261137820944008926")
|
||||
),
|
||||
4 => Fq2::new(
|
||||
Fq::from("2203960485148121921418603742825762020974279258880205651966"),
|
||||
Fq::from("0")
|
||||
),
|
||||
5 => Fq2::new(
|
||||
Fq::from("18429021223477853657660792034369865839114504446431234726392080002137598044644"),
|
||||
Fq::from("9344045779998320333812420223237981029506012124075525679208581902008406485703")
|
||||
),
|
||||
_ => panic!()
|
||||
}
|
||||
}
|
||||
fn frobenius_coeffs_c2(n: usize) -> Fq2 {
|
||||
match n {
|
||||
0 => Fq2::new(
|
||||
Fq::from("1"),
|
||||
Fq::from("0")
|
||||
),
|
||||
1 => Fq2::new(
|
||||
Fq::from("2581911344467009335267311115468803099551665605076196740867805258568234346338"),
|
||||
Fq::from("19937756971775647987995932169929341994314640652964949448313374472400716661030")
|
||||
),
|
||||
2 => Fq2::new(
|
||||
Fq::from("2203960485148121921418603742825762020974279258880205651966"),
|
||||
Fq::from("0")
|
||||
),
|
||||
3 => Fq2::new(
|
||||
Fq::from("5324479202449903542726783395506214481928257762400643279780343368557297135718"),
|
||||
Fq::from("16208900380737693084919495127334387981393726419856888799917914180988844123039")
|
||||
),
|
||||
4 => Fq2::new(
|
||||
Fq::from("21888242871839275220042445260109153167277707414472061641714758635765020556616"),
|
||||
Fq::from("0")
|
||||
),
|
||||
5 => Fq2::new(
|
||||
Fq::from("13981852324922362344252311234282257507216387789820983642040889267519694726527"),
|
||||
Fq::from("7629828391165209371577384193250820201684255241773809077146787135900891633097")
|
||||
),
|
||||
_ => panic!()
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq6() {
|
||||
use fields;
|
||||
|
||||
fields::tests::field_trials::<::Fq6>();
|
||||
}
|
||||
|
||||
pub struct Fq12Params;
|
||||
|
||||
impl Fp12Params for Fq12Params {
|
||||
fn non_residue() -> Fq2 {
|
||||
Fq2::new(Fq::from("9"), Fq::from("1"))
|
||||
}
|
||||
fn name() -> &'static str {
|
||||
"Fq12"
|
||||
}
|
||||
fn frobenius_coeffs_c1(n: usize) -> Fq2 {
|
||||
match n {
|
||||
0 => Fq2::new(
|
||||
Fq::from("1"),
|
||||
Fq::from("0")
|
||||
),
|
||||
1 => Fq2::new(
|
||||
Fq::from("8376118865763821496583973867626364092589906065868298776909617916018768340080"),
|
||||
Fq::from("16469823323077808223889137241176536799009286646108169935659301613961712198316")
|
||||
),
|
||||
2 => Fq2::new(
|
||||
Fq::from("21888242871839275220042445260109153167277707414472061641714758635765020556617"),
|
||||
Fq::from("0")
|
||||
),
|
||||
3 => Fq2::new(
|
||||
Fq::from("11697423496358154304825782922584725312912383441159505038794027105778954184319"),
|
||||
Fq::from("303847389135065887422783454877609941456349188919719272345083954437860409601")
|
||||
),
|
||||
4 => Fq2::new(
|
||||
Fq::from("21888242871839275220042445260109153167277707414472061641714758635765020556616"),
|
||||
Fq::from("0")
|
||||
),
|
||||
5 => Fq2::new(
|
||||
Fq::from("3321304630594332808241809054958361220322477375291206261884409189760185844239"),
|
||||
Fq::from("5722266937896532885780051958958348231143373700109372999374820235121374419868")
|
||||
),
|
||||
6 => Fq2::new(
|
||||
Fq::from("21888242871839275222246405745257275088696311157297823662689037894645226208582"),
|
||||
Fq::from("0")
|
||||
),
|
||||
7 => Fq2::new(
|
||||
Fq::from("13512124006075453725662431877630910996106405091429524885779419978626457868503"),
|
||||
Fq::from("5418419548761466998357268504080738289687024511189653727029736280683514010267")
|
||||
),
|
||||
8 => Fq2::new(
|
||||
Fq::from("2203960485148121921418603742825762020974279258880205651966"),
|
||||
