From 9e458130a6e97b0cefcdf9105506cc21c7f6dfaf Mon Sep 17 00:00:00 2001 From: Sean Bowe Date: Sun, 11 Sep 2016 02:19:11 -0600 Subject: [PATCH] Public API, reorganize tests, benchmarks and shootout. --- Cargo.toml | 2 +- README.md | 20 +- benches/{fp.rs => api.rs} | 201 +- examples/dh.rs | 34 + examples/joux.rs | 24 + oldexamples/dh.rs | 34 - oldexamples/joux.rs | 24 - oldsrc/fields/fp.rs | 167 - oldsrc/fields/fp12.rs | 294 - oldsrc/fields/fp2.rs | 146 - oldsrc/fields/fp6.rs | 192 - oldsrc/fields/macros.rs | 107 - oldsrc/fields/mod.rs | 54 - oldsrc/fields/tests.rs | 203 - oldsrc/groups/gt.rs | 32 - oldsrc/groups/macros.rs | 107 - oldsrc/groups/mod.rs | 355 - oldsrc/groups/tests.rs | 76 - oldsrc/lib.rs | 406 - oldsrc/params.rs | 432 - shootout/README.md | 11 + shootout/main.rs | 29 + shootout/test.cpp | 44 + src/fields/fq12.rs | 5 +- src/groups/mod.rs | 61 + src/lib.rs | 172 +- tests/fp2_vectors.rs | 10035 ------------ tests/fp_vectors.rs | 20086 ------------------------ tests/g1_g2_vectors.rs | 20069 ------------------------ tests/serialization.rs | 30114 +++++++++++++++++++++++++++++++++++- 30 files changed, 30500 insertions(+), 53036 deletions(-) rename benches/{fp.rs => api.rs} (62%) create mode 100644 examples/dh.rs create mode 100644 examples/joux.rs delete mode 100644 oldexamples/dh.rs delete mode 100644 oldexamples/joux.rs delete mode 100644 oldsrc/fields/fp.rs delete mode 100644 oldsrc/fields/fp12.rs delete mode 100644 oldsrc/fields/fp2.rs delete mode 100644 oldsrc/fields/fp6.rs delete mode 100644 oldsrc/fields/macros.rs delete mode 100644 oldsrc/fields/mod.rs delete mode 100644 oldsrc/fields/tests.rs delete mode 100644 oldsrc/groups/gt.rs delete mode 100644 oldsrc/groups/macros.rs delete mode 100644 oldsrc/groups/mod.rs delete mode 100644 oldsrc/groups/tests.rs delete mode 100644 oldsrc/lib.rs delete mode 100644 oldsrc/params.rs create mode 100644 shootout/README.md create mode 100644 shootout/main.rs create mode 100644 shootout/test.cpp delete mode 100644 tests/fp2_vectors.rs delete mode 100644 tests/fp_vectors.rs delete mode 100644 tests/g1_g2_vectors.rs diff --git a/Cargo.toml b/Cargo.toml index f72fe0f..96b41f9 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -10,7 +10,7 @@ repository = "https://github.com/zcash/bn" license = "MIT OR Apache-2.0" [[bench]] -name = "fp" +name = "api" [dependencies] rand = "0.3.14" diff --git a/README.md b/README.md index 0462b30..dc2ba8d 100644 --- a/README.md +++ b/README.md @@ -23,7 +23,7 @@ extern crate bn; ## API -* `Scalar` is an element of Fr +* `Fr` is an element of Fr * `G1` is a point on the BN curve E/Fq : y^2 = x^3 + b * `G2` is a point on the twisted BN curve E'/Fq2 : y^2 = x^3 + b/xi * `Gt` is a group element (written multiplicatively) obtained with the `pairing` function over `G1` and `G2`. @@ -38,19 +38,19 @@ In a typical Diffie-Hellman key exchange, relying on ECDLP, a three-party key ex ```rust // Generate private keys -let alice_sk = Scalar::random(rng); -let bob_sk = Scalar::random(rng); -let carol_sk = Scalar::random(rng); +let alice_sk = Fr::random(rng); +let bob_sk = Fr::random(rng); +let carol_sk = Fr::random(rng); // Generate public keys in G1 and G2 -let (alice_pk1, alice_pk2) = (G1::one() * &alice_sk, G2::one() * &alice_sk); -let (bob_pk1, bob_pk2) = (G1::one() * &bob_sk, G2::one() * &bob_sk); -let (carol_pk1, carol_pk2) = (G1::one() * &carol_sk, G2::one() * &carol_sk); +let (alice_pk1, alice_pk2) = (G1::one() * alice_sk, G2::one() * alice_sk); +let (bob_pk1, bob_pk2) = (G1::one() * bob_sk, G2::one() * bob_sk); +let (carol_pk1, carol_pk2) = (G1::one() * carol_sk, G2::one() * carol_sk); // Each party computes the shared secret -let alice_ss = pairing(&bob_pk1, &carol_pk2) ^ &alice_sk; -let bob_ss = pairing(&carol_pk1, &alice_pk2) ^ &bob_sk; -let carol_ss = pairing(&alice_pk1, &bob_pk2) ^ &carol_sk; +let alice_ss = pairing(&bob_pk1, &carol_pk2).pow(alice_sk); +let bob_ss = pairing(&carol_pk1, &alice_pk2).pow(bob_sk); +let carol_ss = pairing(&alice_pk1, &bob_pk2).pow(carol_sk); assert!(alice_ss == bob_ss && bob_ss == carol_ss); ``` diff --git a/benches/fp.rs b/benches/api.rs similarity index 62% rename from benches/fp.rs rename to benches/api.rs index 993309b..040aa6c 100644 --- a/benches/fp.rs +++ b/benches/api.rs @@ -1,5 +1,3 @@ -// TODO: later move all these benchmarks to within the code itself. - #![feature(test)] extern crate test; extern crate rand; @@ -78,148 +76,6 @@ fn fr_inverses(b: &mut test::Bencher) { }); } -#[bench] -fn fq_addition(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] + v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq_subtraction(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] - v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq_multiplication(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] * v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq_inverses(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES].inverse() - }); -} - -#[bench] -fn fq2_multiplication(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] * v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq2_addition(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] + v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq2_subtraction(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - let v2: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES] - v2[ctr % SAMPLES] - }); -} - -#[bench] -fn fq2_inverses(b: &mut test::Bencher) { - const SAMPLES: usize = 1000; - - let rng = &mut rand::thread_rng(); - - let v1: Vec<_> = (0..SAMPLES).map(|_| Fq2::random(rng)).collect(); - - let mut ctr = 0; - - b.iter(|| { - ctr += 1; - - v1[ctr % SAMPLES].inverse() - }); -} - #[bench] fn g1_addition(b: &mut test::Bencher) { const SAMPLES: usize = 100; @@ -327,3 +183,60 @@ fn g2_scalar_multiplication(b: &mut test::Bencher) { v1[ctr % SAMPLES] * v2[ctr % SAMPLES] }); } + +#[bench] +fn fq12_scalar_multiplication(b: &mut test::Bencher) { + const SAMPLES: usize = 100; + + let rng = &mut rand::thread_rng(); + + let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect(); + let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect(); + let v3: Vec<_> = (0..SAMPLES).map(|i| pairing(v1[i], v2[i])).collect(); + + let mut ctr = 0; + + b.iter(|| { + ctr += 1; + + v3[(ctr + SAMPLES/50) % SAMPLES] * v3[ctr % SAMPLES] + }); +} + +#[bench] +fn fq12_exponentiation(b: &mut test::Bencher) { + const SAMPLES: usize = 100; + + let rng = &mut rand::thread_rng(); + + let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect(); + let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect(); + let v3: Vec<_> = (0..SAMPLES).map(|i| pairing(v1[i], v2[i])).collect(); + let v4: Vec<_> = (0..SAMPLES).map(|_| Fr::random(rng)).collect(); + + let mut ctr = 0; + + b.iter(|| { + ctr += 1; + + v3[ctr % SAMPLES].pow(v4[ctr % SAMPLES]) + }); +} + +#[bench] +fn perform_pairing(b: &mut test::Bencher) { + const SAMPLES: usize = 100; + + let rng = &mut rand::thread_rng(); + + let v1: Vec<_> = (0..SAMPLES).map(|_| G1::random(rng)).collect(); + let v2: Vec<_> = (0..SAMPLES).map(|_| G2::random(rng)).collect(); + + let mut ctr = 0; + + b.iter(|| { + ctr += 1; + + pairing(v1[ctr % SAMPLES], v2[ctr % SAMPLES]) + }); +} diff --git a/examples/dh.rs b/examples/dh.rs new file mode 100644 index 0000000..c0f89b9 --- /dev/null +++ b/examples/dh.rs @@ -0,0 +1,34 @@ +// This is an example of three-party Diffie-Hellman key exchange +// Requires two rounds + +extern crate bn; +extern crate rand; + +use bn::*; + +fn main() { + let rng = &mut rand::thread_rng(); + + // Construct private keys + let alice_sk = Fr::random(rng); + let bob_sk = Fr::random(rng); + let carol_sk = Fr::random(rng); + + // Construct public keys + let alice_pk = G1::one() * alice_sk; + let bob_pk = G1::one() * bob_sk; + let carol_pk = G1::one() * carol_sk; + + // Round one: + let alice_dh_1 = bob_pk * carol_sk; + let bob_dh_1 = carol_pk * alice_sk; + let carol_dh_1 = alice_pk * bob_sk; + + // Round two: + let alice_dh_2 = alice_dh_1 * alice_sk; + let bob_dh_2 = bob_dh_1 * bob_sk; + let carol_dh_2 = carol_dh_1 * carol_sk; + + // All parties should arrive to the same shared secret + assert!(alice_dh_2 == bob_dh_2 && bob_dh_2 == carol_dh_2); +} diff --git a/examples/joux.rs b/examples/joux.rs new file mode 100644 index 0000000..ba1a6e0 --- /dev/null +++ b/examples/joux.rs @@ -0,0 +1,24 @@ +extern crate bn; +extern crate rand; +use bn::{Fr, G1, G2, pairing}; + +fn main() { + let rng = &mut rand::thread_rng(); + + // Generate private keys + let alice_sk = Fr::random(rng); + let bob_sk = Fr::random(rng); + let carol_sk = Fr::random(rng); + + // Generate public keys in G1 and G2 + let (alice_pk1, alice_pk2) = (G1::one() * alice_sk, G2::one() * alice_sk); + let (bob_pk1, bob_pk2) = (G1::one() * bob_sk, G2::one() * bob_sk); + let (carol_pk1, carol_pk2) = (G1::one() * carol_sk, G2::one() * carol_sk); + + // Each party computes the shared secret + let alice_ss = pairing(bob_pk1, carol_pk2).pow(alice_sk); + let bob_ss = pairing(carol_pk1, alice_pk2).pow(bob_sk); + let carol_ss = pairing(alice_pk1, bob_pk2).pow(carol_sk); + + assert!(alice_ss == bob_ss && bob_ss == carol_ss); +} diff --git a/oldexamples/dh.rs b/oldexamples/dh.rs deleted file mode 100644 index 2e07f3c..0000000 --- a/oldexamples/dh.rs +++ /dev/null @@ -1,34 +0,0 @@ -// This is an example of three-party Diffie-Hellman key exchange -// Requires two rounds - -extern crate bn; -extern crate rand; - -use bn::*; - -fn main() { - let rng = &mut rand::thread_rng(); - - // Construct private keys - let alice_sk = Scalar::random(rng); - let bob_sk = Scalar::random(rng); - let carol_sk = Scalar::random(rng); - - // Construct public keys - let alice_pk = G1::one() * &alice_sk; - let bob_pk = G1::one() * &bob_sk; - let carol_pk = G1::one() * &carol_sk; - - // Round one: - let alice_dh_1 = &bob_pk * &carol_sk; - let bob_dh_1 = &carol_pk * &alice_sk; - let carol_dh_1 = &alice_pk * &bob_sk; - - // Round two: - let alice_dh_2 = alice_dh_1 * &alice_sk; - let bob_dh_2 = bob_dh_1 * &bob_sk; - let carol_dh_2 = carol_dh_1 * &carol_sk; - - // All parties should arrive to the same shared secret - assert!(alice_dh_2 == bob_dh_2 && bob_dh_2 == carol_dh_2); -} diff --git a/oldexamples/joux.rs b/oldexamples/joux.rs deleted file mode 100644 index 273508d..0000000 --- a/oldexamples/joux.rs +++ /dev/null @@ -1,24 +0,0 @@ -extern crate bn; -extern crate rand; -use bn::{Field, Scalar, G1, G2, pairing}; - -fn main() { - let rng = &mut rand::thread_rng(); - - // Generate private keys - let alice_sk = Scalar::random(rng); - let bob_sk = Scalar::random(rng); - let carol_sk = Scalar::random(rng); - - // Generate public keys in G1 and G2 - let (alice_pk1, alice_pk2) = (G1::one() * &alice_sk, G2::one() * &alice_sk); - let (bob_pk1, bob_pk2) = (G1::one() * &bob_sk, G2::one() * &bob_sk); - let (carol_pk1, carol_pk2) = (G1::one() * &carol_sk, G2::one() * &carol_sk); - - // Each party computes the shared secret - let alice_ss = pairing(&bob_pk1, &carol_pk2) ^ &alice_sk; - let bob_ss = pairing(&carol_pk1, &alice_pk2) ^ &bob_sk; - let carol_ss = pairing(&alice_pk1, &bob_pk2) ^ &carol_sk; - - assert!(alice_ss == bob_ss && bob_ss == carol_ss); -} diff --git a/oldsrc/fields/fp.rs b/oldsrc/fields/fp.rs deleted file mode 100644 index 5ab6ca2..0000000 --- a/oldsrc/fields/fp.rs +++ /dev/null @@ -1,167 +0,0 @@ -use rand::Rng; -use num::{BigUint, Num}; -use std::ops::{Mul,Add,Sub,Neg}; -use std::cmp::{PartialEq, Eq}; -use std::convert::From; -use std::fmt; -use std::marker::PhantomData; -use super::Field; - -pub trait PrimeFieldParams { - fn modulus() -> BigUint; - fn bits() -> usize; - fn name() -> &'static str; -} - -pub struct Fp { - value: BigUint, - _marker: PhantomData

-} - -impl fmt::Debug for Fp

{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}({})", P::name(), self.value) - } -} - -impl Field for Fp

{ - fn zero() -> Self { - use num::Zero; - - Fp { - value: BigUint::zero(), - _marker: PhantomData - } - } - fn one() -> Self { - use num::One; - - Fp { - value: BigUint::one(), - _marker: PhantomData - } - } - fn random(rng: &mut R) -> Self { - use num::num_bigint::RandBigInt; - use num::Zero; - - Fp { - value: rng.gen_biguint_range(&BigUint::zero(), &P::modulus()), - _marker: PhantomData - } - } - - fn inverse(&self) -> Self { - if self.is_zero() { - // TODO: this should likely bleed through the abstraction layers - panic!("cannot get the multiplicative inverse of zero") - } else { - let mut res = Self::one(); - - let mut found_one = false; - - let exp = Self::zero() - Self::one() - Self::one(); - - 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 Fp

{ - 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

{ - fn from(s: &'a str) -> Self { - Fp { - value: BigUint::from_str_radix(s, 10).unwrap() % P::modulus(), - _marker: PhantomData - } - } -} - -impl Clone for Fp

{ - fn clone(&self) -> Self { - Fp { - value: self.value.clone(), - _marker: PhantomData - } - } -} - -forward_ops_to_field_ops!(impl(P: PrimeFieldParams) Fp

); diff --git a/oldsrc/fields/fp12.rs b/oldsrc/fields/fp12.rs deleted file mode 100644 index ffd7d88..0000000 --- a/oldsrc/fields/fp12.rs +++ /dev/null @@ -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 { - a: Fq6, - b: Fq6, - _marker: PhantomData

-} - -impl Fp12

{ - 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 fmt::Debug for Fp12

{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}({:?}, {:?})", P::name(), self.a, self.b) - } -} - -impl Clone for Fp12

{ - fn clone(&self) -> Self { - Fp12 { - a: self.a.clone(), - b: self.b.clone(), - _marker: PhantomData - } - } -} - -impl Field for Fp12

{ - 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(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

); diff --git a/oldsrc/fields/fp2.rs b/oldsrc/fields/fp2.rs deleted file mode 100644 index 7c9523b..0000000 --- a/oldsrc/fields/fp2.rs +++ /dev/null @@ -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 { - a: Fq, - b: Fq, - _marker: PhantomData

-} - -impl Fp2

{ - 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 fmt::Debug for Fp2

{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}({:?}, {:?})", P::name(), self.a, self.b) - } -} - -impl Clone for Fp2

{ - fn clone(&self) -> Self { - Fp2 { - a: self.a.clone(), - b: self.b.clone(), - _marker: PhantomData - } - } -} - -impl Field for Fp2

{ - 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(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

{ - type Output = Fp2

; - - fn mul(self, other: &Fq) -> Fp2

{ - Fp2 { - a: &self.a * other, - b: &self.b * other, - _marker: PhantomData - } - } -} - -forward_ops_to_field_ops!(impl(P: Fp2Params) Fp2

); diff --git a/oldsrc/fields/fp6.rs b/oldsrc/fields/fp6.rs deleted file mode 100644 index 2fe4bd4..0000000 --- a/oldsrc/fields/fp6.rs +++ /dev/null @@ -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 { - pub a: Fq2, - pub b: Fq2, - pub c: Fq2, - _marker: PhantomData

-} - -impl Fp6

{ - 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 fmt::Debug for Fp6

{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.a, self.b, self.c) - } -} - -impl Clone for Fp6

{ - fn clone(&self) -> Self { - Fp6 { - a: self.a.clone(), - b: self.b.clone(), - c: self.c.clone(), - _marker: PhantomData - } - } -} - -impl Field for Fp6

{ - 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(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 Fp6

{ - pub fn mul_by_nonresidue(&self, other: &Fq2) -> Fp6

{ - 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

{ - type Output = Fp6

; - - fn mul(self, other: &Fq2) -> Fp6

{ - Fp6 { - a: &self.a * other, - b: &self.b * other, - c: &self.c * other, - _marker: PhantomData - } - } -} - -forward_ops_to_field_ops!(impl(P: Fp6Params) Fp6

); diff --git a/oldsrc/fields/macros.rs b/oldsrc/fields/macros.rs deleted file mode 100644 index 00cc91f..0000000 --- a/oldsrc/fields/macros.rs +++ /dev/null @@ -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); - } -} diff --git a/oldsrc/fields/mod.rs b/oldsrc/fields/mod.rs deleted file mode 100644 index 0c24f0e..0000000 --- a/oldsrc/fields/mod.rs +++ /dev/null @@ -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(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(&self, exp: &Fp