Fq::from("0")
|
||||
),
|
||||
9 => Fq2::new(
|
||||
Fq::from("10190819375481120917420622822672549775783927716138318623895010788866272024264"),
|
||||
Fq::from("21584395482704209334823622290379665147239961968378104390343953940207365798982")
|
||||
),
|
||||
10 => Fq2::new(
|
||||
Fq::from("2203960485148121921418603742825762020974279258880205651967"),
|
||||
Fq::from("0")
|
||||
),
|
||||
11 => Fq2::new(
|
||||
Fq::from("18566938241244942414004596690298913868373833782006617400804628704885040364344"),
|
||||
Fq::from("16165975933942742336466353786298926857552937457188450663314217659523851788715")
|
||||
),
|
||||
_ => panic!()
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq12() {
|
||||
use fields;
|
||||
|
||||
fields::tests::field_trials::<::Fq12>();
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fq12_test_vector() {
|
||||
let start = ::Fq12::new(
|
||||
::Fq6::new(
|
||||
Fq2::new(
|
||||
Fq::from("19797905000333868150253315089095386158892526856493194078073564469188852136946"),
|
||||
Fq::from("10509658143212501778222314067134547632307419253211327938344904628569123178733")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("208316612133170645758860571704540129781090973693601051684061348604461399206"),
|
||||
Fq::from("12617661120538088237397060591907161689901553895660355849494983891299803248390")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("2897490589776053688661991433341220818937967872052418196321943489809183508515"),
|
||||
Fq::from("2730506433347642574983433139433778984782882168213690554721050571242082865799")
|
||||
)
|
||||
),
|
||||
::Fq6::new(
|
||||
Fq2::new(
|
||||
Fq::from("17870056122431653936196746815433147921488990391314067765563891966783088591110"),
|
||||
Fq::from("14314041658607615069703576372547568077123863812415914883625850585470406221594")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("10123533891707846623287020000407963680629966110211808794181173248765209982878"),
|
||||
Fq::from("5062091880848845693514855272640141851746424235009114332841857306926659567101")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("9839781502639936537333620974973645053542086898304697594692219798017709586567"),
|
||||
Fq::from("1583892292110602864638265389721494775152090720173641072176370350017825640703")
|
||||
)
|
||||
)
|
||||
);
|
||||
|
||||
// Do a bunch of arbitrary stuff to the element
|
||||
|
||||
let mut next = start.clone();
|
||||
for _ in 0..100 {
|
||||
next = &next * &start;
|
||||
}
|
||||
|
||||
let cpy = next.clone();
|
||||
|
||||
for _ in 0..10 {
|
||||
next = next.squared();
|
||||
}
|
||||
|
||||
for _ in 0..10 {
|
||||
next = &next + &start;
|
||||
next = &next - &cpy;
|
||||
next = -&next;
|
||||
}
|
||||
|
||||
next = next.squared();
|
||||
|
||||
let finally = ::Fq12::new(
|
||||
::Fq6::new(
|
||||
Fq2::new(
|
||||
Fq::from("18388750939593263065521177085001223024106699964957029146547831509155008229833"),
|
||||
Fq::from("18370529854582635460997127698388761779167953912610241447912705473964014492243")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("3691824277096717481466579496401243638295254271265821828017111951446539785268"),
|
||||
Fq::from("20513494218085713799072115076991457239411567892860153903443302793553884247235")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("12214155472433286415803224222551966441740960297013786627326456052558698216399"),
|
||||
Fq::from("10987494248070743195602580056085773610850106455323751205990078881956262496575")
|
||||
)
|
||||
),
|
||||
::Fq6::new(
|
||||