) -> 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; -} diff --git a/oldsrc/fields/tests.rs b/oldsrc/fields/tests.rs deleted file mode 100644 index 82f48ea..0000000 --- a/oldsrc/fields/tests.rs +++ /dev/null @@ -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; - - #[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 = [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 = [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; - - #[test] - fn field_ops() { - fn test_field_operation 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() { - 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(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(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(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(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() { - can_invert::(); - - let seed: [usize; 4] = [103245, 191922, 1293, 192103]; - let mut rng = StdRng::from_seed(&seed); - - rand_element_squaring::(&mut rng); - rand_element_addition_and_negation::(&mut rng); - rand_element_multiplication::(&mut rng); - rand_element_inverse::(&mut rng); -} - - diff --git a/oldsrc/groups/gt.rs b/oldsrc/groups/gt.rs deleted file mode 100644 index 4855272..0000000 --- a/oldsrc/groups/gt.rs +++ /dev/null @@ -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); diff --git a/oldsrc/groups/macros.rs b/oldsrc/groups/macros.rs deleted file mode 100644 index cb4dca6..0000000 --- a/oldsrc/groups/macros.rs +++ /dev/null @@ -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); - } -} diff --git a/oldsrc/groups/mod.rs b/oldsrc/groups/mod.rs deleted file mode 100644 index 1a16c48..0000000 --- a/oldsrc/groups/mod.rs +++ /dev/null @@ -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; - fn one() -> Jacobian; - fn coeff_b() -> Self::Base; - fn name() -> &'static str; -} - -pub struct Jacobian { - x: P::Base, - y: P::Base, - z: P::Base -} - -impl fmt::Debug for Jacobian

{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.x, self.y, self.z) - } -} - -impl Clone for Jacobian

{ - fn clone(&self) -> Self { - Jacobian { - x: self.x.clone(), - y: self.y.clone(), - z: self.z.clone() - } - } -} -pub enum Affine { - Zero, - Point{x: P::Base, y: P::Base} -} - -impl Clone for Affine

{ - 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 Affine

{ - 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

{ - 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 { - pub fn mul_by_q(&self) -> Jacobian { - 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 { - pub fn mul_by_q(&self) -> Affine { - self.to_jacobian().mul_by_q().to_affine() - } -} - -impl Jacobian

{ - pub fn new(x: P::Base, y: P::Base, z: P::Base) -> Option { - let tmp = Jacobian { - x: x, - y: y, - z: z - }; - - if tmp.is_well_formed() { - Some(tmp) - } else { - None - } - } - - pub fn random(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

{ - 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(&self, other: &Fp) -> Jacobian

{ - let mut result = Jacobian::

::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

{ - self.add(&other.neg()) - } -} - -impl Jacobian { - pub fn mixed_addition_step_for_flipped_miller_loop(&mut self, base: &Affine) -> 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

); - -impl PartialEq for Affine

{ - fn eq(&self, other: &Self) -> bool { - self.to_jacobian() == other.to_jacobian() - } -} - -impl Eq for Affine

{ } diff --git a/oldsrc/groups/tests.rs b/oldsrc/groups/tests.rs deleted file mode 100644 index 1f3d267..0000000 --- a/oldsrc/groups/tests.rs +++ /dev/null @@ -1,76 +0,0 @@ -use super::*; -use ::Fr; -use fields::Field; - -use rand::Rng; - -pub fn group_trials() { - fn test_doubling() { - type G

= Jacobian

; - - let one = G::

::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(rng: &mut R) { - type G

= Jacobian

; - - for _ in 0..50 { - let r1 = &G::

::random(rng); - let r2 = &G::

::random(rng); - let r3 = &G::

::random(rng); - - let s1 = (r1 + r2) + r3; - let s2 = (r2 + r3) + r1; - - assert_eq!(s1, s2); - } - } - - fn random_test_doubling(rng: &mut R) { - type G

= Jacobian

; - - for _ in 0..50 { - let r1 = &G::

::random(rng); - let r2 = &G::

::random(rng); - - let a = (r1 + r2) + r1; - let b = r1.double() + r2; - - assert!(a.eq(&b)); - } - } - - fn random_test_dh(rng: &mut R) { - type G

= Jacobian

; - - for _ in 0..50 { - let alice_sk = Fr::random(rng); - let bob_sk = Fr::random(rng); - - let alice_pk = G::

::one() * &alice_sk; - let bob_pk = G::

::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::