Fq2::new(
|
||||
Fq::from("5134522153456102954632718911439874984161223687865160221119284322136466794876"),
|
||||
Fq::from("20119236909927036376726859192821071338930785378711977469360149362002019539920")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("8839766648621210419302228913265679710586991805716981851373026244791934012854"),
|
||||
Fq::from("9103032146464138788288547957401673544458789595252696070370942789051858719203")
|
||||
),
|
||||
Fq2::new(
|
||||
Fq::from("10378379548636866240502412547812481928323945124508039853766409196375806029865"),
|
||||
Fq::from("9021627154807648093720460686924074684389554332435186899318369174351765754041")
|
||||
)
|
||||
)
|
||||
);
|
||||
|
||||
assert_eq!(finally, next);
|
||||
}
|
||||
|
||||
pub fn ate_loop_count() -> Fr {
|
||||
Fr::from("29793968203157093288")
|
||||
}
|
||||
|
||||
pub fn final_exponent_z() -> Fr {
|
||||
Fr::from("4965661367192848881")
|
||||
}
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
bn crate performing 20000 pairing operations
|
||||
|
||||
real 3m28.831s
|
||||
user 3m28.797s
|
||||
sys 0m0.020s
|
||||
|
||||
libsnark (ALT_BN128 with USE_ASM disabled) performing 20000 pairing operations
|
||||
|
||||
real 2m3.656s
|
||||
user 2m3.543s
|
||||
sys 0m0.007s
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
extern crate bn;
|
||||
|
||||
use bn::*;
|
||||
|
||||
fn main() {
|
||||
let mut a = G1::one();
|
||||
let mut b = G2::one();
|
||||
let c = Fr::from_str("1901").unwrap().inverse().unwrap();
|
||||
let d = Fr::from_str("2344").unwrap().inverse().unwrap();
|
||||
|
||||
let mut acc1 = Gt::one();
|
||||
for i in 0..10000 {
|
||||
acc1 = acc1 * pairing(a, b);
|
||||
a = a * c;
|
||||
b = b * d;
|
||||
}
|
||||
|
||||
a = G1::one();
|
||||
b = G2::one();
|
||||
|
||||
let mut acc2 = Gt::one();
|
||||
for i in 0..10000 {
|
||||
acc2 = acc2 * pairing(a, b);
|
||||
a = a * d;
|
||||
b = b * c;
|
||||
}
|
||||
|
||||
assert!(acc1 == acc2);
|
||||
}
|
||||
|
|
@ -0,0 +1,44 @@
|
|||
#include "common/default_types/r1cs_ppzksnark_pp.hpp"
|
||||
#include "common/profiling.hpp"
|
||||
|
||||
// CXXFLAGS="-fPIC -DBINARY_OUTPUT -DNO_PT_COMPRESSION=1" make lib CURVE=ALT_BN128 MULTICORE=1 NO_PROCPS=1 NO_GTEST=1 NO_DOCS=1 STATIC=1 NO_SUPERCOP=1 FEATUREFLAGS=-DMONTGOMERY_OUTPUT
|
||||
// g++ -std=c++11 -O3 test.cpp -o test -Isrc/ -DMULTICORE -fopenmp -DBINARY_OUTPUT -DCURVE_ALT_BN128 -DSTATIC -L. -lsnark -lgmp -lsodium
|
||||
|
||||
typedef libsnark::default_r1cs_ppzksnark_pp curve_pp;
|
||||
typedef libsnark::default_r1cs_ppzksnark_pp::G1_type curve_G1;
|
||||
typedef libsnark::default_r1cs_ppzksnark_pp::G2_type curve_G2;
|
||||
typedef libsnark::default_r1cs_ppzksnark_pp::GT_type curve_GT;
|
||||
typedef libsnark::default_r1cs_ppzksnark_pp::Fp_type curve_Fr;
|
||||
|
||||
int main() {
|
||||
curve_pp::init_public_params();
|
||||
libsnark::inhibit_profiling_info = true;
|
||||
libsnark::inhibit_profiling_counters = true;
|
||||
|
||||
curve_G1 a = curve_G1::one();
|
||||
curve_G2 b = curve_G2::one();
|
||||
|
||||
curve_Fr c = curve_Fr("1901").inverse();
|
||||
curve_Fr d = curve_Fr("2344").inverse();
|
||||
|
||||
curve_GT acc1 = curve_GT::one();
|
||||
|
||||
for (size_t i = 0; i < 10000; i++) {
|
||||
acc1 = acc1 * curve_pp::reduced_pairing(a, b);
|
||||
a = c * a;
|
||||
b = d * b;
|
||||
}
|
||||
|
||||
a = curve_G1::one();
|
||||
b = curve_G2::one();
|
||||
|
||||
curve_GT acc2 = curve_GT::one();
|
||||
|
||||
for (size_t i = 0; i < 10000; i++) {
|
||||
acc2 = acc2 * curve_pp::reduced_pairing(a, b);
|
||||
a = d * a;
|
||||
b = c * b;
|
||||
}
|
||||
|
||||
assert(acc1 == acc2);
|
||||
}
|
||||
|
|
@ -100,10 +100,7 @@ impl Fq12 {
|
|||
}
|
||||
|
||||
pub fn unitary_inverse(&self) -> Fq12 {
|
||||
Fq12 {
|
||||
c0: self.c0,
|
||||
c1: -self.c1
|
||||
}
|
||||
Fq12::new(self.c0, -self.c1)
|
||||
}
|
||||
|
||||
pub fn mul_by_024(&self,
|
||||
|
|
|
|||
|
|
@ -735,3 +735,64 @@ fn test_prepared_g2() {
|
|||
assert!(expected_g2_p == g2_p);
|
||||
assert!(expected_g2_p.coeffs.len() == 102);
|
||||
}
|
||||
|
||||
pub fn pairing(p: &G1, q: &G2) -> Fq12 {
|
||||
match (p.to_affine(), q.to_affine()) {
|
||||
(None, _) | (_, None) => Fq12::one(),
|
||||
(Some(p), Some(q)) => {
|
||||
q.precompute().miller_loop(&p).final_exponentiation().expect("miller loop cannot produce zero")
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_reduced_pairing() {
|
||||
use fields::Fq6;
|
||||
|
||||
let g1 = G1::one() * Fr::from_str("18097487326282793650237947474982649264364522469319914492172746413872781676").unwrap();
|
||||
let g2 = G2::one() * Fr::from_str("20390255904278144451778773028944684152769293537511418234311120800877067946").unwrap();
|
||||
|
||||
let gt = pairing(&g1, &g2);
|
||||
|
||||
let expected = Fq12::new(
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from_str("7520311483001723614143802378045727372643587653754534704390832890681688842501").unwrap(), Fq::from_str("20265650864814324826731498061022229653175757397078253377158157137251452249882").unwrap()),
|
||||
Fq2::new(Fq::from_str("11942254371042183455193243679791334797733902728447312943687767053513298221130").unwrap(), Fq::from_str("759657045325139626991751731924144629256296901790485373000297868065176843620").unwrap()),
|
||||
Fq2::new(Fq::from_str("16045761475400271697821392803010234478356356448940805056528536884493606035236").unwrap(), Fq::from_str("4715626119252431692316067698189337228571577552724976915822652894333558784086").unwrap())
|
||||
),
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from_str("14901948363362882981706797068611719724999331551064314004234728272909570402962").unwrap(), Fq::from_str("11093203747077241090565767003969726435272313921345853819385060670210834379103").unwrap()),
|
||||
Fq2::new(Fq::from_str("17897835398184801202802503586172351707502775171934235751219763553166796820753").unwrap(), Fq::from_str("1344517825169318161285758374052722008806261739116142912817807653057880346554").unwrap()),
|
||||
Fq2::new(Fq::from_str("11123896897251094532909582772961906225000817992624500900708432321664085800838").unwrap(), Fq::from_str("17453370448280081813275586256976217762629631160552329276585874071364454854650").unwrap())
|
||||
)
|
||||
);
|
||||
|
||||
assert_eq!(expected, gt);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_binlinearity() {
|
||||
use rand::{SeedableRng,StdRng};
|
||||
let seed: [usize; 4] = [103245, 191922, 1293, 192103];
|
||||
let mut rng = StdRng::from_seed(&seed);
|
||||
|
||||
for _ in 0..50 {
|
||||
let p = G1::random(&mut rng);
|
||||
let q = G2::random(&mut rng);
|
||||
let s = Fr::random(&mut rng);
|
||||
let sp = p * s;
|
||||
let sq = q * s;
|
||||
|
||||
let a = pairing(&p, &q).pow(s);
|
||||
let b = pairing(&sp, &q);
|
||||
let c = pairing(&p, &sq);
|
||||
|
||||
assert_eq!(a, b);
|
||||
assert_eq!(b, c);
|
||||
|
||||
let t = -Fr::one();
|
||||
|
||||
assert!(a != Fq12::one());
|
||||
assert_eq!((a.pow(t)) * a, Fq12::one());
|
||||
}
|
||||
}
|
||||
|
|
|
|||
172
src/lib.rs
172
src/lib.rs
|
|
@ -6,65 +6,129 @@ mod arith;
|
|||