(); - - use rand::{SeedableRng,StdRng}; - let seed: [usize; 4] = [103245, 191922, 1293, 192103]; - let mut rng = StdRng::from_seed(&seed); - - random_test_addition::(&mut rng); - random_test_doubling::(&mut rng); - random_test_dh::(&mut rng); -} - diff --git a/oldsrc/lib.rs b/oldsrc/lib.rs deleted file mode 100644 index 9512482..0000000 --- a/oldsrc/lib.rs +++ /dev/null @@ -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; -pub type Fq = Fp; -pub type Fq2 = Fp2; -pub type Fq6 = Fp6; -pub type Fq12 = Fp12; - -pub type Scalar = Fr; -pub type G1 = Jacobian; -pub type G2 = Jacobian; - -#[derive(PartialEq,Eq)] -struct G2Precomp { - q: Affine, - coeffs: Vec -} - -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, 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())); - } -} diff --git a/oldsrc/params.rs b/oldsrc/params.rs deleted file mode 100644 index 2880331..0000000 --- a/oldsrc/params.rs +++ /dev/null @@ -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::(); -} - -#[test] -fn test_fq() { - use fields; - - fields::tests::field_trials::(); -} - -pub struct G1Params; - -impl GroupParams for G1Params { - type Base = Fq; - - fn name() -> &'static str { - "G1" - } - fn zero() -> Jacobian { - Jacobian::new(Fq::zero(), Fq::one(), Fq::zero()).unwrap() - } - fn one() -> Jacobian { - 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::(); - - 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::(); -} - -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 { - Jacobian::new(Fq2::zero(), Fq2::one(), Fq2::zero()).unwrap() - } - fn one() -> Jacobian { - 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::(); - - 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") -} diff --git a/shootout/README.md b/shootout/README.md new file mode 100644 index 0000000..aaf3d2a --- /dev/null +++ b/shootout/README.md @@ -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 diff --git a/shootout/main.rs b/shootout/main.rs new file mode 100644 index 0000000..379252a --- /dev/null +++ b/shootout/main.rs @@ -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); +} diff --git a/shootout/test.cpp b/shootout/test.cpp new file mode 100644 index 0000000..ed5c01b --- /dev/null +++ b/shootout/test.cpp @@ -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); +} diff --git a/src/fields/fq12.rs b/src/fields/fq12.rs index a68e115..cb11e2e 100644 --- a/src/fields/fq12.rs +++ b/src/fields/fq12.rs @@ -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, diff --git a/src/groups/mod.rs b/src/groups/mod.rs index ba15e72..bdf5889 100644 --- a/src/groups/mod.rs +++ b/src/groups/mod.rs @@ -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()); + } +} diff --git a/src/lib.rs b/src/lib.rs index 8261bb2..255f122 100644 --- a/src/lib.rs +++ b/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(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 { fields::Fr::from_str(s).map(|e| Fr(e)) } + pub fn inverse(&self) -> Option { 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 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 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(rng: &mut R) -> Self { G1(groups::G1::random(rng)) } +} + +impl Add for G1 { + type Output = G1; + + fn add(self, other: G1) -> G1 { G1(self.0 + other.0) } +} + +impl Sub 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 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(rng: &mut R) -> Self { G2(groups::G2::random(rng)) } +} + +impl Add for G2 { + type Output = G2; + + fn add(self, other: G2) -> G2 { G2(self.0 + other.0) } +} + +impl Sub 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 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 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)) } diff --git a/tests/fp2_vectors.rs b/tests/fp2_vectors.rs deleted file mode 100644 index 7427acf..0000000 --- a/tests/fp2_vectors.rs +++ /dev/null @@ -1,10035 +0,0 @@ -extern crate rand; -extern crate bn; -mod serialization; - -use bn::*; -use self::serialization::*; - -#[test] -fn serialization_and_deserialization() { - let mut a = Fq2::one(); - let b = Fq2::random(&mut rand::thread_rng()); - - for _ in 0..10000 { - a = a * b; - - assert_eq!(reserialize(a), a); - } -} - -// TODO: write "invalid representation" tests - -#[test] -fn fq2_vectors() { - let expected = vec![ - "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000001", - "183227397098d014dc2822db40c0ac2ecbc0b548b438e5469e10460b6c3e7ea5183227397098d014dc2822db40c0ac2ecbc0b548b438e5469e10460b6c3e7ea6", - "09f6889f2e5d0a62f13db3ffed7c832253e5f04b1d085e685f33e09b4ab0524127da227cb974298bc4f6cfffb5f20c894f97c12c742179a17ccf826d2ac14917", - "22b5e4160c16ea9afc823348548e71190f5a9c365f5f8474cd3086a5d050bca828f9784e326c40ff7b1d031d23ba196e86ced52f1535be6298d813949c19a090", - "107755f505ef3425b55415d2417b8debb6ec2b907d1e9e3f899f6d3d3525067407e7a381f0e680a13dca8276ff44b9a397265ad4805c779df1e491615048973b", - "2f558c8932a976d3e84cd80921bae989f79e4d5858e1db2eee9cada84f6f94360e4ba585b83a2579ceaa37188d1db690cf257dc476efb8a852ecff43398e4995", - "1c577d6ec82d63421d4391efb14ec37892998381d8210474db612a6fa297d56317adbd14ef2e622ab8951af9174c394c28fef8cf61b77aad0f5e8eac67b72134", - "2b32f16c3b40e38c9d987f99c98194d82b3212f6fcff92afa0c58f135461e7402ee13c014daa9b7d89721a71d1fb101b240046c73a06e6e6d0db76765d4c0834", - "02b45889e10e86aeccc6859f98f7ac79e68f25507b5679869556a567dbbc964e2e000c9514ef203904f6957b9dec055f5c88440e87f54e276696953a614d9311", - "12c7fb3ab259f176496262845cbf8143c798b1536d4ef1c3df2a9c1aa3b6e8c51fcd0b7aa7de2328d635fd6c7c6104ac88351a379eb6c0ebdb3f171f3b2d9d85", - "2057f6876ab3bd6faa307ab0480b58abde3de66776d27297d0b8a93550f102981231390debc24822843a0dec6b393b9b7b8f2d4e42e52101527a07a14d8af5ca", - "104364a58efb0b58e264541a2cfe7b02f21dc6cbeb0f23b84ff1550804fc6252074f012925498f3bbaa267eb3000b4db4fb327b8f45285a06833ea1b2222b0dd", - "28494cfec72e7404ab038fa232d25fb7582cb92fb4161b77fd526c739ae0635e21d53fe66f004bf7cafd712835eb080e99498b38da3d87d790842a8140becbac", - "0435c1b47dd01cdc3f337f969983f0ffdd09cfa1f26d5d0f5d19ca71337236b80da90a829d15d0c223340de4a3f75b6bda02155442b22db440b95ac5b0adb461", - "1e732e1f5cca11d95114cfd1de9efd39c4e6e686cd70473ae20871a2550232f31c85562f7b5e3b0ca95ae0e0eb5dd7323a39399036a0c113d03adfa4698c7a28", - "1a2f981ba2306812f120485b214ad75de3cfe58f76036f4e93519c854a5c73c323fa029a9039bbef93d2e00a110ca9570bbafc55bed47c7cf2723fbf6c7928cd", - "18a1d04e2efaaacd5c172fef292bb0daf74ce2b2afa146897f5fa8f83e36925312b914d6de86fd0de76f1adff2bbf78b5f9ae6fac6da144c4631e56cdbfd1823", - 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"267ebfa522a82f58d3cc83e9346fa4813d7e63d2672324ab843095dd230a19130ad9cd59ebdc08af9f2603fe3e0ffc6f82ae05b74f8d12d7f0995fc1a0c205ae", - "114b8053ffa468ab85b66a44d2db546711e68da6942e826410971fd838b1781c06245c4257a49bf5500455834e47beb370af89bb79e5a120465add0dd9cb0396", - "0acd3cf0430815fe1cde4d3ec53d130ac85f5505d4624bf54dd07a4b20a3ab2f00b9c5dc07acb876548a66b72bfe43811e739602a52fe01d4d6bd09343bfc5df", - "0ea44d332d6c72da342871639b3e9b206759eec74902fda6841c99054b9e616b2a25983f04a1ac6fd00cd123439cb180fbf064b5865b00b764ac661f3a36a5bf", - "158486981eb5e6886123b7f305abac3e859c0002b1b475e1d213b22d51f642ae10982febbdcf6f710df93d64a241f5d958f111804ae5e6a4796722c7f70251ca", - "232075855c40868e4f6f891bb7ad8652907f792571b40961400fcde64cbd756003a9a97cffa6dcd6bb867a11815aada68c907eee0a2313c5a1f831a0492efcda", - "26c5e44c663d03a0ef45790bceda3da0bddfabb0b443607f9940855d580a5d482f6a384de189bffa62ec13323d353626f0d6c280e93412b3233cdec23a148f67", - "0f72b779cedb38ffd553928c7ec5194cea37134f9945db43a014307acd154c03202ea6fdf16ef367f1d4b807231e19323342f1af0592ffa6ec9c9a04d4f170a4", - "266587ea18f736aa7b52068579d84b67cb358cc2201fe7a875f13d914d12154603ab5896a8d76199692f63aee8d497bb761f45c6817f0d0a96be3421c0349727", - "14168f309e989c3e816e6aef926c86c21d194818750f396f249cf62d68e1c83518b4ee349f029d0bfbc227f64adf25644c784f7eb8cd476a1c3be5f4cca309cb", - "00d20fd0d3f33e99a4e712623473bbca3131a5110cd7c5ba88d0b9ceba0df2f506fc8f8b11a3e0447eb7b930bdd5691c1ca45bbfbdfa4633e49dc83a47d4f966", - "24b404d7231ca3ad5e47c2722ce83ee75d62da6b88ff2cbb78e86590b0dbe07b2ff234029fdd186fa0e63ce5c3623b520b2c90581c6cff3c14cc29736a540a92", - "026dd8850909151978e2253491b24f5b31b97e71e582c2190828dd59815d277911b3eceb287bd36fb2fe730b16129fe3a1397b837e5fb7cff2ecc853aa662dd9", - "02cf2f2fdbf455d1982b40d6ed2b902eaf05974e770c4d8f05e056ee571d42520672170e2b7edb2e7fbbe7a9e75b6b6c388bec836567df0c4cf43e075b0436e6", - "0193658c0d21432c089b393e99453f124f0fc4c52cb7154ddb758774eac45b9211461c74c797e8354690a275e865e4f0ac7099eef1e29e9feb6f5144f1750732" - ]; - - let mut acc = Fq2::new(Fq::from_str("1").unwrap(), Fq::from_str("1").unwrap()); - - for i in 0..10000 { - assert_eq!(expected[i], into_hex(acc).unwrap()); - assert_eq!(from_hex::(expected[i]).unwrap(), acc); - - acc = acc * acc + acc + acc.inverse().unwrap(); - } -} diff --git a/tests/fp_vectors.rs b/tests/fp_vectors.rs deleted file mode 100644 index 06651fa..0000000 --- a/tests/fp_vectors.rs +++ /dev/null @@ -1,20086 +0,0 @@ -extern crate bn; -mod serialization; - -use bn::*; -use self::serialization::*; - -#[test] -fn serialization_and_deserialization() { - { - let mut a = Fr::one(); - let b = Fr::from_str("17").unwrap(); - - for _ in 0..10000 { - a = a * b; - - assert_eq!(reserialize(a), a); - } - } - { - let mut a = Fq::one(); - let b = Fq::from_str("17").unwrap(); - - for _ in 0..10000 { - a = a * b; - - assert_eq!(reserialize(a), a); - } - } -} - -#[test] -fn test_invalid_representations() { - // Fr - { - // modulus - 1 is representable - from_hex::("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000").unwrap(); - - // modulus is not representable - assert!(from_hex::("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none()); - - // ridiculously large numbers - assert!(from_hex::("f0644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none()); - assert!(from_hex::("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none()); - } - - // Fq - { - // modulus - 1 is representable - from_hex::("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap(); - - // modulus is not representable - assert!(from_hex::("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47").is_none()); - - // ridiculously large numbers - assert!(from_hex::("f0644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47").is_none()); - assert!(from_hex::("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none()); - } -} - -#[test] -fn fr_vectors() { - let expected = vec![ - "0000000000000000000000000000000000000000000000000000000000000001", - "0000000000000000000000000000000000000000000000000000000000000003", - "2042def740cbc01bd03583cf0100e59370229adafbd0f5b62d414e62a000000d", - "1eced988f1c4e0f7f7433f99dc0eb1b89dd2a1b7c00a6e1a5df4900b27c8a6b3", - "02363a20539db6638514cb4ba7ec49c91b2c5d405b7e5c021d3a0bf834f2ef0a", - "09889144b32647e7a6a9ec0646bbabe83d9b7d9188c3bdcd3b002c55c9aa80ef", - "014ced1876c520cc926b880803323cb80b4554f8c2588032f6cb727157371641", - "179da4e61ae3117b9b12f86f5aa4f14e1fc3b46bf05d1423900f9ce6228b6d40", - "067140865d6292881384dc2252b9dd20111c942dc2364e8c98f1da3c28da888f", - "2ca25f36b7b20358489b49421b20f6a10eacf80e7f3d2bfce7593d0777fef418", - "2bf0a17a3fa0670820f4f2469774a98f9bcd6a5e490e97d6e11f361c914cfe8c", - "29a228ca3b4b8ed9cf1c2957a826aaf9cc3d1bdccc99996092b42907e8d763d4", - "296a1aae3b4d8c87257609dba587338419937a3f7a8e37234deca0eb9b761478", - "05c9dd8d3da17bb45967ad595e6440ba84243707a5b2a45568f22731b7f2055c", - "2e99a1f1b911be2b5eae798a1bdb87ec8b6b66015af43114d4c4f0c3081808d8", - "0500c67659a93bcd482ce6e2e198e671bff5e9bf276891b0c7f79200da6dd6b5", - "020a4cdd4381c2c7e2a1885ac88036bbacc0d6aac38ca1113c10efe9226e5744", - "29329d9432d2146f11a0d9e2578c09f7f1182b9cb20f988c6bad57bcb614e48f", - "09507fcafb26bb82d68228ef5f5ed7b71aab295bbe4cdc759df141917d11d79e", - "00a0ba7dcf0405380408feb28cdeeb784a19d0b9679d1adc005e9f1ab34f251a", - "067517b1a7f50aa3a3c9dd3db988b0e2e87a8e6b3fb1184b8a06cc3529141132", - "13e5c7527050b265295b9739cd2f95312932bfb62ce4c159c0ab92a61f0dcdab", - "2a737c37b6881ca875205b949c313108f54eee116d876d4685a88e77a88a7589", - "1103f082a016eea4c4dde6b7caf6d5f23d45007920eacd4ac8c952a9ece70d33", - "12f45350d4c50366dd0c88a77ce35b802cf1e6929210449ff83a73a627ae8a9b", - "18b04aa529992886a880fbabdcc834a983bf07bfb23cfa7bba660aec0a10a8ae", - "03820dad30db55157ce87fc6812ec0a4e659e7547b18206d5844a6d1f28399e1", - "030dfdd27e4e180392ec965b8bf2586d3203fe8931be034c966c37433625fd9a", - "08a9b73efb3282526bee3e609fb408449503b70f617b3bab42919108852cf44b", - "184b6a8fd93b49422099e5d75090dce92edf553115452635bbc8e623ce312ad3", - "030273cc32bbe84b480930f2313491a19c00e2dd39fbd30993603bb8b5495e95", - "1622dd450399ca70b99e94f60d87490b1078ff0dc3ce82cb32fd7dce0c4a4499", - "0195e53a05f7b95040d27b2819f7b23b40c0871dbc476e3c102e4cb64904483e", - "2910b512191aae4c5f27f90aea2f41b3b0e0f2042d57ebc8dc51901d06b10024", - "2e795bc0783c41c950330abcbd7e92a6d7e558787e7f579b4c2e4aaf9f66630f", - "0c34e777e38a18cb4edc5e9d3f4f07dbb1b074f38347dd53a015be494f24c0b0", - "277348139e45c362741e424e4dc10b94df979bbf14f7c4b6dc144a0a0c593e1c", - "1dff63c029e19454c2360a88baf804cafa60f6a50cbb71a79715c2832cf47408", - "23e84f6518e9bab5af850cf1f38a873fe8be0c2f786d1d4e1fdaf32d46150500", - "211b26970071c65390a8c6d822423ab281aae480a12a6fc836b40884a4337e53", - "296abf4e45cc54ba75225ebac4fe863d5cfe725105cadfc9f9357f791d7ffdd9", - "22cf34de7b862a2c4874a03b7ce9a9ac8e748e4741a7d01ef7e443430a543b33", - "2fca5ad500e198625c9d542e0d4aefdcda28d246edf9a83f34c57ac1cfe98a34", - "2a471ed73102e6918e55b0ef00822a5281ef0e49b4586cce10ab2671ddf95731", - "2210b49819b69ca317b63ccfe3a4fed4fcc9b9b368dee5d988624487f7cd7d99", - "0ac117037c41ac977dfac11e614ff3c1f0604fdf1e934addd96ca426a2d56c45", - "18a0c2a40073a85c4a4cec75dc9e049a18def78960c7429a9c6abc1cde4d1c42", - "229574d27795392985547b551380cda18972a32c2caf87b910746ebda6615ca8", - "1c6f0bc008a80d5d36cf483df553e24ac4f969d7a02f45e93181441d79fb72fc", - "1060b506a53a740169a80954eb5fcfc6b261cfca0c021a8113841bfa2b10d3df", - "23ecc4f3237f76dc81fbbb8e467d253ebb6b4e99b9f2c607daec1bb599a63108", - "2350041950c0d7144e6790f939fa4f2f53165b82e6f5c1c730b7129ff1dd6075", - "179de2653b84e8e5d925b21cf206b9886ffe9df14dd300ef48341707f3a8e43a", - "16c670be2c945714cf9e5b30cc54b846a86ade34ca2f19e95cb9782cd1a1f4f6", - "2a6ac3b3bd2a3ca35792323fe39384b7ba44fd70b8788bfb9a28f0397e6c58f2", - "27c800eb72d3f1ac091747cedb323b02178e9cab5951f1b1c97b70430bc93f49", - "0acb5953cf1583df3f5be7fc264a01d561642171ed8ad66cb0750ef84637919a", - "239f76d1622590038d64e710422cda6cb6e3e12d1593b07b08faea2dd71848de", - "2dab87d5e027c3aa07b95691cf313088176763b92a1a101142b202224c889319", - "2ebb685e594b7ae133c381606c8fc1c7a07ec46c653b1d5e73734362bc8cc31b", - "238274a880a47a28cec6660f31ca766e7c024fb458f7e1df5cc8d9f1fa49b364", - "27c5e092fa1ee06da63928770d5ecc7931845869260b3966d6523ea526db2789", - "00dcdcb4cc0015ab8b8bfca1d52e335275b6fb39b58d41c2b30367a104dc2fec", - "22c7f9595340b66a5f0781fc8c6856facc2228ef749ebe8f4e26a3c9ab74465c", - "2ea0cafc90188c763ae65f132d3d5c873e4bf9a50ceb079874d1c346ab8fb63d", - "180066c34e34c473953b3e66d98660e733729376074b231198e921d4ae28ac75", - "0cc81637599da9f5b8285737283752575daedabd7b463e02992933126b59e167", - "274ced6e1efb4148e7fb778afdb6e7a41a5af073df6c43b7103f291efac8ca76", - "2dccf0cb2b0c9165392462712673c4075a99d1f1e3118ffb3deadcda415768a6", - "1d0128b4b0f47f814b2fb6491f03654541725612c465267f02b73ed28074fbc1", - "264770a08b4fcfe8dcde0161cb4cfe1d851227fa5538adcdef80827636d95f92", - "08cd18d2188a1b7e7103b95a1b7022cb56f14916b5b5a8b4db2b7305d222fb1c", - "2b0fa450d5c7dda8eb466723cd25e0b762968e52fb8a558225ad2b0b3c9f15e4", - "0fb89c9eb27d7e49d4988722e645714fe5be1fd5d1dd7b9f475a10222aef9fb0", - "2384e79d245f048e6433b04a3c7e527a736c198c67682a23cccc127e0fe341c3", - "240c04ce80bb543b5b9dc19abacc681c8c58778141349e9e3f492515c54dbfdd", - "1b2c3e4505b9325d56c1fe596f839bc3bc023ca08485a3f71f575994e61e4e9a", - "2c341055bdfd39ae1c9012b5456790d9e6bb603a56cd215b8fc7ff5df23babda", - "2a618fada6222167ec179c0d2d5a3db64b07d04a0d8ce903ffcd878708131fc6", - "098505eda76826a820e63e004a19ce3c16fbc465d5c294e4710121781e476016", - "2198b95feb3a29a0bc7439a763caf039448143e464d12c3a5753fa4b4039b97e", - "23e150228a041db5a598c4955ad4b763b2edb6208b5f4caccf790d0a2d927215", - "1806b48868d9900275573f4e57ecc9257f0b8787527a2b96d2e24f1cfd4b6ac1", - "2b7b0225bd8e48a401ab3a10507845bf3110c5959980023d166dc4be0aabdadf", - "1b5d5b3c9f454b4019116206d223c708bba4ee71138fffb32ed8674943c72486", - "2a495d1c7fcaa4f27be5914c7c6fed4fb65ee46e6d7974a55141d9bab30b39b4", - "1fddf00cfacfef6cf8dd5e88e04298fd376934a40938aee523338677258469ca", - "01fd18b9683b1aac8675185d5d06773aaab0e19112ddc9bb63e2c63bcde49db0", - "140899d53f48c9b200a48a8618dda9f24ba27a9acdb63dcf633107feae16fe98", - "0a0a0501eb8fbabf040f420ecad8797db587601e3deab6a01ce4b0d306be7cc6", - "2fa5a098db8149032e6bb899bc0b97c6b2ffdd6cfcc955d17ea2afe6a3cc3990", - "26162db3d4a6e6172f0b8d1d7ec1f706f9eeb7c6d3b0c2a510d7d0e04fe4eda6", - "1fc0dbbbbdea0ffaf2864ccca1b7e937efadd6987ad73881c5fd534ce2ae55ff", - "00dc4562c8483647fe1d924d50c574fb00b53973333cf3f42b24cb0412d1949c", - "2fcdf1fcbdfbec79a47715a340effb55d042f522b0b86acbd4c2c286d8afbbc1", - "0b11546ba7759df51528a4b9656d09ab5c2b7423ea82ed36d7acb01fe96cc8b7", - 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"2afb5783862e61d85ad07ceffcf9eaadb4bf356cc087a6e00f063cc061921249", - "115bf3266f333035ee4fe881f5174acde6badebed4a8938bba8c0f93e2bbbd18", - "0c883b272f8d4df33709cc198827c1e824a17d14894e613e00ce3cf276af30a7", - "09bc9db172bba04348f3129b0cac84edbda4db19f8c3a26e25cfc4aa02de3f0e", - "1217481522fe8e99f0eb2f0543fd97079a876144549df2f15abe119ca9626c8a", - "2bc0654015030b29571086241ab881d5bab80d589a922cb896f0c7962c07d509", - "1ba66d34c3a034efbffdbc70788baff1a5c2c6947d3d2e39f20e067e61dd30a5", - "171c6eb8e3b7feeb8ffc180d36f3feba07568c920a4485bb48494ff5261ebd88", - "000f2aa6f3c58ced4f2f0c538a3fb177d78805ae1288aa3cf066d877b2401977", - "199c3394332b5cf6cc76a7ebe77610044b332aecb42a1771edbd65104833f4af", - "10513888b62572e6acf4147465bf4a7ac6416dd48eb03c49b13a4b4332e18c4c", - "14267072085228373a584741bb0bdc84b2eadf76b3943431f964f56de37db0db", - "0bd0afc8b66c76e1a9c3f1df18dec78cfd4d5915eff635f4684fd17f740efd67", - "07a1ede5b2a43711f9d1590fb40adb80cf66de2d6890a230c8f7d51a06af2c39", - "25e69119f1a08617ab204097e820f82e9a05606680abba0fde0db81e1fd0bad3", - "2f52c04cd7657c69c53a1007cae1388b105945bc81071e79a8f278b498972a28", - "197634de804ecbb8f59ac82ba53146144dc962d42388727060291eca44f588c6", - "170de61cbe837571c926773b36c73bf13f2f5540c559b43a4257bd3fb2445bcc", - "0796e72aeac8238d979f6878c0ffa8bf81fdd5223c0fb19ee005d7d17cfc93fa", - "10e297ec13f69da265157f71f56d41507b689b80e15a684a7d3fdae2b4d2e758", - "2f5284398d7fa56a116d581224ea9b82427f4fbefd6a0aa90ec15ffcdfe6ef3a", - "032e7d83353e1909df1b2924dc6925883feb94e14d61847c7f7918aa7f1ecdeb", - "12ecc47b36279fda239b5262b4b1966d9c044500c2300abbf38a5954c3b0dd11", - "14cc1fb590aef7dc954efd3a4c53a4b1e286d09cb2476ce507b601fb82a084e0", - "2cc55c74693f6a65bdf7ade43d1bed32c9d2fd61dc357c9a41adf722be784455", - "05aa5b48bb735799970ccfa1029b4e28f48c3ea6f3410df016c033ed043a68d7", - "0bc0975e876478f57e2a7b031f8ce2a38dee2029959cd536a96af64c650cf304", - "283121e657b0ad713eafcb2503d1c808bb1d51ea82582330999983db93f13198", - "16d5f557f636d7eac66776a87ead7d3957605a4e17839c5f7d32dc452b48ea8a", - "28394c22094dd78bfb942e3bf4e1f305538bd9eed5690715bb4f27c1c0ca5cfb", - "1af54931d760a0661b21cb5985522848d165b47e5260fe6c02b582ac09f1adda", - "28d32bb1e175dc93a86357b6b39e3102f1390a9e6c3934c73de9250b1d6e373b", - "1c8668339c126322317b90c15406a1b2f08475d0cbfbd1320172e3151eaf530f", - "2eddf87dabd2df616e6afcadb6c1dce2c0dcd074d9eb44dd3a670f9b5e081106", - "071f91fef7e3a13e6e98f1d2f4bb3b08973df8c6715f066cb9f70f47db8db3d4", - "0c9462aee892e3b878c67bf9c0a99a0a7dd0302a807bffd347cd76a48106bfe9", - "0d447987f491bf61f15fc0a9f909919a93b2210d624195293fd600a2c9266fe8", - "0e3dadc74b8817b2b4cb32a78a6c910060e5a4cd79cbfd6a1146069a87e420a7", - "278c0bc5addb7303cff9b3570df6176493de54f43f15aae2416d9bc170957333", - "17dfe0688d2afde487cae0e14a01f02384e7b5c61a659c8bf4df4f36cbf6012c", - "08b4dff73178cce114f19cd5d5d665f4811d23913e988af6e2e9848f94dbacb4", - "1ffb1a7bb1827965bf2259c61f4cc3a579c475e00551939e0201486e51fbe0ab", - "1462aafe0e864b2e54e7d62c594059b464ba9a3e4a3a220e28b22bc598d1df83", - "1d52e0faf9391bc44ba1f66fe637e8e95dde8e7eee9491f9471aa8aae5ed133e", - "13246f6065b8696cb848322da363344f1786820d3d1847dd7210c2fec44393d6", - "133d1b51829583b18d2afaa251686a4148f8ca24dce3fc378ba9ddc1a3d66a4c", - "06f5e01c175eb4bbdcfc07728b092480f2cf0d396fd72e7ff7694357b386c575", - "08c5195b776aab95da6ca17eac81849df8785af3373526ae6a76e7fa4fe95673", - "14889763041484601e85d4ff8159336a8793f18d5edb865974538ad5b58db01a", - "0d454faa86f40794dd02f256c1a338c22f3c814c847b4e205cf20082ff1a5827", - "287e7a4cea0baa17d1c3132536df29f057d03abf655feda515cee4bd45001de8", - "1658219d6a2fddc4251f3432bbc8b9e49684fcd79aae97a0e78df0104d060ff0", - "15cb0566bc07a7ff76ce7fb625640816c32716f2fcc031844aafb2f09b3266eb", - "251fba7c2bccc579147461d7caed44ffc4d7aba749f7c480a143fcc52ff6d0d4", - "0f88bd8cbf293e53bd7ea661309647621bf243b07c3010867a71e81d56daa32e", - "2e50739ded1d40ef1faffa7247fb35f3f3d8738bb300053009720f464b245b4a", - "08a860efa3e963177cd69cd935fd4ce61812deb1ef476eba5c18b53a1825f73d", - "02ef0b5bfd2869670ddc1dde1c9a29ac9a93a28633dd55cd543dd93d031a3776", - "00ad678ff09f4f1d62f3eb67a93e95202c4002b4435a3930b2e97fc8a437c860", - "2c53a9ac608631a119e7f57ed5cb0498134671e6f517757546b3ff61dc24ea9d", - "0b262e363290fd3157aa34482f7d3b63e7293e766a34c528fcaeac7b78c669ab", - "2c729367130f7492d6c7fa81d933e572ceb2cae48abff54290364f7ffd98bbe2", - "0c52b752688f7c1231a81213da5d399f0de08127a0410ab6cec26224520a7302", - "015ed07c528f1f75c39013233daae79023c9a10051e272b2a0a5596745b50def", - "054c68de3da880b3efd04d6dd592070402cd24056b7c170657335e9ccfb45ed9", - "0653a2625249ca142027b136af44aa3bea7ce98801ab7964102b20385ed3e38f", - "128265fbcf4f8dc26f44e5de2ccbd57ac858b7a1a3d955a1cafe98de79d239ef", - "290a90817d105423426ab71c2b097df309086c3cc0b83ccb1bf90486cbce4114", - "0ec81adacd88f9f1401c42ceb56348bbf36181a0c03f2512e34fdef39f23859b", - "0059843dff350356ce8db94fc588542dcd43c7621d326a56c7de9126548a84ef", - "05f1d7d0fc3a5e6bfc55ce75e7688236e879a7f60cb52f138f52069b048f05a9", - "2dadc5fa46bbc50df63dadfc9b4fa72bd344e26e93f0fbc184f03bf4a76b51e1", - "1bf5f44265a2400afe65e220ed0c8b49306770e192cfcbe06c8c28206a42cd78", - "0f484d2249c289e95f4c1b2fa0330572037b157ae41187aebf92468d617dacd5", - "1a4dd8999a4847cb26d5cc32ac2b94ff7f5e4e6a37263e34cb18dd53d8be1b75", - "2fbf545602120abfff0a56316d9143d152d43816ef782a67780e1b8f9252a4ff", - "1835d89422d3d824fad14501a3f3c8a6ae474df2b5a29011b5c36030c2b8bdfe", - "18c215d302d89a958d8d9cdad60b5010024e91b510bcab7ffbb384cd21b625da", - "0179533ed710624344ced7dd685ab4dbce139efd5ea097e8adbd02c32aaac947", - "07b91c56dd39dd5d5de474540858aa9b5cd0d91cad2099bd14befb060f4f3b96", - "2a79af347cb1fa3996755c7f68ad83f86b86ba81bd2b9fa98948cfcef63cce23", - "0c38e0161d3e3d317108e518dc74150f8205fb74083fd47b3b88aafc9d0130cf", - "0d65129efa0b7fe99f91e540166753bbbff12cdaa9b5777208f26ba72a87b52a", - "065923e0aa248690099aa247581f481061d9243cedec15a538c6f3dabc54ed3f", - "209749a7661b281882cd713683824ed6122820968a9552ed27f208a45c2837ec", - "0567e0493586c14d0ef128252f9a20c74602ec56626b5c2f3644fc79a7983a16", - "2a3746ab2d1fd023c90559abcb8c36d3273b3685b7da3332b3162e894a6cbcea", - "2fe83a4aa399397b998bc1bf32a322b69e58244d60ccfb546c013ec9818e1355", - "2cba41b38555075f0caa9773c8f358d018620c4fec64c15142e33bae27ff07be", - "262d890f3c3d9ebe6eb150754a0677d94a64f645ddc813eb87f82418160376bc", - "184043dc9ed8d23817f34010c7689116620fb892ebe7b92e7afeb2dff8203bb0", - "16150e6cd627f1aab252d573c715c3e132d63d714e232c200a86db5279dc24f9", - "1aa1be02875b4dd93beaa0841dc74dd43b2f69accd3c3625cd28e720fc3077be", - "0870eb40106c6c25725f4e303741257e730098d7d4f7c07155bc89c805f3e573", - "2c174e5eaedc48a0f83b0638038d79d5ce719a7ba41a974f68dc307a4d7df27e", - "1c5f8c2978c5db3c6483e6c59ecfa4b4591f81c346f882166fe1395f09067c01", - "25a5229df981407d38b35494facd5d3be74835427a084bc796046ee533804256", - "14198c56049b0bafe24c1e58227a15dfdc1730f7570a0425cc3f5175078d3b46", - "06f649866a0de8a7127623c9a87e528dea9d7df9a761fd1bbce65bc1dccc06aa", - "1164c0172f7edcf878d89bec7c593dbac32f366f7c26136c219c9ff79fb4ba8f", - "1d57c7d112c7559eef860394ffa55686dc4addc269e1f4763a3a329d85b9203c", - "29c8787c8830fac709c646dbfda04db6ecf9f508e056fb42d9a7efd3bb0a0360", - "23ef9d9c4a48657f835f302dd6f6efa94f21f7d65fd188fe53c540bc7fbb48f2", - "259ff75fdd8a23943f9d9e91e335395223a11bde135182fc543af4763a9c491b", - "1b14061e2f2c468feb62b9ce08729d60a700aad2f37e7aefdcd977243a50f02f", - "2a79870f9070251178edd6c30596db17a75375b7bc163d39cfa97f42bea1e487", - "2920015344e43aa0e279bb8bbd180ad00f80a2d88d7ee3d75f794ea94f788c5c", - "262f785087e1fb1873a803e55d7f1b6e1d31ae6ce6c25ad0a1ce39f3dc870765", - "2f34183f18efd7f36cf92ef3310ea2b5fcbdc68a08ec1246f86ec7821bdd3593", - "24976ddc28c17b43f06aff004f5237fdf5216bcc98656c4cbfd80d2ceb28f5b4", - "1c75ba32a127cae227f83616357be97ccf95559f4e10a202f6f073f6615708a2", - "29a2d25cbda9f5b67fa860e6d42bd3408a8538b9c6879851db68d2a6bcafc02d", - "0aa84212e380e99137636932c0aadb021c2ecd448bfde7f9bba46dbfae9847c5", - "21f78689e3e2585bd2fa23848df576d8ca6a20c1e22ad912ba5e9bd9317f072c", - "293a1159d1c02a6429adbb0da020a819a687ee7047679c3c60d58c3ff98ae3ea", - "1a7d485f430c376e12fc7d1b3613a511822193599e15e0b30d214cb989edd72d", - "148f89c16be581d1dde28de8b229a14509505effd37e672e3f47a90515f0767d", - "03c2411a03c742bb60b08116a2fd8ea86e1cbaa1f6f82b45951801caab0a6448", - "05b054684c6e494317541efe51da10ca76fb31a10452b442e4993814a08b6bf1", - "1ca534bb0ce1f2ae8149ababf167c5491f00edb4b144f6ea92a7d7918b6d4cd3", - "1c2740412825060b5f2a80d387fd83d5023d1be26ba6eb2b0a5d8e90ecf98f44", - "15832c8f5667b380e31a84435232af18e685d784d201faf7b9bbae68c20aca82", - "14d6fefe0a848db15e0baddc508b71614642dc5dca6e267a4c082eedb7f22f3e", - "0c0a1384c660a036ad581bcce6af24ca06f7b647be7fea648cef6355901fadb1", - "24d5243e9dfd338ac19c7a01a6edb2ddfafb256e6b84964d3c50cb3fd8dca48e", - "0a4d7c32d85fe6458c9b48597aa03087ff6ad9a766ae6e3db65e2b23b6d7dd52", - "1db213ff1511c1dbd7f764afcafb3d1ac5811e7a5795fe61f00ab8abad903bdd", - "1665a557b4a74548ceec6f598ab5684f32bcaa867c12e8d1abdd6acee1285792", - "2fd5d39615c3cfbe8ccc5e362e635cfe06c588e9bc0cb1d95c1df71dad1c0b7d", - "100e6f9483e9c38ce0a7fe26cfd8bd1d915a967ef85e9c3126b6f97b8c67ab0f", - "02f04bc9ea7e55f3901d844e427bc348f934f48551eb0b60051f9ee756a6aa3c", - "18bf6a3dc3320590adae58baf410b4367785d21d0a38e1fd8ad0b5ac73ecf609" - ]; - - let mut acc = Fr::one(); - for i in 0..10000 { - assert_eq!(expected[i], into_hex(acc).unwrap()); - assert_eq!(from_hex::(expected[i]).unwrap(), acc); - - acc = acc * acc + acc + acc.inverse().unwrap(); - } -} - -#[test] -fn fq_vectors() { - let expected = vec![ - "0000000000000000000000000000000000000000000000000000000000000001", - "0000000000000000000000000000000000000000000000000000000000000003", - "2042def740cbc01bd03583cf0100e593ba56470b9af68708d2c05d6490535391", - "05f549777735c612f97ae4737de107ce0595b32ccf5ba7ee06a25fa9a2ba0eea", - 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"12b5c306a0c9c2395d5c8136e0ab2bbc87ddb5208f952c43133e3bb006f163ef", - "2ed3a29fc700319e791423611cb9338f091fc6a3a27dd4149142bef7b8c6a6ae", - "18d0bbd2f7b6549b9a6fd031da5e90c70117b249ecba30324391adfa2dccf40a", - "1d0141680ed9d4c565c23ceb32ef14bb1cc850da92b68b42ead2fff263a50dc3", - "0596f155f08160ab8c1f499b53390914b811c64a8a8d70e5b00a7802e4acdf0d", - "076eb4c9c6ad667ae7dd8b1f76870b67875f1134868da6c48965e80e04125d87", - "1ba8aa1a91d70f2c5bbde3ecc0a8a8ec5eadd9109707bbbf9dc42f201dd7781a", - "0b309588aa15ca721b860e9e16b63e4bc0c9fdbf9f33c803864c2186faf546fa", - "1d26d1b2fa587e552742939e1f7a5c1094284d73ea26300dc0164296d1add353", - "0dd88cf71704e5a22780414827f9d3f901e26a7eaa03bf02fbb9d257459e29b7", - "13e02ee85bb3a1dbd4140760f883735c44a9df7b7cf6fe36ef47cc029243bfaf", - "26b072961338627a467fe65b4d9b840eb6adeb62c880880949506c200b72b159", - "1b99c0d332ed873997650ab60f2546a58c5db89db8eedc577cf360dd05c5a175", - "1d595d764c0920d9b829e486845d24357400a14735b0cdeab09274be0c087f20", - "1f0807972bcdcd4223e8fcc5d9aa66dcb3547763dccf039be8810e36d86b59b5", - "1129abbc9892b557c6cc1bc5e887dbf3bac555fae48d14dd29dd7fe047306cec", - "06fe41202ffcc22a7175c24e1276c68be31fd025a5f7701d7a58e2dea387f3bf", - "11c8c337e529eb09ec48a2af3d260ab53f5f5e1a075080d6a92a29b99b206ab9", - "2d0faba58fce65e3d9f4506917a2e349e6a83d7f240c011d7020479e27e2b457", - "2f4f26f8db0b4bf38398616c1e30563e92c2b3d6273ea31310d6c09327d7166a", - "17745d3a6e217f23fdf7e9b249f9667ca49665c4130661f5ad6ba3d2b9997263", - "2b1cf0745a1fb1b55808db2eccdcd5a075618ae476f231baee9b36f8957e691c", - "23cc30c9d4cfdee0d8a61d2d70bd59b9d37be22c8bece8f7d3b11eece18d77ac", - "2714194c494be47166bc32801e3b7bafa83073f5054d5e39ce9e536d2797ace5", - "1ae0089176f96175631a459a378462df32b6bacc53e06dd95ecc1638d6694e6d", - "15c1bac5b8fbfe6770f6cfba64bc668ba6fa58aa3a0b7886ae97be77652b99c9", - "03b9f1628697c6da5226d87f8f93503f6bdf47aed5f78b6faea742c36fe62057", - "2c828412192724cfdc6af3b165d3d0c0a8c71c4659b3df1b150a79c9ad0bb5bc", - "018b680160db10cbb31241f5b637c06e62fcfbfe58492dfeab1b4e3799abe82d", - "0b535a898c2dbf2a4f65d15207f368185a9c8306ad8e5c5edb86be8e84ecff50", - "29324096c65af5453b3396d4bc3e4027d340bdf010ebb3a24e6468e896147463", - "2b178d913c35ef5f24d35af5c1defd0f525456328267130cd04b0a337266ff9a", - "0427f640bd8e11be9e83acfdedafd4e4b69ae12e663cb9fd447e2e73089a2f03", - "29a30a42fde8bf7f79bc57abff5ba6ac4c4e77993a37ec07f9914c99dd8d1b3f", - "12933a990c79258d28d90e9fb5fa451ba219206ae6e7cd56339b4ac5f6e9c6e5", - "2ca30dc3c18dc52f9e8fd59d80cecfc41c2210163c044a9cfc46a8234abe44a1", - "15039ba21746a75f4052e59167c8fe61befa3c228b67688926692ae34a8f8af9", - "0d013043d7f43c1c3d7aa1e9771d4f38eeee78d6992f2a84a7c64c20632e54cf", - "24770a0fcfc79a72d55c7a7f90d1a66494c745643aab2a08b4b47562d643a4ce", - "00f5edbb6253299639f0e366835edff5a941a1e29c954571283455bfaf94c0ce", - "28d5f124104d0ed06f3225e41b28bb431e7271e383935f708e558ba5d05bf667", - "00b8c2bb4918bc3a3bb76636f0a1173374c803aadb1003dc414a5fbb46e81174", - "08d20b914f6a7b4115a092b4976ea22ecea0ae58cfdf1679320b6b6bae9152c2", - "017b4defb2cc581e394d666ea82c4b09e56b57a1b503c8a29b2053b5c4b49a15", - "0591f82cb330a66704560c33f4189e8395e2646d0e0bcc8afae9d061dd928cbd", - "0d45e88a959bdd51c13a22e35cf22e30d9ef425fcca3aaef605e6359a0e7bcb2", - "15d320a4187dfe9ddef4378687932e16ff24583e7f9872855b566cef8d6fa00f", - "05cc9867eaf7a58de61bed98fea0df793ad0e6b9224a3566cac59ca647de5fe4", - "14418f317207f95eacc37db9e6bfd42d2594abda2e09e4d8bf853366453431c5", - "045456a3b2f901ba8a4cb79701218c4cad120a11830d7ce95f33130a0d994aea", - "1ad7a2c79c70078007734dc96d3647224a8e51bf7be88fdbd9e7dd12a65846ea", - "289469ff983ad3a6b33ce1d25435381344d13a3dc7b0b15f15389dccb078ecea", - "2da5ecce164e53c79a705da5ec8d46efdb8fc2fe102ac7e4307cf8c9f71540b7", - "19a4a3a81f818d5cd64a8858047f7312e16a074ee00a5730f07f35b611a06d8d", - "140239abfb94dbe1c517b537c230e0e36b15e6ff28e249d1573e412d2e6392c1", - "046ff7e86f24a11fb0e200a979f7c7a27a4dcc114a368fd618153b68c37e35a1" - ]; - - let mut acc = Fq::one(); - for i in 0..10000 { - assert_eq!(expected[i], into_hex(acc).unwrap()); - assert_eq!(from_hex::(expected[i]).unwrap(), acc); - - acc = acc * acc + acc + acc.inverse().unwrap(); - } -} diff --git a/tests/g1_g2_vectors.rs b/tests/g1_g2_vectors.rs deleted file mode 100644 index 587c1cf..0000000 --- a/tests/g1_g2_vectors.rs +++ /dev/null @@ -1,20069 +0,0 @@ -extern crate rand; -extern crate bn; -mod serialization; - -use bn::*; -use self::serialization::*; - -#[test] -fn serialization_and_deserialization() { - let b = Fr::random(&mut rand::thread_rng()); - - let mut a = G1::one(); - for _ in 0..100 { - a = a * b; - - assert_eq!(reserialize(a), a); - } - - let mut a = G2::one(); - for _ in 0..100 { - a = a * b; - - assert_eq!(reserialize(a), a); - } -} - -#[test] -fn serialization_edge_cases() { - assert_eq!(from_hex::("00").unwrap(), G1::zero()); - assert_eq!(from_hex::("00").unwrap(), G2::zero()); - assert!(from_hex::("23").is_none()); - assert!(from_hex::("23").is_none()); - - // not points on the curve - assert!(from_hex::("04177cedb64589bde7a64ad24f89bbb8c9f05535810865aaea8fbf8184ff9e120313500226b2422d2068614d1c8c7146c806a97743e78d9901748a9ded08ea9e5f").is_none()); - assert!(from_hex::("041800deef121b1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c212c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b").is_none()); -} - -#[test] -fn g1_vectors() { - let expected = vec![ - "0400000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", - "040e97c669de7c670d734ca98a3bc5176c8f82aa5e44f9a8780998c22dfa5fb5ea19305ad020d76d8529f57dbdc43f7e77a637f17b2d5db5b06a2554c1151b1255", - "04070eef7bbfe7c9fa76338ed6d6a12b84f61a1a1b5b4d54c009b3993e2262c5fb1f4118919fac6678cb671ccfe5a3ab7ffc42dae56e8f4382ea3e6582ea7fdd15", - "041ce66de558c33edf36b637bd39478e2f317f674e0559025d1e428f37dda84c342e916be0e1e8ab1ba6a9ef642a2f1de44c1f6f91aca23991cb636dbb997cbc01", - "042e8d7e2ab119b53b2e2e5f8ddda2116aa821949ae0bd00a6ee6ebbe130397c0709e07974bfeae5c973c098c6dff65e864ee6ee05e9ccd1d61c8ca72e0c49232a", - "040460253e7e4e9804bdc30e1d76f98d7f7fcb4a6845fd6f9df0f06a18e1a2ebb3066fddd38227281acd80b6b6253f5d89e401918586254edad1a56fbb8544dbbd", - "04130f5f5f20846ffcd6dbfded402bebb7bb07e0a4cb2024bc84262de67498dd7e18dfc445b80fd0a1843d6ddb5ffc16cb8872c373b7adb9fd1b98ccc922318966", - "042849878760819716f11108e902836a72f4bba88eadbe26b5b9f53e75c1f8714f0732eeeaacbbde8dce07be752d413d58538fc11f82a1c434afac5c27760e8688", - "041846eb3215c26d8be94d8cb688f19f59db6c771bc8155d1fff826440bdaf8ce720553790d70aeccfb178e6c33f4331b8cc24e02c8ae8b5a0bb9b57a9c1132001", - "0421f8b0a60f933351788799a7271fce8eb3349b98b1e0dae6a1de4eebba06daed2f966958654ace4bad972296bfd8d3f1568954bec25b665c0fc8f64f1a0c9856", - "04163ddafd9f4677caa2b8feb510a6b0ef09191a00adfd9f09ae3e59d687af8ccb1a47d8362079b22c9064718f02948da7832a8e123b8c6e3730a9e7e137f84da7", - "041ac98fe325a2faf01816da51b3733edb8a13935dc0b82a6fc2667773d09461ce258861533cd79b9ca801a366e40dbf61431296ca6431b51e61adb41e389328ea", - "040dfcd832e70b1ebfc5f07d66ef71e88f1903eb69e25a43e17fcb119305f936a101f6022efdd7bb49bb2f9882d1edb54a618117ac9a213776ee09661dc813cb90", - "041c11d08dd28ed037fb7800988bf9ed0ffe5dea2ee321ba36725bbc2fbda12df82151ba8776a883a4d2fdb5daefb681aed75636db330956b36a795031b238494a", - "0407592e35e3444f61a5cd4bd3b62765ab5d67ff57b88aa781bfc0a14017746f9f2ff61c2caf223a33ea998503491389ec7b5ef2797f9d7bf5b63640cff086bc11", - "040a5e52f3b28b3d8a4eae2332ddcfaeb3300432f9c11409c4388607dfe2a0dd171781fd5e8fffab898a916ee4436f487b7ff9a0a7ffdae2e0f98d6fc1075f60fe", - "042db55c23fcdffc4000befcc40b612d1bc38d8e34ba4c1eb68f7a1446f851630d200c8cc5cf724a332ac366160836f91c086df5c8e023e0131eac51f1c18431c3", - "04283f5279f2bc83c2c0829d1814f066d1828c267c95edc39ad4853c5cb35c02dd1f0f1bfd04a340863a34d8638c0b7c254473da29ec0c0a95fae6a7ccde78c740", - "0401cf54e2dd9c2c97a96b809781114b82aee7d0b9f648d91fe01533062f99fe590037123d18acef099417572bdb041f77ef044b9c3fbef0ef0f9894f9a4061313", - "040b0115940193b2c17fb561c317ed88d5b5bac173f4eacd887fc8de03b9915ce62be17e169ae45579e2f0982b686a611309a8435d1e2f0de9a49c97f72679c795", - "04194e71fb26deed74c5681a0e616ed67135add9f3eb97fba96202539876fe0a642b27a2f7a125e849eca00af763e532d5c86ab650bcded04d47d26d8c6c62c139", - "04001082425143d275f44e16040d7f8922ccdcd77892cd80796a86051f4ff5b2de272e4a7dbfccbd7ef79cae19d0de3a0697adc6cc44d99f014187a99b6c26d7cc", - "041e6b87d81c1af93bacf529258f36145b434b84e843e0963674c529133b7ccbdc09384b95b6c343d8012f4a8b3a1bd6f34142d7688963df85c38369638b1c3117", - "041e34c8d7c0ba039b67537c75939a14fd61598babc9a448cd103601253b93692c1eb61a4444ac063eb1ae75e77df30f69cda5dadc08912727ce2426276fca10ad", - "041cd5b925c2174a380cf78f14a57388711b91c90010c55c0bea173cf77443869f1f7fdb3f0414e61d12589a46d8ae49f95ef9b1bece46a85d2d14d2deed1cbdaa", - "042826a17e76e78d1883003a32e8cabf44ea62087a2ec95ef68d72ed31f0dc0eab11d1fcb397c18539c7ed620a502fba6f4ee19adc17aaf9501b801e72a21c7b9d", - "0425b7a1770cc9e63055969af6b201dc7b6b5c8ac819b6ef82f39d3dec427a41c914b4f4c56c3fd44b34430f2a5cb7ae272c1a6fbcd86a22255db728fcc91d14b3", - "04150f39cb53bcf80d39c77a2a2d52ed7f3e0ce5b576a89981b9d9d6aee05110131ad181c717291b23eb881845ba88903859be7f65fc6e795507574452a03d4e25", - "041555ccb4555301cd5e3beaa6d0b8778a4505b72135567322f9a5a540e3b8a4fa127f16e181d7e3a75a2d944091c78caf9849eb6c3f3b24242c514e42fd30c0b3", - "042349519b9c99cf376534801d42d098b2541903f5fd07e0fa81d71ea68c806f89086bad59e91f4341cef634582513b9359c751e3640c0fa9a205a6bde1fdaf697", - "041033e55052e5ad95302c5dbd98a7be3387d605956d0eec74576a4251eb58f4da2534b51e49ce5768a4bef802e159fe1ffa37dba8437669d4c31292a2ecd24e4d", - 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"041ae5ec96dcbfa223f504eae49bd7e804fbd0b17a968b701a2360f375b7c019ec1ffa2788d9996473a854b657a0b3dca8e14287de5c032c2127502f9d516e738f", - "042dbffb2c2ff6c1772eb52647c6eab4bf72a7d8e93ad0156fbe4bc2e83ffcb1822a5b10b3e973d3049a5092e10ebc4bbb62af19cdf21483243f81f0703e4a7ee1", - "041db4578f2a48385a7f4e4333a3a99e0716657c9b2087ce3ee0b6eb2052311d0408846afd50ba1bb0bcf1c511dfade9a9b724e6ccc8f96598773d59d047c7b135", - "0404d9b7acf40cc2601842ad5df57cf8017c7e61bb0aa3f5fbe2bb17e17ca738431128987bf4eb7873ac0ee3493ef4a12bf1220d9a3b2c6244385679aa17c4b07d", - "0400fd6838356358072a63dbb2ada3b9c1580b7b27ffe349bb8623c7254056435021130c8ea14ccde0d53bedb88e85e2b104326a94cef98e62fa44f8d7b727bf34", - "041695a424a7ca05f6b86265e4cf38e9f994295901aa00f55e345cc1f256f2a37e11e93a451fd6473f8647cffbfcb8e5e88a08fd27be3075903e75573f7bfed3f9", - "041b65de7d91cc0f07a2f1400986ef30776f82269809db03fe8e678ad495984f73266ffc1fde898324c2c45ba6a68ba01ba8ad4ed1f6bd7536ece655d0134e27d7", - "04088989a891cb9e3933bc4b39f872cf7c4258a03b35dab2ad4631b7d4b3c18ade28c45749db4ba761ae208d76ea6209e4db6224d6449621e7ed71cf9802a1704c", - "04299da297b4cb97d4a53111246d30e8139193bfa36d4414ed3f636761aa1380b20d710c8ad3ae2f1b0410faf99874a519782bb6564f1247d5e504b4d572414d7e", - "041a587ba03087c2eadfe9e28de4bf3852f6f037f76682757c05ba38058ccb52e00fe96ee800a1dda0758f0bd8de09c4dbfdb43b3935dc9027bac1591993b929a2", - "0407de369afcca2867a456489c0196aaebaebe5c8918ee0d0703f62e58b441be0c2ec36deb8f82eef0228c9b5f258d32fd4a1b20c6885b02d5dcfb76aba346e614", - "042a58c7b42a30e920b8452ffda805d04f8dc9ff0abb50e8c1572a622675a9a9f612002af09f168d0fed93dd53aad456e6d6b1ab7c9c91c3bb5c91f7aa10811eab", - "0419329242c09bd2eb48142f905e017a5b6bdb16923ba08fd8aef4743045db5f3a2a1897eea7c9fc6fa5b6d04640aa05402de9e182678dcd07eaab39014c5b646c", - "040aad228124bbf77ba295de70bc7f706bef61408d9df745099df476ea73602298184ea4b758e80e8108d74b03b34f7493eac7e39898ecc649449dbf3ae8de5e07", - "04120ebdc28ae75eacb634b08c899b8d69c5169cd546ce8cb2dcd71332c65b5aea23f462800f85090cf093b48313f42e2393ff59bf1961fc37b00061c7bea51cc7", - "040e6e91db838cd81b6050d8450900edee1909885db64aa0210e7e8f880ce6710f16a95384832929b34715bc748fccf98823fa538cc2197d5f3aeeb9c38b60582a", - "04146b6f644556092e484177c3dbf605fd38b1a9a2c0103a9a75a520fc05d3fdb8044b74a909c4a6b3c2331000923afd3032af41c5b5e30bb5748bc4fe761745b1", - "0405f6ad5a1e1f550cae7008c2fc8fe429b0cf4bb181a0b7232a06bf32b7ee2d970e68bfb230d4fa30a7e7b3591e8cd3894071b1f9df6888f00d488a4f25205631", - "04252c651e2c65e304a69f238f2ba44d8130b4b2759950239a1765985bc8a2148511e39d1cf7cea1661b35b8eb381a2a5697bd69bd745bbfa1cc8f039d3ecc9c9c", - "041c470202c3bc79abeb8ac5dbbc9d7a32ec695269229c9f73fd8e34e076a7353928226defd9aba470204d10e989b16ea18f04870d24fd03ca39239c97448a92d2", - "042d81b6e18797b962f46687512d92e46a4a07b4b08158ff0651f555cae926134819944530c26c6370a0b2690fbc844efc7b72c95c1543a8ac7551390e533e1940", - "0407ec1a7f17116d5260d1aca211cf8d6d41c9e2242110965eebf72bc93e052d9d2afcb3bd2d0dac62f2c57cb4f261d924c69222080d3d517595d9a3982fd3af1e", - "04164e98f79b15a9a0a96547151cc9a05c732fc7dd1e78ac44c6d68ab4a6ab21c42f708da63a29a89bcec03685a7d853b67739ebf01d3150f22b000c446686dd4f", - "0411be9eb2675f561271541f1637aa3f7ee6e61cb7c56f2ea78786e2a5b57a311f2aa4fa347c06b24b8430963c8bd80cf0eff6069fbca1f7b8e436a11e965dad13", - "0408558b2de18c446638d2da513f83ec316ca299b7bc823d3a7300a2f2bf205ac003b7cc869dab6aefd9cc8d91fc80d91a8720e2db7ce4c5fc57996e4dc1e1d210", - "041594c1d20ece1b3433ca1ee39b4476b3637376a0c74617d610052ab39d5195440de80e37a34878badaa241710c00665059874ac69e485a9cc85f765b6f364a32", - "04216d92167c9a925eb55403e14e01f428a266de374d923d2475d2ca44763de1d40fe8f70b4a8582a15d71735e1c86d475c754e0991ab021317a369cb55b6d7077", - "0407bb9f4748af5a1a58f7303c9f4ced9f365c1b2c7b9e5b8dd9f4450ca078623f29718e3995657751da76bdf259548b1a4e42de4c5f7454513ab9fdd842b96b4c", - "04058c9cd670184da6bb007379234e0fd2db702211f0e57f0af0a4732847a060ae113f7b29411ac80915bad1fccbbcb3a4036fbc3b8ec760dac65e95d3ce4499d4", - "040b09dc346bcf005e484a0c858287076b289059c4b8983024548efdb1b446612e198ef0d6881c40c186d0a4dd1036283d3a21148fc0955381793979c09dbe0896", - "0424ae3f2b0e02a5e62f07ed251e2e6f4a855095dcdba6973e0cb8068e0399ae652a725d32318cbfea203c0349926be5dda96b6965bcf40d2fc8dcf28ca1d326e0", - "0418f85db37b280d36012b3d632655af37818acd26d3f728c7d75144f3e20b92f826f2d13f37a852f8348531e2e0879dcf7ff65806f3ea66c3b6a8dc0b1c39d43c", - "042736509f322640b10fb1692ccb00c7b62569c98150e32bfca0bb11c7ae9eab8304ffcc57689996edda19f7a970755d675d914b0a6b6de5a580a4959656c73e7f", - "04285a9a4cf39e825ba5087c6f8a510796bb6d9032ac850e4bf03c24141926f0ee03aba476e4c6ee490cfbb0a6ba7099c51e8c8d1b49d76d745f5fd2facd5e8200", - "0418285e97e1e0e28dc1a5fc83a6e1c31ca5519981e34bf1319629184cb703f7861b23cd8d3edc96cdba32cbbcd4e2a04e8b6dded2c85e85fa2468e700d6010309", - "041ef5b3b3fc4bff399672777c708a88ee42262673fc6c57e3a9bdeabde2db582919290c138b58db2673d5bbef77610797ba81085908b12163f8fb93ae64c1ab8f", - "042c26105a9aab37f29b053e856954290848b78be38f699c07b294c0019603501d14a3bd1b9ad9c1969f6dd44cefa5ff983f3e6cecd088e98c72450513c89dff23", - "042630e3f0ae0769000e292e99c3502e2835b465e22192fd8989f64c1735bee7d002242fb42015c31d3d82d24422b06b420f7515cb7022c4a90ecba8a5ee7e786c", - "04231d053240d7dd683ac4197f147d3f3456fdae9e275b5d5ec70f49fcf32d84752abf113de9b0b66f8216824484dd77abbb28490e15fd1e996d72ea43078752ac", - "04067ea7ab3c7436c0e5e599aad6ac93a8da911d0b0c8a4dd675514cf38c2b26bd1d5568576f01af2c14af20512a1562fd99c4964ba8a6b87f050ed48a0d651a3d", - "04022ddb868647dfd693233aac44a9118c48c03bd625c7282e785ec39cbac810660da0f9cf03835c77517478b6da2f3588dcba969b8c7e0eab53a20bcabf094f8c", - "042e6c41d5cabd81dc0cae667747f8f2a05c1f05547e0a35538e68ef8d6821e1440a39d78cc2608cfaa1899eb9b7e365595f0b1130af5baf63029ff7e10f814c8b", - "043028979488a631eac9c78b04e3d46992f5bd73384c40a9a96c8738983ab592bf1aef71cac4a3bcc5cadbf67d91a9f8011d004f97a003578e373caccb4229933c" - ]; - - let mut acc = G1::one(); - let by = Fr::from_str("23938123").unwrap(); - - for i in 0..10000 { - assert_eq!(expected[i], into_hex(acc).unwrap()); - assert_eq!(from_hex::(expected[i]).unwrap(), acc); - - acc = acc * by + acc; - } -} - -#[test] -fn g2_vectors() { - let expected = vec![ - "041800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c212c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", - "042c67838d2375c9478515736afbccbd342f2b27bc29f369a319dd2b29d50bd184193ffd9e54ef29c23952aa9ae94f6802a446a7ecdd3fb1f00050395137e4911c23851278a4cdf1b7653ce00932b20a7ec13fd73136807426be6326b07efee3651e45839e5349b05cac07f7a81a4d3a048a01a74af15a0a2d6f37b39525e45cd4", - "04279ad80fbb6eb72d134d52d0be1411e481afe72c638c86bd61db2909c31438ca11a6e74fe8a08754b4fc659bf7b069ec777d1ffe427d8642748c43ed1993ae2b156af13cccc742687f9966ec175a92bafdc1173bbab1bb204d34627876d1316c082f9249e1f6858650cba798b55165a6a73e28283714fec5fe73b980f99552ee", - "0423634c3ea29fcd751c4d671cb0dc2daf7988615f79fbd4ee445a37bc9e2e12f90ae5b6ab289fbd7a0695df2fee58226fec3382817512a31cc88718817ac03a392456d22e31bdf4407331afd3bbdeccfbfc0f3732fb0ebd8523e886e180b0579d0e339aabf3c64e1293285ec14d30ccf15c68d281afeb7af1d9cf7c64773b50d3", - "040c5934295f223bef0e1f44831f08b75c6fc552eff0beb648bb90c4e258b14db806705cef42e05a314f80be7b7bb23ec40eb6a90d5a66859b499d1d296dbbea361c0942411501cb08e7e55dd22bbced47794425fd99fe3ea1e209af95f1d619831c6008bc42af94a4ff0a5b7e5425a754f6ab0d733b5669cd744c38b164c918ad", - "04031464e9b247fec775c333ecb0679ae89c27475ce719977a5fc1b0040c789fd80ad528045f711392803e848793ae4e083e37451fdb854bb620ed0f72336788231bafb4e31a99738e56d052f989cf7b1bca5013947713526c695ecffdd035e8492e2460e141dbd6bbe2ceda50695147a8b3765c150747866b1f5ceb446185c822", - "041de296caa2d2039da52400b6f2f91736fd9182e4f4440db9fb954e793a111d85289eeec2ad6569c3deb666827263c0a5aa9f7fc359d65485f2842a2c23f4dd5005559f3ad1aff95d175c1b4a0580b8ea0ac1b6494301904f5087bcad94a39b7a187d5586ff24a34c19f1715d7c7d8b7f09d0f89ce0038aa763fa86cc06506f19", - "040483068b8e81116e03b4c0799641a969736bd8a148c1a831a8ff20518d27d4bd270577354d458f6788564de9e65bbd2ad10d595e18e621b6d09530b9ad055ef42965718433aab1d43b22bd356337b32d737425cf2e740c219ebaf703ace3051f178390c62692c8ffb5332fc623a43d9f4237c16ad296f6caef8160ac12513ed9", - "042a5414a4a6919ec4ef64f47b0ff21677819b0f6e4b912b83998b705b18b8e194199936d35f4a25b8fa509c51428cd1c5a0ad044026ce0fd94a691d18af55f66a27db9e27be985a916d54cceeaa14fb15760f8a42603fce9761256b37be948838181377f7e6ac6f8520ccac4ca1e6743a9d4fe5a358fe7d7219c9902715a6dc15", - "041b05fa148081bd5fba93120cc1213a54b8b5f273922317130eb2b4e26948e88f0310164a849e7807c9c157c81086ef09778b39f0bb9cecd41e61c4b6b7a932ff291a22436df666eaf40657583f7b18dfcc84385ffb53677ea9d77c8f7169b30f1807ca324bb6f74298091fd5b9d9fd1e3b844b079ab6654c031bd05c3a1e1c5a", - "0428c80df84cff15d5df27e2f0ec8c76294e12c79a88dd075b30d6154ca2c0053314298bdb83bf74d32273ba8dafde5fbed8330ed232efafb09babe53f4c346daa1c5f8d06b0471666655e9905348a8743ec03df1fd3a3ac4eca65a2a7298b2ac028896eef381991e3474ca48c2a5792f2a256d6fbf358234cd719862581b91508", - "04273e061f73b2c571927fbe3ebd4aeb35e6624d6d6c6f8ff5935d8ff5762f9043233563946114b9a15c48456d6a593079f2cddf8fa5a8486c02f4f7543b0855851ea949747bc481f673b8861ac58046647a652b6e297f0a889068a70b57fded6b1af7b3c3245f528b7133c1a13a69344bc0a08d043268d7f708247b41fb708992", - "04267d591d58ac0d192e14ba80f9ece4d4dec7e5fcd9a57f872223de65a3102d5a00dc2dd4bd57261e3e6b64cfcea5b044992925a98eb689c20072cd2f773138801463e2ac0887e862af0041cea40528529815c2883af6782546a237305894c5aa2d20dafa6c094f4d869a73e1f87f264c6ee36c1773c0b72322a7cda60e3f0b21", - "0405b9a785035b4f31a7ddbcda19d64d43983a8ccbd27b1d40af3883bff14630b308326a3c40cfa870ff36275b68d819fe2e2606f9ad44e25b89a2f19db2950db512a30c62572f61bf2576c098a360b1741b2de06c15058b248052709ff244cb432f4bba791cde6457a45bc8f50cb1816e3f48ce1788d6a387d8dcfc2bff078d58", - 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"042cf87fe2cb60ea7ef4ced02ca07c2305c9d7b2fc8ced970145a747ba9e7c817d2561e0cf2f2736516acad6c81746464db8f686014ac8f48024eba3388f37d0cc2b8c345794a33425bb7c32911b942c81d13b667cc478178126f3196260c9de5a3010af4059fdc4afd003e9fd8e32168e38e5f66d66ea97491a4a304cf52ddf24", - "04246ea3625d8278a8558084695bdd9aa75289d9b1bf9cd5801093d32a8cc5fefb23ccf9fc0448c208a3056ee0e7251207ee48e10b231d7fd50bead67f5e443e972a55d4df4bfef031156c56bbe9b622f137e245c747d3ac069fe24cd1d03cef070bf00134bd506164ae114e69a5afcb3e9f5fe95df1291b56bc4810d271af5ecf", - "041738591da86673d444d502785675c9a5583f398a48ef1277d3e0cb627088fcdc22a38a8aa5d89efda8951a5917485c061cbbd5d48b262c15d8438492eab9af5e24063e43e8cded9a95fdb521606e4ffc9563a04bd7bf26eb4cf325f3037e838e21a49ce8a3d626808f0a361fe9a98e7742d6cf9dc299946318fbc8739113f0ab", - "042f57fed83a2681e07bc98b484b1ace3ba49092fc3e970a43a7acee6fdda27ee10b81f1e114e2c3e4bb028c697aaf8b083aac7ce31c4d5bff669fe3032613000e11e38c97fae5a0ed670ee09cd00384268eddb41bc814c8c6f2be5a2f68ec7f0513d740fa6208ed52f0cc3ca65753567784669ee64d9ba413953cb72632463b94", - "04218eb4e113650df0743396c824e614f0354d014f4cf67ed42477f72f741ea6c80e49e91280d9a32b0a2878461b05e5d313819091a1e6d4b10dc152f311c0fa7b11af2d1cf5ede77b6a7053839e2ec94ab0c7ac8fe3f1d2ff818549e654bb99e52dc90357ad0c42796669683c0f9f722b6c367dd54954fef73c99b0803e1f7002", - "0408b16716a9c6f39b7b1ae426aab6e68ed6856c2b1cc7f3e3660f202d23b6a725161ed76b01951b06007b00e0c42ac94d4fb7e08b6f3e0276b53055d778c92d4114802030dff74f2bf79fe0f96550f483d392de5bedee72ece7f2d574a06d948a1ddaf45829ae1c27bb3ba4b419fc8bebac2a6adcc6f9e03c44646eaac429b0be", - "0423eab2a22b464dfb7ecbb3bbbad6adca021bbdffa4f3ab7ee82c635f15063b02044eb72c7e0fec6c5ac4d915fff834b505fd6374f656678b19aff845f1a4de1404681e1881d58ded0258684f1d13dff888cfe02bb04014e33dabeb5906676a7a1d337a6913842c6b8afea5758597d48e79631eb5f2aedc653701769428b75fe9", - "04296feefa792621b35955cf75374822d3d64917ebb64e240e9e92ea4aee95648a216e29e63fb853fb442ad9cb9986beb5b0a81cb55e5654b5597cf14c297c69e2144fb945fc0e2a1796bcb47f6694a0ec8eeadea8f13e37ff0b693802524b2c9114a823f52dd49fe270e683b86d1d4914c5fb68fbf6c8d84cbb3d02e96c8fea1f", - "041f1d23a32a74f3d49ca088bd92ab536580f41201f4b05fde71ae3f326dd7f1971286f32e01e22721fba126f21092f0790e0b55e8026934b4d7c93eea66947715078b583f42c84bfa6f89e72204512f6e3529189f119ca08d5d0f21f4e92bce6009fe74952aafef03f6f4e5dae814587bf811cd86daeb8d0b85fa2f39695baec3", - "040e6103aa16522f4c6e337c40b693dd05f4b5768b367d417b993e3e919b36f8a10609eced8fbe3cefd7675798333665d39c62ff2a098ccc0884f46a7fb117bd2e14c78d2dbfc9205d19b9e8f93c2d3a63a88518ef16409be9eb37631155a8084f0555f1841fec614ce28688939e1799212a6790851a3d637afb32323b093ea11e", - "040c06186d5335ec1361f1b331c7cd43b97af684773ae7bf2b54aca490d964d37525f7c35e63661e4f6fb3d0f1575aac4c1cb6625cb54fc68729af0fd91a2303e8137eabc895e1e8a3e32c1ea0901fe952d2674dff962f4d7ca1174bd6677472770d6f60b402fd50df4f4147fc4fbd71754647385366fdcf461f466de7bd444713", - "04008ead15a27a269f0d3a63ab8a73189429589d8330b81f2b95632e639cf89f38188319a12ae6529d3adaec6719da00ceb2d693f2926afc0ac2a4ffa5fb3ead610243788a2cd65790db8312b84ceaa7cf0d5d93a447e891797980bb70a8c906f928a4df487b0d10fe978362eaeec633ea821a2f221d2f55c40df9289c410a55e6", - "0430619b12592e765f5e6cbf59e03f9b3e8ac6fff137e4c247dfb94e8f86faf5dd2a8265675e7ae08d517564e408e80b7343fc34238e76a89c787737c0fc54796f2a58a4d5b2c80511fe1a57a57e921341908ce37edd6484d2cdebd7b3f852707c19a06e8e7dd56581a61545da1a90cbb512495726e7680e0f03a45ea6f5b398bd", - "04244c4a8f4b4bd6c6f06733069fdd59e4271c654efa00c0e849ef4bf3c86bc4fb2e68b48cf21dbe84b0cdda35c65b9f12104286e70c249289c783d13c8465f7521d68730ba0f3ee87984518e27a9f69d07d9a3e99417384e53185b09849c95ec208c3ce03a3bce2ccf8ca8fe7fee0a2c62ef6085a165d413021ff21bdf8e44613", - "042d8cf94684f05abc66f8ef29361c85ba639b30ea3b1e5b7bb37ed8bd28d854c32c6043796eb38e1f0b81cc7457f6ead402a64971473d6abc93cf7835976f05801259245bd9f5cc17dde1c895913a2bc97de6eb7d5c08190b4024b27ad2a0ab1a123ccb6fc013466fb7fe615be1dc70b5906334c6661b6430aaa94fdc534ac2da", - "042393b51a751d4f81b581a51158a1f6d39520147b0fb1195656bf70ffb53be6960c5028d3118a274ae0bea0e2d81a2e1b2b11746d1efa39193c26dd24db60a179025af6e2e7eb33b0b6eeb3bf2610163d925031b5b9b7d6325feb5b4a334c58d5075143b2a8a65608df5eeffd528a67e4dee3f390d544e55271f7abd76082e370", - "040f7441c00eb78328312438370386ea7a71c8612b6cac187d34501326737c16bd2d1a384225136974b78150b3cd1f2f10b67ecd663d1c10d9d8f960b222876100044166a93408859004bc8a6e288467e956f56fb665dd39742edaa51e5c348fe72b0d99ff24dbec44fda35095a33acbd45b87e8eab52ad0dae9f6bf70c22f6afd", - "04042a8273bbf6715fa8df49100e49d3fea4da16699cfd8d98cf9809a8212afb14060a7dc24f3d169a5a4127551ebdf5ba78aa889ed2bdef430069caf501ac43bf18c6c87157d704fd2dbd86eed864453bc4cf5630026c0f1a765f1949d83146f91f12ccef31797dd5e5ca5d1191bca2aab239dade5ab5eaba0a1ea0542732fe43", - "04049a2ef693f4317d257019794e63f25d91a81a1589bf8107e320bdfc8193030428016e2f4a168a9302960a9d32d3464649b4ea4bed3263e32f402dd2025635c92d4b28408d611bb485df35357bdffe8581fb4a1c951cf07dafc4ba9f9ee70fd422d08d0aef7fadfb305d519fb0d6bc1867414b5fb6318865711c9e00a90e3da0", - "04029266295337b1ec5f81f1040eee7b69ab581fd6b91e48a6e27aad8926bc7b0c1b4c7bc8b11776eebd101e5eda1d2d7a51c38cd42efde937de2d067ea8ab0219294bfae2c42b1f3b469ed03cd2aff5bfef3fa62881f4e2c85f24324c84960bf80599966422f14ba6643eab1c2ba27c5ccb9c433d16efa17788676a6f46674783", - "040bc7bbe359df6e01118c39a0fbe3ea1b3e044af8eafdb46a9e5303621d8c2c7b0f72cc85b9334002b43a920ffa9f59b1f1de3695761aad2f47d70d09553ff1451d841b5cd6d8e9cdca36ba8308d0b28665648bedf80802071c817a24e6470e6f28573cd74c09b3c4ab68e6a66199963253022f7f901c2862d148e34db03e5216", - "042bd8340061111e24ab27a84301f6a1063142bb272334488b71f34eede30cc14110d3354d23627d9883266a678458d40e7df33b4a26c943e9721be2d31da710e92943bfad7163bce393f17dad22977e58897fca9b0cb8b1340ced5f7d644cea4d20dc9fa71177e2e38be0ee95e4f2c798b3f6d59e19b55c1a321f9c6a50d6d13d", - "040e482d3cbb2af8d9e06ef44387381700468e801cb662c577f94661688e90f7790268232b7ab12aec831b224d4678719dc10ca1640f9d4525e66bf0b9529748b40ce5447fbae31d61d27605324f7ee27a96ab2ef394b95dd88d7eafe874632e7b1aad3a14620e66cbf923e75cc5a8f0849b086b10dec66e9422aae3679476de52", - "04224b135262145c2cfb13761155cd395b5851f7fade027ec8d2edbe510710480a0f33b1d1482d9d34aa2121b1ddba210eac053cd05beaf6627a9276bf1b9d287816048b291a9969111f816488f28c5cd86f8aab16fbf7612b739896e6a4b4ab9112466b5a373236c0e37c333d198a9999af8ee275dc6682b2ecad4945ad627755", - "041305c2596d63ecb8925cb04f3bfe01917c6a5a7e03e4d59958b34aea94b71ed309129f818261df6a8a4f22c1abbb16afced007a1e6bbfd7a7c7d3b45ec32d22508c1eadc2505bee0d000cc0c203a7028f0a63de60ab46d28bb6e5c3890c9f5a413c61af7642e12a6892180c9275d70caf4dae0350d64b90ddcf0d77395a0d4d0", - "042d9d946d0d5829955fc5fc1851bab2656eba9f83fa25690e59708e8bda213bc01740f9e5b547cdd96149c34b806b9487b15994af1ebe3635787fd243b6c4970e139b37e319350f0c9c3470b106e46aa4a900e88686f9eada4eadf3030f9a41ad1ac7454136f497df64e3b877a20752f38c7b838458bda188aec766c6de3d57f5", - "0427b0180706c49b2d83a803c4c5c56ea5d0d229fd5aeab00898239ac1a53036612f05dfd14182175969150567c7a06c0feed668ad346315d874266b8bdca3a4320e8c5ca6460a9f28abd3917eae8922f9449e22171cd0032c1e9aafbd431c1ff928cceda4836a704e70a7528405b35be5c0b28092ca68be5b6431929ee9d9b982", - "04032b8646b3a1f528db77b9d29cd6df6d2be25c8bf38bf5166cf5be73e63afdba23d94c9106dc698e1d850afb41a1688487f6f2db57407de4fd52d92a15c28d960bf5e02ac6f60c95210c8976cd05ad0549d72327451b01ff9eaf7fd6b28d8fcc2012fd6f37d1596cbcc29ff21a91842d7a815c54a48b1100654a7a7cc6c13417", - "042cc0d1b7832e5d19c1e1f2624286d3699deaf6460b72ba45dcb77e0a6a404a59045cd63cdd598295a50ad4f6feecbce116349e8827a9eda3126bb023ccfb2a471c5e99ea45248d43c2deeb2662123bc1a3c5d65124390cbe4392925047aba0b5071ff62729923ea66497a5d6a406ab1d8e2ec2030780fe877598ae8141d1b221", - "0406939813f76c28590786b32807f3c90b0bbdea67cc28f59569f04b599a32d5f30a9d0bfdb2654bc4c7be2739a427e73c90070652660cd1f77ac8d5fec5858b6d283e5a075c8c06a7856aa3fb34fd07c7998a80270bb2c86d5fb7cc6cff397f8913571721477148e0a53502c87cdb3686c5e3e965121a44db61dcc9fc3f4a2059", - "0401af82a2af67957bc6f919769303f137e829f6ab4305dc4376e7e76916fd687c1ae2bfe3108173f7d2cc1b489d8e35820de4ca4137a6257f91e3a04f67763843284f8fc6b2ca3c148ca4633c73966d877ddefa808759524bf342e137bd64be5d2f64986c06aae9b8a8614de1fbed123ae4f26c7b096dbe663fd36dcf57287e37", - "041be485f30959702efc92ee4b89c0c8d66961163c2b058da6acd8b19e5fa9fad91df599488e5099df6cdb82fb739e1987f13cccee4b9d7dfd9f51c218f17276ee1cb8b1af5eb41541b657b63f681861868f779b6be673de778d9f0bd5b133822a152a93c8dfccad9ec7c61d8052079cedba736795ec2ba378d6d2f2491fb8d251", - "0419911ca364e492ebe2cd1c4810757b1e072bb3a7e17bae19f61accabffc65a530ad273b59427853637dc215fe262084f5bc7814a6d97e53d684647f8939a1a07110122450e41be0b7635802dc1c1b3cd7d4fab981f1c6773c01ae0613b7991b817236a87c4b4148a2027bc1951e84735662e7b33595f765e3c1010afbaddafde", - "04264c1f5744eba1058129daf595ac3b92abe982daddfe1901ba23bd391e9b62d0272f0a3e10c62838ca0420cab64c05b9f0a870d7de936e9a27de1a93f24885251d8e55de68e34936e547685348bbc72e421addc1b6113b8306743584320c6b640d99fb4769101b668560b509ad380965b58327886a1da5ec863d7ff065e275eb", - "042927b07e722dd540a3e0d7c5cec64a9ede67cb33a967a87ff506d1125a7870070ef80b94950eaa1711cdf27ed6c720db47545a7f82687b9a18398b5ff1afa176274e115a4f4ffc072757146ace63b8f3f63cad1e1b32f8060b6fd174a469d103145eedb6a8d4dfb8bbcc35aae9ca0c7cdac69e64d0b80b31a9ebb12d308591cc" - ]; - - let mut acc = G2::one(); - let by = Fr::from_str("23938123").unwrap(); - - for i in 0..10000 { - assert_eq!(expected[i], into_hex(acc).unwrap()); - assert_eq!(from_hex::(expected[i]).unwrap(), acc); - - acc = acc * by + acc; - } -} diff --git a/tests/serialization.rs b/tests/serialization.rs index d7c94af..c2b1272 100644 --- a/tests/serialization.rs +++ b/tests/serialization.rs @@ -1,10 +1,14 @@ +extern crate rand; +extern crate bn; extern crate bincode; extern crate rustc_serialize; -use self::bincode::SizeLimit::Infinite; -use self::bincode::rustc_serialize::{encode, decode}; -use self::rustc_serialize::{Encodable, Decodable}; -use self::rustc_serialize::hex::{FromHex, ToHex}; +use bn::*; + +use bincode::SizeLimit::Infinite; +use bincode::rustc_serialize::{encode, decode}; +use rustc_serialize::{Encodable, Decodable}; +use rustc_serialize::hex::{FromHex, ToHex}; pub fn into_hex(obj: S) -> Option { encode(&obj, Infinite).ok().map(|e| e.to_hex()) @@ -21,3 +25,30105 @@ pub fn reserialize(obj: S) -> S { from_hex(&s).unwrap() } + +#[test] +fn group_serialization_and_deserialization() { + let b = Fr::random(&mut rand::thread_rng()); + + let mut a = G1::one(); + for _ in 0..100 { + a = a * b; + + assert!(reserialize(a) == a); + } + + let mut a = G2::one(); + for _ in 0..100 { + a = a * b; + + assert!(reserialize(a) == a); + } +} + +#[test] +fn group_serialization_edge_cases() { + assert!(from_hex::("00").unwrap() == G1::zero()); + assert!(from_hex::("00").unwrap() == G2::zero()); + assert!(from_hex::("23").is_none()); + assert!(from_hex::("23").is_none()); + + // not points on the curve + assert!(from_hex::("04177cedb64589bde7a64ad24f89bbb8c9f05535810865aaea8fbf8184ff9e120313500226b2422d2068614d1c8c7146c806a97743e78d9901748a9ded08ea9e5f").is_none()); + assert!(from_hex::("041800deef121b1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c212c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b").is_none()); +} + +#[test] +fn g1_vectors() { + let expected = vec![ + "0400000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", + "040e97c669de7c670d734ca98a3bc5176c8f82aa5e44f9a8780998c22dfa5fb5ea19305ad020d76d8529f57dbdc43f7e77a637f17b2d5db5b06a2554c1151b1255", + "04070eef7bbfe7c9fa76338ed6d6a12b84f61a1a1b5b4d54c009b3993e2262c5fb1f4118919fac6678cb671ccfe5a3ab7ffc42dae56e8f4382ea3e6582ea7fdd15", + "041ce66de558c33edf36b637bd39478e2f317f674e0559025d1e428f37dda84c342e916be0e1e8ab1ba6a9ef642a2f1de44c1f6f91aca23991cb636dbb997cbc01", + "042e8d7e2ab119b53b2e2e5f8ddda2116aa821949ae0bd00a6ee6ebbe130397c0709e07974bfeae5c973c098c6dff65e864ee6ee05e9ccd1d61c8ca72e0c49232a", + "040460253e7e4e9804bdc30e1d76f98d7f7fcb4a6845fd6f9df0f06a18e1a2ebb3066fddd38227281acd80b6b6253f5d89e401918586254edad1a56fbb8544dbbd", + "04130f5f5f20846ffcd6dbfded402bebb7bb07e0a4cb2024bc84262de67498dd7e18dfc445b80fd0a1843d6ddb5ffc16cb8872c373b7adb9fd1b98ccc922318966", + "042849878760819716f11108e902836a72f4bba88eadbe26b5b9f53e75c1f8714f0732eeeaacbbde8dce07be752d413d58538fc11f82a1c434afac5c27760e8688", + "041846eb3215c26d8be94d8cb688f19f59db6c771bc8155d1fff826440bdaf8ce720553790d70aeccfb178e6c33f4331b8cc24e02c8ae8b5a0bb9b57a9c1132001", + "0421f8b0a60f933351788799a7271fce8eb3349b98b1e0dae6a1de4eebba06daed2f966958654ace4bad972296bfd8d3f1568954bec25b665c0fc8f64f1a0c9856", + "04163ddafd9f4677caa2b8feb510a6b0ef09191a00adfd9f09ae3e59d687af8ccb1a47d8362079b22c9064718f02948da7832a8e123b8c6e3730a9e7e137f84da7", + "041ac98fe325a2faf01816da51b3733edb8a13935dc0b82a6fc2667773d09461ce258861533cd79b9ca801a366e40dbf61431296ca6431b51e61adb41e389328ea", + "040dfcd832e70b1ebfc5f07d66ef71e88f1903eb69e25a43e17fcb119305f936a101f6022efdd7bb49bb2f9882d1edb54a618117ac9a213776ee09661dc813cb90", + "041c11d08dd28ed037fb7800988bf9ed0ffe5dea2ee321ba36725bbc2fbda12df82151ba8776a883a4d2fdb5daefb681aed75636db330956b36a795031b238494a", + "0407592e35e3444f61a5cd4bd3b62765ab5d67ff57b88aa781bfc0a14017746f9f2ff61c2caf223a33ea998503491389ec7b5ef2797f9d7bf5b63640cff086bc11", + "040a5e52f3b28b3d8a4eae2332ddcfaeb3300432f9c11409c4388607dfe2a0dd171781fd5e8fffab898a916ee4436f487b7ff9a0a7ffdae2e0f98d6fc1075f60fe", + "042db55c23fcdffc4000befcc40b612d1bc38d8e34ba4c1eb68f7a1446f851630d200c8cc5cf724a332ac366160836f91c086df5c8e023e0131eac51f1c18431c3", + "04283f5279f2bc83c2c0829d1814f066d1828c267c95edc39ad4853c5cb35c02dd1f0f1bfd04a340863a34d8638c0b7c254473da29ec0c0a95fae6a7ccde78c740", + "0401cf54e2dd9c2c97a96b809781114b82aee7d0b9f648d91fe01533062f99fe590037123d18acef099417572bdb041f77ef044b9c3fbef0ef0f9894f9a4061313", + "040b0115940193b2c17fb561c317ed88d5b5bac173f4eacd887fc8de03b9915ce62be17e169ae45579e2f0982b686a611309a8435d1e2f0de9a49c97f72679c795", + "04194e71fb26deed74c5681a0e616ed67135add9f3eb97fba96202539876fe0a642b27a2f7a125e849eca00af763e532d5c86ab650bcded04d47d26d8c6c62c139", + "04001082425143d275f44e16040d7f8922ccdcd77892cd80796a86051f4ff5b2de272e4a7dbfccbd7ef79cae19d0de3a0697adc6cc44d99f014187a99b6c26d7cc", + "041e6b87d81c1af93bacf529258f36145b434b84e843e0963674c529133b7ccbdc09384b95b6c343d8012f4a8b3a1bd6f34142d7688963df85c38369638b1c3117", + "041e34c8d7c0ba039b67537c75939a14fd61598babc9a448cd103601253b93692c1eb61a4444ac063eb1ae75e77df30f69cda5dadc08912727ce2426276fca10ad", + "041cd5b925c2174a380cf78f14a57388711b91c90010c55c0bea173cf77443869f1f7fdb3f0414e61d12589a46d8ae49f95ef9b1bece46a85d2d14d2deed1cbdaa", + "042826a17e76e78d1883003a32e8cabf44ea62087a2ec95ef68d72ed31f0dc0eab11d1fcb397c18539c7ed620a502fba6f4ee19adc17aaf9501b801e72a21c7b9d", + "0425b7a1770cc9e63055969af6b201dc7b6b5c8ac819b6ef82f39d3dec427a41c914b4f4c56c3fd44b34430f2a5cb7ae272c1a6fbcd86a22255db728fcc91d14b3", + "04150f39cb53bcf80d39c77a2a2d52ed7f3e0ce5b576a89981b9d9d6aee05110131ad181c717291b23eb881845ba88903859be7f65fc6e795507574452a03d4e25", + "041555ccb4555301cd5e3beaa6d0b8778a4505b72135567322f9a5a540e3b8a4fa127f16e181d7e3a75a2d944091c78caf9849eb6c3f3b24242c514e42fd30c0b3", + "042349519b9c99cf376534801d42d098b2541903f5fd07e0fa81d71ea68c806f89086bad59e91f4341cef634582513b9359c751e3640c0fa9a205a6bde1fdaf697", + "041033e55052e5ad95302c5dbd98a7be3387d605956d0eec74576a4251eb58f4da2534b51e49ce5768a4bef802e159fe1ffa37dba8437669d4c31292a2ecd24e4d", + "04070ca0593d04d87f769bb59c63b76cc1478fcb5eb5528b2d32ec6294eaa155351aea25fbfd40948c8fd8d202e31c4a1374869cc9eabd991ac2e00f5b2baf4e78", + "041d61b6c3dfba531cea1f35f652f6f94dbdbd1f62c43396dc378f70b6b0990e5b23b161cbce3acc6673a44939abc55b4a86f683e1e8ad4e0aec9e0e991c4ffd09", + "04131d5925f21a50af1da2367abadf38f2dfd9e7257523dc4662d0bacbc0808f130dbf763b7934a0a6224c34de1b4d5a791d88729df242434e0145bb713a38288f", + "042bfe71e528ee56f4c1c6f1c1de11864fe3d67e56b87dfb97cf608a83c4c2f18a2c2383632ed6378da76655cf8a5e151fc692ef5e07bfceb339c3d9504555a47f", + "04058210b550fc16609877b5fc0fb3722a44e77de300ea96de918d913e952f0c401a03daecc90ce916f495fac309acf7c33694a2f77bbbc770384460c2c98fd13c", + "0428ae164d26d0987c3c875e691d78b346d8c32a0aeb6fefe1510e5528e7fe05232a52f102a41d3dda80ec1eac66c6f759b405257bb836eec514b298747129b6ca", + "0422b56318bed36b21b46827b3d39a6a63fd327d84ad09efdd6fd9b7d5bd71c22505fc11eb76fd14c4b5b692723e28c454f7db0a36eace914b2f2c87f9b81e52ff", + "042a3e5a4c98a171667d6caaa396b0ccd03aee91724c0f3349214523861e5fcfa81ff385ef6803e70830ded0e23c2e76fa4d94ec16043290b16ac805dc2ca51153", + "0420be7bffa5976e062a75eae9a4dca83c27207152d8e7301c92bf990e2eddec35166a2963ed3c15a5350c685cf5f9c6580b9b96de49afcd5842344350a9d4d03f", + "0422e11534dc3c78583b6be6a70f21bd3f91b2d65f0776b88e871be1444c5323c21fb10a5e7f3f001a0476a99ed6eef5988d8899916f2e89c1d813a59d19bbdfcc", + "040da396124abe233d7227258003fabf15f50e21fea5c48fd98c805104240a084113368c4132a31a97f20762b7c0fcdda013936649d410ed33575d9fd727fdd22e", + "04278100c505a2dcdb395665dce5b91afb7d458deb9b2e148f63671f8bad4f67910271a00bb8db2441412cbe445219773f4be7b7d628a2123d667f2fca8a05055e", + "042ccfdef921ed73c7c5bfc7e77f630048631e0e1d9dac267a2cc55fd15d9648ed30380375c926c49823159426aaa804e7aae72012d0a10373466c6c09c27ee0dc", + "04016b16f7158ea78ed57cddf9eefee37f652faf139225b23fbbe72fdbeaaa1c5900deae79748f9742b576cfc8936fb1b24c86401e5756457791925764e4088fc3", + "042e27be22937dac068c73fd21b5d70df22a95a7c5fc1902f28ee36f1c1211c46421657c8e8d11664c0dc1d0ea02dc0126e0430448cf415e1d7d2449dca37a06a6", + "040d3b6892d20ddf0eb053e3fb40b71461a35f89212d25b8e6ff4c7b3e4272d5a61e8bb4cce229d8035ca37cf6a9fabf103299ce19b05a2cef38cb0948dee5b799", + "0411d389c11fdc323af24c9e3488abb5064b1b0b312f641c2041572777922525ef26f06bda6216d6310b1d2d9997b1d721b34f8b13c5c9c06fa19badf43da68e72", + "0425f96f8440bbe27602bcbec4ef5ae8d1bddcf2933a915438320c8d652823c9902508cabfce8c45cf54c9598cdf75371b7d55dc73cabf16e0199e83b5d06d203c", + "040d6229b56cc2c4005612bb667790d1e5ef7d7737ed62c31b97b84d6af2e160ec03190f4f4bb3fcb136b89a99f82f4941b1c54a2b3d7224e56e04f9273c0b8d79", + "042fcc98351a49c7137bbcf3644b6961e6b40adc959207dfa5894705da09d3b898028570506c9076b553b9399a488060c7b80c8279fc461ae9e150fcf55d4a42f0", + "0400662d7bf0d66e45ce36e706f3c762933ed4ab09e664a58c557c3323e1eaab67118a6509dfc87dd195a650ab7781c410ebe0fbcaf1f462ab4f7966cfc705463d", + "0413aa3bc49295213ae2369d60baacce80e2468b482a5e2a36233d9cac99c2d3f00a22280c564152ef48f9310f91a58658b39624b5d0f44b77f2d7388ed63392a9", + "0418c6fc464fc1098293f4bebdeda8914e3eac056daa6c6fb9f0178750810cbf8d22f99251d98ea9e8b737863c65534759143af10ed2c83067b6e9b4a3dd713672", + "040edf342ebb44b3f2f265e649376826fa04ba65e7d3800201066ed794f30b6ddd14c36e6cbb4125b46131f589e32d766f57fd36c34359f58b104e96a81473e2fe", + "040d668b047386cb0acab1550b0c1afbeff2536de23a689bf1e129bc2ac61f6fd51f69419fa97ec0382f147232ed59c682df6fda581e2d2009522264fa67e213dc", + "04283c1e0f0f38a5728c609b5e1ed6192ff14130c1d47245e1c26762566a4e93500553b00c7ad4aa30ccb8c2123cedb190c3d26630430071914b51800b06e88597", + "0418799821c0ff5eabbad869f09253e0a7fd4b3e7a55aaf549b3ee84a9a198af4e2aab3995cbf05b1f4bd826d04f2f51052b620cccc2a3c22b83bcef70a1e64c73", + "041258ee1a09c598dbaeb9955644fd23f4fc6328f1675c0ad6c847e338e72d086f16e0e91972ec2d221d9c08269298ab19fbb0cf7007e56936fb8b665af0c936fd", + "0410bca800784c7b06518136ac6593c81187a36283a4164d2c827ad02f49610fd9137495b1e03a5c3e7d7d7980b16d6fd99baedce9cee07389066f0c68fc68d444", + "0429e65fad8bdbb365d8001660da7e46c40e6b15c38e69066e1d7343e6a1b2cc9d248e0bb624695732a765f71e95022aad7b2961a8108e258b4da9273983450c93", + "040a9bd379f4bf47075c922d7b4ead1f508c34d6ca473f599bd552c5858db58f8a05d0415d73bf2de7449651e777c3a06c73755a6a8881561e9c11e9c030fb97ef", + "04127e9fe4f365ce4fabc527f22e215fdc95ffa8f43c2423fec2421c213e46dd0a001304a6ca915ac381d1defcf09faf4dc6afb9fde0983f5014a7185ab8a7f855", + "04032f66d5cc0b6dc7c27cc507cadb19bb840b8c6a12478c439ff2a8fc1af14a4e19fd2ef95cd96eac5d16a8d0bc91c3f68b4f481ad31e5d422f91b5855dcbd1c6", + "0429af69da99ef4ed6d4643177a965008880a352e1cd65097baa5ddc68c0729ffb0b166d20c0cd537d0334b0151a16c4a84ba7ac5dafbd802a765d3a69fb50a18a", + "04023855247b32407f9a5bfbfcc7733e37b1a4532cfa25bf013c93bb36042cd6a612c41afa730d0f79a56b45d5b31260c79f0e8406e7326cc64a5ba6a414988f6d", + "041d590dda59ffa35ee80b36b9ef648a612371f969f9fd2e090f6a7bb06fc243fd1287c81725da751779a0a27ccdf7319dad0579b36ec50aa23af7f54b5948df3e", + "041c1b3fb17a7ca5372d347b1148f674a7bc53e24dcc7147cbe057735bb7b1e8601aa4254d52c25d0e58cee341ff330bbc2c1df303c3ad6846e2da4a4c9b00e620", + "04037760bf6086d972002ee9b0122cc933765c20c51f08c7253b40df056a74a3bf2f81e7da90dc63cf09bfa0c249f3763741bb2d7b4a45033774abe451eaa3df54", + "0409502fa9818247c38d09ffd257915d9371a4be3c957c6d490548726faed2d64805fc11694e318e19f342221696736184dc33a41fef436e237c084b45277cb24e", + "042f55cd2a97b83fa8a4f0fefc89f1c72a49387595e98ff0cfe2ab19b30f4986ec28fb033ba715a19674c95be4946fccbde8ec8575d76fa9c2436b84dc38ba9e34", + "0424b087bc584dfe89078b53b5f5ff46c46469143b83157495812ba1ab472502270d009d7f3efc72c50ddfa885ba63535d4b5b252861aab4b69f5b9f124a09db20", + "040214dd33fd7456040855bcf76c0fad63483dda6b16bf7ee4dff4c9f2b9e57eea0acab70e80260581971d5f4f89c7d2a4301d7861dd4afa79384601fd6be7c204", + "041288e052afbafb93b9dc4f27cf1b784964e75f53d8fc6a745fe80f6be21a89fe1b2937ceb73db1bc37377cec36d4923cb90d13e7f266c820e0f1fa4eccff87be", + "04083437a88bb12b190ea01231bd7a8bfcab248718102d7aa57898dd3c5e05bc97040af4ce25a856774c0787e1a4ff1a570e59cb4193d15c0df1c30f9a07b058be", + "0416f6496b027c9075d10480283802830d5a3aaa9b9757313ed892fef671da7fa405807d9578f0b3ceffc3a3da85febbd1fa050cfec1d73fe75881d0bc86cacb56", + "042276d5f089287953346046bddf1921e329fc76bb287e6825dc34f4bf8f58dc0c1c1bd1dc93e17e227a672d3e7836061842171169d410ec7d58c4f7188c40a7d5", + "042b0204c64f406ec4db650ab811e8402e53dffbc7009858b7a85e0d31b4434d871fc2c3c493700eafab3064b9c9bac4c7c9849272acc57a6b15e3074b7b919072", + "040f7881321a7953f9a8219f2ed0b286764165a78cdf967e4ce84a0fcdc1575f9f295a7615a5dc665da1586430fcbad27b8f404267a416a70c17cf2d0ec390773d", + 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"040df8904cadce2158a11b8a292f9726a6fbbdf3639826cf5f117e4750704f25a0161b1bad132c36f873e96d42591f23b22c53b3b65318d3ef8fa717febc06147a", + "0408afb9df968d0820204c466c1012689732f389ce6d72fa4a7edc01976eb91c872e1b25d1bd568a0145b7c869de070529010f08906e9b8a38a359243fa69b4ed1", + "041b998860ee614fe296818a6e4f5dee13a7ed089b929acd5ffb6a32e04ef225d5159e14ce10edd7f7b2e5fdf7f8039a4edf5063c7abf9edc49261822a9640f2b0", + "04155bf26f6596411a2b8c4caebcfefc0062addaa821515860e2115c502ad547ba16eef090cc64432e31777769a26520bf2cf57fe247d125ba22c00dd4321a35a7", + "040b60980b8aa37754adcf1f83bf488493336f503a7b88528f6b99c6cfec6d20f9136459f9270e2c200889340def158344b6dbf1ebb95893e19d4a17e5b51c441d", + "04006c487257d0e18e4e2350132bb7533957665a01dd3b33062e98583b8b06c86a002e1604dc8b51c436810e6ba1c11b26eac141be27befbd64955a95f073b4b7c", + "041d41edde3a34497c779735ffb995b3878ce471dbc597814272b16ee710e56a2600f2ae4c42d2e4518ca0305dc66ecf8b42a001fd6df7220aa30208a40a5e815a", + "04091b055c42114e75f7606fce64671e871ab1701fb5de2fe9e56954aa069a3018163c3245518f9c0267f4c5f08363aa29480d290edafd72dc999842de552c3597", + "0415c78b48c8552e06503ba44cca1ad32e555b36898adb326e0d140eca9c35847f1cad4499e22147a3df230ef4b048673d40e12b219134606129c42d9a36080be8", + "0408d1fe0f7d9e084f1c5b6405c95d64b51c218deaa1d0958927215e7514e4b8d823ce42e907511208119447fedfeec1ab7637120eeb25880909e96a16b54bc5c0", + "040b6b0a35196e08dccb956c15a926adb48359d2b3ecc39121a0fae7dc3a5b3c5a0d6016643625224ebb3dd0f17b40645436d0a44bfea6b793d47a1c1e4bbb5940", + "042548f458301badf56dee50807a84e05cbe0c507cb2547e31238bcb7042783f662685f007d508db54318b83409ba11368ee1ba8a47d33ec74199740441398ab88", + "0404ebc99e529df74a4b132b18156b031e7c75b09e223dd5b94db6a6219a5efbac256c74fbf196fda3022a18c4949fccb41a84f6df19ab63df3233aee0eb21033a", + "04212cc832aadad2518aeb40db2a72e14624f2e92699709a67745822a339deebdc03c7f2ff9ad01f2bab839aebe4a9735730360d07b967924b11727127250d7b8a", + "041931a1350ff024f9dfd911677151f3824e5dfac8941850c33cf879ed21fa41e92b57f9c02dfc594a8bf11770c387a5ada7e990b9e4d944eec746e7f377291cc4", + "04241468a4dfcd57bd8b6734d65591564da809f118150781c2bf7c35832a89d0231ce9926d21f0daa42103451b96cd30f70db481eb84a6caeeded0fb3fa03cd7bf", + "040f91c7b2a45d34c0d6baba929e637ce927cf2b5771c540a6fcf3c180321baa910b0f1089f4212a82942b56d6c949928182d5b446f7591d4a11b6a8be4bf40175", + "0415e2730712374f95827b97e1dd936f84dac6cc27fc26160884a216a9f6447c8a1b7c7b170a112b99359aec85cab360383d3bfe0ab299cbf90cbd3b9437d61754", + "0410fef649a7d4116aaea79d149b07e572d7fe67399d8f021d45ba2791e4aae339146366e1c69cb9a3b6e47c32d7e31904026bccbe2176b537df4dcecece3a3472", + "0400c1e00c9abff3ef07d90af538194fb1ae62c43818e7fcda2380804dc38203d9017b46c2eda7b72031d15e549dfe67ce0005c2f384372faaaf8a1d3dea663996", + "0410828f8d594f9cade7f5ab73fec0318972f26f0fd1710a6b68d483ce21dcd1c023b5ae87fc7a00d7bc5fd4e825fadcbff446fc69d9bfa0e6bb3d0040547bc801", + "0401a2a6f83d4656911f23ae55d26d37ea5bfb8ff9ec0b3549007ff0a7643178d52563afd5b6ef6c05dfa5609f1f2c4b961eaa0424fb1eaa6947629cc9d75e1a65", + "04148c3513f361cc46c7150da10376bcbc125c6e62d2411523b938f657428480fb004ea007e9c2f000a09755352f2eb2f7d174996e7bd033fb0377917695a6d546", + "0415d8840c3cf52ade817a4ebaf6e1ee814d7ec19ef8792f4585de23d677f8d9692f3f081e27cbe2aec4ce789fe9178013312eb91f92542cd8eaddbeb033b6fd99", + "041dab4e2eecb3beebdd8e37254aee6df9c0b2a14dbfeb16eedf3008ae35e06afa2572a89d14dd823dc87a28266158f2386b890fa8a6f74ea48a6f4a05fee1467c", + "042de4bb0c6bb8a9a042a38e36d066c0bcc2f9ab385f8f2d3feebf405d411f7b3a1b9adb9b0cbd036e06133c7a274039f5401bdb59ac6ebeec0c151c0b5a06ff0c", + "0408fbc77b4a83d22e540b8186f1257c6ef64b2671cfa9dc8a1497865e282ff1c70501a5ea347529a71fe104a364ec1546521afcc95df343805f10f7ee4b806502", + "041fad37fe9ed6e47b2ac15055d81826a40e2555a394520e84429581eb07a9cac81f3d7716a76b5920dd3f6c803de1a74cb22ac0a4c0c6400fd576f7ed870b3609", + "040e430ed906ee8528fb0a03f1e91b70db60a1e1708c9973b810fff8945a644ae70f2171d833caf9588e5213781f086ca89906ffa75f817262c772727205818c73", + "042b16e501f6ebab5e5f2effbef9467810a2bedc748088bcf7bb32768f5040089b0212431077ed025c0ce6a1052cb549838423fe89684860658ffa5465d5c5853d", + "04192079606933425a5dd5b8daa2cd2b1bcf6b60383a82fb6a5ede88fb4509971c17b9fe2ae5768c56c5479ff70f4735ffc9ee736e2d67f5cda491eb275f3d8f7a", + "04156ea1af468dcfd230b9a73cdf4fd33fcec6e43cd04683b9fb971bce6ce69c0c21ece63e5f18106fbc303c5641b123b0cfa8421cc0f47145856c6858a4e753d1", + "041f142829448711a3dd1539b0ddf51a1971dd36516a286c1f53ec43f28cb50d420009131fce4dd9a529dca1df030942d0637ab87d3db0d641950fe623a9710b2f", + "040f95e2dd2d15bac272dce10e00b917256b708dfc693fb25ea25ea433f5d9e3501093ba0b0f3e462bab61733c23925d108a141b597a4293e2c4fb7a6f6fd263bb", + "0421f8d262df86103354f237af9c68288a235437f1e99083987b1f55a87f948e2b201d775af427ca9d1f297300496d4e82582011b0c08270aa4cbfc67eb33a049c", + "041378253dc2f480760934f0f04d54e49f2099fa2c694de510ba05aee1f841cb980109bda84b8ab6261fbbe8848733ef939c69a67523f9cf5501852000fca52574", + "041ae5ec96dcbfa223f504eae49bd7e804fbd0b17a968b701a2360f375b7c019ec1ffa2788d9996473a854b657a0b3dca8e14287de5c032c2127502f9d516e738f", + "042dbffb2c2ff6c1772eb52647c6eab4bf72a7d8e93ad0156fbe4bc2e83ffcb1822a5b10b3e973d3049a5092e10ebc4bbb62af19cdf21483243f81f0703e4a7ee1", + "041db4578f2a48385a7f4e4333a3a99e0716657c9b2087ce3ee0b6eb2052311d0408846afd50ba1bb0bcf1c511dfade9a9b724e6ccc8f96598773d59d047c7b135", + "0404d9b7acf40cc2601842ad5df57cf8017c7e61bb0aa3f5fbe2bb17e17ca738431128987bf4eb7873ac0ee3493ef4a12bf1220d9a3b2c6244385679aa17c4b07d", + "0400fd6838356358072a63dbb2ada3b9c1580b7b27ffe349bb8623c7254056435021130c8ea14ccde0d53bedb88e85e2b104326a94cef98e62fa44f8d7b727bf34", + "041695a424a7ca05f6b86265e4cf38e9f994295901aa00f55e345cc1f256f2a37e11e93a451fd6473f8647cffbfcb8e5e88a08fd27be3075903e75573f7bfed3f9", + "041b65de7d91cc0f07a2f1400986ef30776f82269809db03fe8e678ad495984f73266ffc1fde898324c2c45ba6a68ba01ba8ad4ed1f6bd7536ece655d0134e27d7", + "04088989a891cb9e3933bc4b39f872cf7c4258a03b35dab2ad4631b7d4b3c18ade28c45749db4ba761ae208d76ea6209e4db6224d6449621e7ed71cf9802a1704c", + "04299da297b4cb97d4a53111246d30e8139193bfa36d4414ed3f636761aa1380b20d710c8ad3ae2f1b0410faf99874a519782bb6564f1247d5e504b4d572414d7e", + "041a587ba03087c2eadfe9e28de4bf3852f6f037f76682757c05ba38058ccb52e00fe96ee800a1dda0758f0bd8de09c4dbfdb43b3935dc9027bac1591993b929a2", + "0407de369afcca2867a456489c0196aaebaebe5c8918ee0d0703f62e58b441be0c2ec36deb8f82eef0228c9b5f258d32fd4a1b20c6885b02d5dcfb76aba346e614", + "042a58c7b42a30e920b8452ffda805d04f8dc9ff0abb50e8c1572a622675a9a9f612002af09f168d0fed93dd53aad456e6d6b1ab7c9c91c3bb5c91f7aa10811eab", + "0419329242c09bd2eb48142f905e017a5b6bdb16923ba08fd8aef4743045db5f3a2a1897eea7c9fc6fa5b6d04640aa05402de9e182678dcd07eaab39014c5b646c", + "040aad228124bbf77ba295de70bc7f706bef61408d9df745099df476ea73602298184ea4b758e80e8108d74b03b34f7493eac7e39898ecc649449dbf3ae8de5e07", + "04120ebdc28ae75eacb634b08c899b8d69c5169cd546ce8cb2dcd71332c65b5aea23f462800f85090cf093b48313f42e2393ff59bf1961fc37b00061c7bea51cc7", + "040e6e91db838cd81b6050d8450900edee1909885db64aa0210e7e8f880ce6710f16a95384832929b34715bc748fccf98823fa538cc2197d5f3aeeb9c38b60582a", + "04146b6f644556092e484177c3dbf605fd38b1a9a2c0103a9a75a520fc05d3fdb8044b74a909c4a6b3c2331000923afd3032af41c5b5e30bb5748bc4fe761745b1", + "0405f6ad5a1e1f550cae7008c2fc8fe429b0cf4bb181a0b7232a06bf32b7ee2d970e68bfb230d4fa30a7e7b3591e8cd3894071b1f9df6888f00d488a4f25205631", + "04252c651e2c65e304a69f238f2ba44d8130b4b2759950239a1765985bc8a2148511e39d1cf7cea1661b35b8eb381a2a5697bd69bd745bbfa1cc8f039d3ecc9c9c", + "041c470202c3bc79abeb8ac5dbbc9d7a32ec695269229c9f73fd8e34e076a7353928226defd9aba470204d10e989b16ea18f04870d24fd03ca39239c97448a92d2", + "042d81b6e18797b962f46687512d92e46a4a07b4b08158ff0651f555cae926134819944530c26c6370a0b2690fbc844efc7b72c95c1543a8ac7551390e533e1940", + "0407ec1a7f17116d5260d1aca211cf8d6d41c9e2242110965eebf72bc93e052d9d2afcb3bd2d0dac62f2c57cb4f261d924c69222080d3d517595d9a3982fd3af1e", + "04164e98f79b15a9a0a96547151cc9a05c732fc7dd1e78ac44c6d68ab4a6ab21c42f708da63a29a89bcec03685a7d853b67739ebf01d3150f22b000c446686dd4f", + "0411be9eb2675f561271541f1637aa3f7ee6e61cb7c56f2ea78786e2a5b57a311f2aa4fa347c06b24b8430963c8bd80cf0eff6069fbca1f7b8e436a11e965dad13", + "0408558b2de18c446638d2da513f83ec316ca299b7bc823d3a7300a2f2bf205ac003b7cc869dab6aefd9cc8d91fc80d91a8720e2db7ce4c5fc57996e4dc1e1d210", + "041594c1d20ece1b3433ca1ee39b4476b3637376a0c74617d610052ab39d5195440de80e37a34878badaa241710c00665059874ac69e485a9cc85f765b6f364a32", + "04216d92167c9a925eb55403e14e01f428a266de374d923d2475d2ca44763de1d40fe8f70b4a8582a15d71735e1c86d475c754e0991ab021317a369cb55b6d7077", + "0407bb9f4748af5a1a58f7303c9f4ced9f365c1b2c7b9e5b8dd9f4450ca078623f29718e3995657751da76bdf259548b1a4e42de4c5f7454513ab9fdd842b96b4c", + "04058c9cd670184da6bb007379234e0fd2db702211f0e57f0af0a4732847a060ae113f7b29411ac80915bad1fccbbcb3a4036fbc3b8ec760dac65e95d3ce4499d4", + "040b09dc346bcf005e484a0c858287076b289059c4b8983024548efdb1b446612e198ef0d6881c40c186d0a4dd1036283d3a21148fc0955381793979c09dbe0896", + "0424ae3f2b0e02a5e62f07ed251e2e6f4a855095dcdba6973e0cb8068e0399ae652a725d32318cbfea203c0349926be5dda96b6965bcf40d2fc8dcf28ca1d326e0", + "0418f85db37b280d36012b3d632655af37818acd26d3f728c7d75144f3e20b92f826f2d13f37a852f8348531e2e0879dcf7ff65806f3ea66c3b6a8dc0b1c39d43c", + "042736509f322640b10fb1692ccb00c7b62569c98150e32bfca0bb11c7ae9eab8304ffcc57689996edda19f7a970755d675d914b0a6b6de5a580a4959656c73e7f", + "04285a9a4cf39e825ba5087c6f8a510796bb6d9032ac850e4bf03c24141926f0ee03aba476e4c6ee490cfbb0a6ba7099c51e8c8d1b49d76d745f5fd2facd5e8200", + "0418285e97e1e0e28dc1a5fc83a6e1c31ca5519981e34bf1319629184cb703f7861b23cd8d3edc96cdba32cbbcd4e2a04e8b6dded2c85e85fa2468e700d6010309", + "041ef5b3b3fc4bff399672777c708a88ee42262673fc6c57e3a9bdeabde2db582919290c138b58db2673d5bbef77610797ba81085908b12163f8fb93ae64c1ab8f", + "042c26105a9aab37f29b053e856954290848b78be38f699c07b294c0019603501d14a3bd1b9ad9c1969f6dd44cefa5ff983f3e6cecd088e98c72450513c89dff23", + "042630e3f0ae0769000e292e99c3502e2835b465e22192fd8989f64c1735bee7d002242fb42015c31d3d82d24422b06b420f7515cb7022c4a90ecba8a5ee7e786c", + "04231d053240d7dd683ac4197f147d3f3456fdae9e275b5d5ec70f49fcf32d84752abf113de9b0b66f8216824484dd77abbb28490e15fd1e996d72ea43078752ac", + "04067ea7ab3c7436c0e5e599aad6ac93a8da911d0b0c8a4dd675514cf38c2b26bd1d5568576f01af2c14af20512a1562fd99c4964ba8a6b87f050ed48a0d651a3d", + "04022ddb868647dfd693233aac44a9118c48c03bd625c7282e785ec39cbac810660da0f9cf03835c77517478b6da2f3588dcba969b8c7e0eab53a20bcabf094f8c", + "042e6c41d5cabd81dc0cae667747f8f2a05c1f05547e0a35538e68ef8d6821e1440a39d78cc2608cfaa1899eb9b7e365595f0b1130af5baf63029ff7e10f814c8b", + "043028979488a631eac9c78b04e3d46992f5bd73384c40a9a96c8738983ab592bf1aef71cac4a3bcc5cadbf67d91a9f8011d004f97a003578e373caccb4229933c" + ]; + + let mut acc = G1::one(); + let by = Fr::from_str("23938123").unwrap(); + + for i in 0..10000 { + assert!(expected[i] == into_hex(acc).unwrap()); + assert!(from_hex::(expected[i]).unwrap() == acc); + + acc = acc * by + acc; + } +} + +#[test] +fn g2_vectors() { + let expected = vec![ + "041800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c212c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", + "042c67838d2375c9478515736afbccbd342f2b27bc29f369a319dd2b29d50bd184193ffd9e54ef29c23952aa9ae94f6802a446a7ecdd3fb1f00050395137e4911c23851278a4cdf1b7653ce00932b20a7ec13fd73136807426be6326b07efee3651e45839e5349b05cac07f7a81a4d3a048a01a74af15a0a2d6f37b39525e45cd4", + "04279ad80fbb6eb72d134d52d0be1411e481afe72c638c86bd61db2909c31438ca11a6e74fe8a08754b4fc659bf7b069ec777d1ffe427d8642748c43ed1993ae2b156af13cccc742687f9966ec175a92bafdc1173bbab1bb204d34627876d1316c082f9249e1f6858650cba798b55165a6a73e28283714fec5fe73b980f99552ee", + "0423634c3ea29fcd751c4d671cb0dc2daf7988615f79fbd4ee445a37bc9e2e12f90ae5b6ab289fbd7a0695df2fee58226fec3382817512a31cc88718817ac03a392456d22e31bdf4407331afd3bbdeccfbfc0f3732fb0ebd8523e886e180b0579d0e339aabf3c64e1293285ec14d30ccf15c68d281afeb7af1d9cf7c64773b50d3", + "040c5934295f223bef0e1f44831f08b75c6fc552eff0beb648bb90c4e258b14db806705cef42e05a314f80be7b7bb23ec40eb6a90d5a66859b499d1d296dbbea361c0942411501cb08e7e55dd22bbced47794425fd99fe3ea1e209af95f1d619831c6008bc42af94a4ff0a5b7e5425a754f6ab0d733b5669cd744c38b164c918ad", + "04031464e9b247fec775c333ecb0679ae89c27475ce719977a5fc1b0040c789fd80ad528045f711392803e848793ae4e083e37451fdb854bb620ed0f72336788231bafb4e31a99738e56d052f989cf7b1bca5013947713526c695ecffdd035e8492e2460e141dbd6bbe2ceda50695147a8b3765c150747866b1f5ceb446185c822", + "041de296caa2d2039da52400b6f2f91736fd9182e4f4440db9fb954e793a111d85289eeec2ad6569c3deb666827263c0a5aa9f7fc359d65485f2842a2c23f4dd5005559f3ad1aff95d175c1b4a0580b8ea0ac1b6494301904f5087bcad94a39b7a187d5586ff24a34c19f1715d7c7d8b7f09d0f89ce0038aa763fa86cc06506f19", + "040483068b8e81116e03b4c0799641a969736bd8a148c1a831a8ff20518d27d4bd270577354d458f6788564de9e65bbd2ad10d595e18e621b6d09530b9ad055ef42965718433aab1d43b22bd356337b32d737425cf2e740c219ebaf703ace3051f178390c62692c8ffb5332fc623a43d9f4237c16ad296f6caef8160ac12513ed9", + "042a5414a4a6919ec4ef64f47b0ff21677819b0f6e4b912b83998b705b18b8e194199936d35f4a25b8fa509c51428cd1c5a0ad044026ce0fd94a691d18af55f66a27db9e27be985a916d54cceeaa14fb15760f8a42603fce9761256b37be948838181377f7e6ac6f8520ccac4ca1e6743a9d4fe5a358fe7d7219c9902715a6dc15", + "041b05fa148081bd5fba93120cc1213a54b8b5f273922317130eb2b4e26948e88f0310164a849e7807c9c157c81086ef09778b39f0bb9cecd41e61c4b6b7a932ff291a22436df666eaf40657583f7b18dfcc84385ffb53677ea9d77c8f7169b30f1807ca324bb6f74298091fd5b9d9fd1e3b844b079ab6654c031bd05c3a1e1c5a", + "0428c80df84cff15d5df27e2f0ec8c76294e12c79a88dd075b30d6154ca2c0053314298bdb83bf74d32273ba8dafde5fbed8330ed232efafb09babe53f4c346daa1c5f8d06b0471666655e9905348a8743ec03df1fd3a3ac4eca65a2a7298b2ac028896eef381991e3474ca48c2a5792f2a256d6fbf358234cd719862581b91508", + "04273e061f73b2c571927fbe3ebd4aeb35e6624d6d6c6f8ff5935d8ff5762f9043233563946114b9a15c48456d6a593079f2cddf8fa5a8486c02f4f7543b0855851ea949747bc481f673b8861ac58046647a652b6e297f0a889068a70b57fded6b1af7b3c3245f528b7133c1a13a69344bc0a08d043268d7f708247b41fb708992", + "04267d591d58ac0d192e14ba80f9ece4d4dec7e5fcd9a57f872223de65a3102d5a00dc2dd4bd57261e3e6b64cfcea5b044992925a98eb689c20072cd2f773138801463e2ac0887e862af0041cea40528529815c2883af6782546a237305894c5aa2d20dafa6c094f4d869a73e1f87f264c6ee36c1773c0b72322a7cda60e3f0b21", + "0405b9a785035b4f31a7ddbcda19d64d43983a8ccbd27b1d40af3883bff14630b308326a3c40cfa870ff36275b68d819fe2e2606f9ad44e25b89a2f19db2950db512a30c62572f61bf2576c098a360b1741b2de06c15058b248052709ff244cb432f4bba791cde6457a45bc8f50cb1816e3f48ce1788d6a387d8dcfc2bff078d58", + "040a61f7c537f8a1c010254ed2cd03c2961c47d319740c94da81d17a910787f3c60a0cba9ab886a87c827cae08637dbd2a9b2c49bf7de75cb1d8231ee8b62f52da092fb7589462a47c2f64c1a0867f21915838cbcdebcdb148f6ce884c88320c2313305bce65af9f1c517425b9613726030c58988df1d6a83ec9fe58695fb86ede", + "0409a76a8e8395ab6e27ee7afca680ebf7eda7dccc0ae4d568e2c5904905ec17ce0567e221d2ee1c11bdca0c42f2faf4c34571870edc298864b3e191679b2f9863193f1d12c8969cb3b0761c372c3032ff13d5edd450afe4fb291e57b2b98fcf170ba1496b526c0f3e8180ff388bd5ba61aade47c95f8d9268c9ff16e2115117ae", + "040de6b76ee29fe6802e54b173861e2af2a23a015a84db220f0d1533e51fa4173f1649836197659ccdd362ff84086f786499b8303506badadcb1adffa1620f01da288445063587b47183b69b7d6a97def7fb3c428f87332855b42fce1d14ac602010a56d61a53bc9c841d9ea3edfeaaaac64cb75c9295dba73319260df6f48ed1d", + "040cb5e808fe49101bd201b8d3559d2a5815dad17018b187a3b81a949439ea0f2d007df6fdc3e34f17adc51274b597129efa388adacd1c46dd63e6889c31c8a86723934cf177b54dd0fde76165c2da4c4a1ed41f08d9ae4abe45c6840b2cae42610a1226f6e88a7c71c1194df7088f883e7b6ee4ceedbd818e1d37e93286f9b68c", + "042503e1ff52371021e561690944e2a146a63e348ce93a8db2d021314dd440d8e214fe6e42967c7404808a25ed89d5fc35a69e68fdcb3520c6d4aae863de5bd9b513d9895ad6948c1c7d8229640282189c99b2155bac3d9ed835d7e494d44224ae2fef3af5995261ce072caf1e616a2940f6652e62f505866f4c6c7d46bf960dae", + "04251a6eafde21e3629619eaead2ca6f7ece40c885f2241e7806dd04693430d61d1d55647f4c38b16f3f0e69f6de1f5f9499d0cd8f6961811eadfbd6464079085420007530016a944241e43df10772776ed2f199e0d47b52543ee0a503c42c661f0ec8ba6e64b08054bf68ffb84734dd3ecf51eec99d0583cbadf8e4178e34ebfb", + "042ccb17853941a9007c8c9f6921daff460cbe035f23fbdb740c2c4cc841c1f311280cbf0ce6184eda7c146120afd86b27e3f2b866a775ffcf91d76285074377ba152fa83c2bdd64683e0f18e00f91dc7f1d87d302202e70a07a6120bc9aa86c28230f4a6007fb38d96e54eaf431d01142e98c7f4975bb46f4a1f45eff340753f8", + "041de6446da4da8d4b1d8151ee6a96fb1ab2f7ca0e97350c712bf39899250eed561acbe29c924683fb239c4eae6ded57929362a0ca3c8c9d2b9636f57b3d04aaac2beea205769545196620d4e215cf1b7f6ec869b2d392656eb862730b9176d1011fec30fac85680e25103a730ff8ad1dd57535c1f51b5252ff3dcffc92e72988f", + "04033b8e1ff68c5a454596a9a49d38e625567517330025d6797c2a579b9aa37c3714e1630a4df34060da8e7f8004f8cda7c759f534a48d1cbef0da9eb9e3326cb10e604ec7cb4e83372663d8e003ee9bcb6ad9cb29bf5bc010ecd17e05e0b85e370e5280b89793cfabab6e5db214faf3e1e2fd189e669fd55f257fe99423770d69", + "0412368d619788ad72eacd84d175998f9a5fbf3a89dd868284fa8d1ef36cdd516612cf53f12354024dc00e82079f3222249df4ee853a7124a0a8993022a4f5bd6b07573c37ab1138f8813348d0b8384a4c92b0f4db54963bb6862e7daf3525e1ed2c1cd47d8129317e265cac1f1e9ebf433db5fea2f93786bf7778e99642f36d68", + "0404860e7ac5fb4dee64bb0de725de0ea01107725102c3ba0419c1100163a123850e4c0febd7e086526d9065f14e449518d3a0d8a8edcbe42c83093ce54867d30018751d3c1260541729dd521a9c2d265da95a4ba348f73f89fd9606b8de4379342006f90146d8697badc8eb8111df7dde13a50b064363e28d2b677704d85bbff8", + "041192d45b120c5c23d9a27ee4ce0b3270df90408f2a932af93d72074e2417de912424f16df602f0ebb1a4cfd2ac85a5650ef6cb9bd04037d7775d97c2f3bc589c21ddb1ff0599cb4ca77a4fef3657841776c588ce8d4d9623f9c82e43f854cc072a83f7871e4cd2f1d17cb5b3a8f876a8812352b16a6306d39b7c0f20cd42c485", + "0419b432925df2cc7227d301aef3b8a65b548310c31e2f8986d2f14cb590dd8e8b29abf84dffdb401b6b8838a0409d36cd41d30edfdfbb83a4331a5925946a0f570aa2c5d9a81333fe7d4d2a0aace97e012f0f7509b57f40def7b72bdc09d5b810265a641456cc7ac3b4af37c41c66c584f4b1374f05eeea17488e7f046f825b5d", + "0417f4df942218a05c2931589d27e0c76c4dcad40e8cb515cf3992685720f4402f0989d04a05ab9fa8a7892915accff791e275d36b763db769d6bcc51852cc31ed2af76ba1783f9823454e30515e1724c997cf4e7f36052edd093e1c2db07dd8ce06723082c9028f6c7f5de140673b1ce7f2709b2ae472a30f16ead9dbad38001a", + "041b814175bf49262329390e827ea26db0269d12c0f0850a180b9e389f3d68da0a1b956b6815abaae280b2f6304df65c47a41ef342a2e5ce47f9bdada5bcc2e1e1119bd4c31b1151e6d7cb1fe1110c8c5af6f8ccf05c86c87518e6d5a0a104287d2780238cbafdf71a3633919e45b7b6fd771c7195fea4ad6019e8201373af8bfd", + "042f2d0d1634ddb0d2085aaa09890d1c05390dc40d99ac63e8f783e8c21adfad0a14dc10c448bbd58e166a35615b5dfc5ae8612d323700c94e3a60fe01a48b49ea2577628e172d241c8f3a8e16bb29add4703ff58fdce33fc1a6ff9d86e4a4245318c8761564867cb2dcb5fc622328f7b89a0ff22a8e4b2587df68ff5650e8c128", + "04112d939634bb34f4f9488143d9c9eaa9fdabc3cfe1ce237e3f03c35b86632d8c049a224a12fb46d35a5e1bba0daa1e7328fa42968173a5c935126a2bd9e5eed2063c0383427600f52e72fafb72c98649cefb15f6c46479c65c78370a23c3c11f0f5530927051ef744644fd55e6ef1bb3008ac1839c38cf8b6d589b05d026ea9c", + "042dd12ba3953527f61314ee4401d9491a11e2ff795d418d90736008e64386893504198484354e1f0627af1bbd676473d46e7137e0ebb45acb504e08dfb94230572d08ac9466593375f0ae100fe27d31d6d394bffcc821f12c201a6dfaaa87d00302767f0a274098916df80c7525d04ea2c33eb60cd28efded2c07cb91168b3615", + "040d700330c2fad6e6ccbcb7fc83edfc5e949afc3306b185e343b482e25e5311e92fe947a37a0468dfa119af5dc4f5df7186613f791f0b6941ca6bbb7714563ca42135dd14c213902f032c15705fc2e798a5070d83d240c4277a85d83d5c257b751cae0a2bc738323f32814bccc1fdfeb314d016f4834e5e41b52ddc73aee238f4", + "0411f5ed01f0a38d5296a156dd3ed54e055faf42a0b465b368ed3166fa0a3f29b62c13fce2bd9be99808c5a4be1c1919296a79abac4440621ea25412e0d38bc0331a89194cf930fb1c74f038cbf1affff5df804600f4d89a7fb35ea1ad3b910f9e104ed2b070ee7886d6691796e5cf79df24661adcb008f52bd470fa633c133670", + "0425102499f3ee67079aea36cc0ffed423d36c14c4b18075d14061bd4671093c1c1ef3d6d120fdaeed6fdcb3470daafe58fc9270cc9aaf8d69b185ab4e155c79b61a7afb30034dd491bb4af689b745921d5de063a30642b1aacb40a2a666f4b58f205555a6a36c286332b3c97c2e87daf4089553a4d212b1a2d3bbce59dce962b6", + "04304e3c0d1831c0912760e2ba9e664f0b01f90923eda55b4b3ac151f046ddbaa51e12c79e7494fe4256da88ff1f831d8f5a7dcb752d7f6fa87b7826d5005555201cae54d76c285c268103fdaa3459144284f85205f5815507f14b45bb45ac168d1e4f79c78e1fe9f43e26b1de95f679ceea3620202ca168a47841a8a154e9097b", + "040f70005a465c6babe2231b02f433c53628db41e2ce417e04d6750ed49a4e004a0a702d847a9049fdff76496066ca89d7468afa38132d1d4c398a81546db1ac690c3495adabb06f204cd7f1395cac16be8ff8a886888e65551738f460dd9900c42f8a8cf5d8cd2cea708145b5e3405752698e93e78ff77688f146135e932709fe", + "042cb71697e712d9ac8ed528f178f7e557939cc2222a29c95351d5e5e865333ef517a9725280e21e37efd4c7d58f14ab7468a1b436ded2357e5c5c9c9a17f731900973fd2cd828bbf2a5cf355f71f596b05bbeb98af159d285d5aca41411ed639109fead94fb9ba55cade075ec58d0c763202b506957409204f7a720f7cfc00b90", + "040a0b4fa2ad4186f08615695828ec9ddf27be0483bf53082597916717d268b74d209fff81f69f3446f86feaebe