mod fields;
|
||||
mod groups;
|
||||
|
||||
pub use arith::U256;
|
||||
pub use fields::{Fq, Fr, Fq2, Fq6, Fq12, FieldElement};
|
||||
pub use groups::{G1, G2, GroupElement};
|
||||
use fields::FieldElement;
|
||||
use groups::GroupElement;
|
||||
|
||||
pub fn pairing(p: &G1, q: &G2) -> Fq12 {
|
||||
match (p.to_affine(), q.to_affine()) {
|
||||
(None, _) | (_, None) => Fq12::one(),
|
||||
(Some(p), Some(q)) => {
|
||||
q.precompute().miller_loop(&p).final_exponentiation().expect("miller loop cannot produce zero")
|
||||
}
|
||||
}
|
||||
use std::ops::{Add, Sub, Mul, Neg};
|
||||
use rand::Rng;
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq, RustcDecodable, RustcEncodable)]
|
||||
pub struct Fr(fields::Fr);
|
||||
|
||||
impl Fr {
|
||||
pub fn zero() -> Self { Fr(fields::Fr::zero()) }
|
||||
pub fn one() -> Self { Fr(fields::Fr::one()) }
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self { Fr(fields::Fr::random(rng)) }
|
||||
pub fn pow(&self, exp: Fr) -> Self { Fr(self.0.pow(exp.0)) }
|
||||
pub fn from_str(s: &str) -> Option<Self> { fields::Fr::from_str(s).map(|e| Fr(e)) }
|
||||
pub fn inverse(&self) -> Option<Self> { self.0.inverse().map(|e| Fr(e)) }
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_reduced_pairing() {
|
||||
let g1 = G1::one() * Fr::from_str("18097487326282793650237947474982649264364522469319914492172746413872781676").unwrap();
|
||||
let g2 = G2::one() * Fr::from_str("20390255904278144451778773028944684152769293537511418234311120800877067946").unwrap();
|
||||
impl Add<Fr> for Fr {
|
||||
type Output = Fr;
|
||||
|
||||
let gt = pairing(&g1, &g2);
|
||||
|
||||
let expected = Fq12::new(
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from_str("7520311483001723614143802378045727372643587653754534704390832890681688842501").unwrap(), Fq::from_str("20265650864814324826731498061022229653175757397078253377158157137251452249882").unwrap()),
|
||||
Fq2::new(Fq::from_str("11942254371042183455193243679791334797733902728447312943687767053513298221130").unwrap(), Fq::from_str("759657045325139626991751731924144629256296901790485373000297868065176843620").unwrap()),
|
||||
Fq2::new(Fq::from_str("16045761475400271697821392803010234478356356448940805056528536884493606035236").unwrap(), Fq::from_str("4715626119252431692316067698189337228571577552724976915822652894333558784086").unwrap())
|
||||
),
|
||||
Fq6::new(
|
||||
Fq2::new(Fq::from_str("14901948363362882981706797068611719724999331551064314004234728272909570402962").unwrap(), Fq::from_str("11093203747077241090565767003969726435272313921345853819385060670210834379103").unwrap()),
|
||||
Fq2::new(Fq::from_str("17897835398184801202802503586172351707502775171934235751219763553166796820753").unwrap(), Fq::from_str("1344517825169318161285758374052722008806261739116142912817807653057880346554").unwrap()),
|
||||
Fq2::new(Fq::from_str("11123896897251094532909582772961906225000817992624500900708432321664085800838").unwrap(), Fq::from_str("17453370448280081813275586256976217762629631160552329276585874071364454854650").unwrap())
|
||||
)
|
||||
);
|
||||
|
||||
assert_eq!(expected, gt);
|
||||
fn add(self, other: Fr) -> Fr { Fr(self.0 + other.0) }
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_binlinearity() {
|
||||
use rand::{SeedableRng,StdRng};
|
||||
let seed: [usize; 4] = [103245, 191922, 1293, 192103];
|
||||
let mut rng = StdRng::from_seed(&seed);
|
||||
impl Sub<Fr> for Fr {
|
||||
type Output = Fr;
|
||||
|
||||
for _ in 0..50 {
|
||||
let p = G1::random(&mut rng);
|
||||
let q = G2::random(&mut rng);
|
||||
let s = Fr::random(&mut rng);
|
||||
let sp = p * s;
|
||||
let sq = q * s;
|
||||
|
||||
let a = pairing(&p, &q).pow(s);
|
||||
let b = pairing(&sp, &q);
|
||||
let c = pairing(&p, &sq);
|
||||
|
||||
assert_eq!(a, b);
|
||||
assert_eq!(b, c);
|
||||
|
||||
let t = -Fr::one();
|
||||
|
||||
assert!(a != Fq12::one());
|
||||
assert_eq!((a.pow(t)) * a, Fq12::one());
|
||||
}
|
||||
fn sub(self, other: Fr) -> Fr { Fr(self.0 - other.0) }
|
||||
}
|
||||
|
||||
impl Neg for Fr {
|
||||
type Output = Fr;
|
||||
|
||||
fn neg(self) -> Fr { Fr(-self.0) }
|
||||
}
|
||||
|
||||
impl Mul for Fr {
|
||||
type Output = Fr;
|
||||
|
||||
fn mul(self, other: Fr) -> Fr { Fr(self.0 * other.0) }
|
||||
}
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq, RustcDecodable, RustcEncodable)]
|
||||
pub struct G1(groups::G1);
|
||||
|
||||
impl G1 {
|
||||
pub fn zero() -> Self { G1(groups::G1::zero()) }
|
||||
pub fn one() -> Self { G1(groups::G1::one()) }
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self { G1(groups::G1::random(rng)) }
|
||||
}
|
||||
|
||||
impl Add<G1> for G1 {
|
||||
type Output = G1;
|
||||
|
||||
fn add(self, other: G1) -> G1 { G1(self.0 + other.0) }
|
||||
}
|
||||
|
||||
impl Sub<G1> for G1 {
|
||||
type Output = G1;
|
||||
|
||||
fn sub(self, other: G1) -> G1 { G1(self.0 - other.0) }
|
||||
}
|
||||
|
||||
impl Neg for G1 {
|
||||
type Output = G1;
|
||||
|
||||
fn neg(self) -> G1 { G1(-self.0) }
|
||||
}
|
||||
|
||||
impl Mul<Fr> for G1 {
|
||||
type Output = G1;
|
||||
|
||||
fn mul(self, other: Fr) -> G1 { G1(self.0 * other.0) }
|
||||
}
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq, RustcDecodable, RustcEncodable)]
|
||||
pub struct G2(groups::G2);
|
||||
|
||||
impl G2 {
|
||||
pub fn zero() -> Self { G2(groups::G2::zero()) }
|
||||
pub fn one() -> Self { G2(groups::G2::one()) }
|
||||
pub fn random<R: Rng>(rng: &mut R) -> Self { G2(groups::G2::random(rng)) }
|
||||
}
|
||||
|
||||
impl Add<G2> for G2 {
|
||||
type Output = G2;
|
||||
|
||||
fn add(self, other: G2) -> G2 { G2(self.0 + other.0) }
|
||||
}
|
||||
|
||||
impl Sub<G2> for G2 {
|
||||
type Output = G2;
|
||||
|
||||
fn sub(self, other: G2) -> G2 { G2(self.0 - other.0) }
|
||||
}
|
||||
|
||||
impl Neg for G2 {
|
||||
type Output = G2;
|
||||
|
||||
fn neg(self) -> G2 { G2(-self.0) }
|
||||
}
|
||||
|
||||
impl Mul<Fr> for G2 {
|
||||
type Output = G2;
|
||||
|
||||
fn mul(self, other: Fr) -> G2 { G2(self.0 * other.0) }
|
||||
}
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq)]
|
||||
pub struct Gt(fields::Fq12);
|
||||
|
||||
impl Gt {
|
||||
pub fn one() -> Self { Gt(fields::Fq12::one()) }
|
||||
pub fn pow(&self, exp: Fr) -> Self { Gt(self.0.pow(exp.0)) }
|
||||
pub fn inverse(&self) -> Self { Gt(self.0.inverse().unwrap()) }
|
||||
}
|
||||
|
||||
impl Mul<Gt> for Gt {
|
||||
type Output = Gt;
|
||||
|
||||
fn mul(self, other: Gt) -> Gt { Gt(self.0 * other.0) }
|
||||
}
|
||||
|
||||
pub fn pairing(p: G1, q: G2) -> Gt {
|
||||
Gt(groups::pairing(&p.0, &q.0))
|
||||
}
|
||||
|
|
|
|||
10035
tests/fp2_vectors.rs
10035
tests/fp2_vectors.rs
File diff suppressed because it is too large
Load Diff
20086
tests/fp_vectors.rs
20086
tests/fp_vectors.rs
File diff suppressed because it is too large
Load Diff
20069
tests/g1_g2_vectors.rs
20069
tests/g1_g2_vectors.rs
File diff suppressed because it is too large
Load Diff
30114
tests/serialization.rs
30114
tests/serialization.rs
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue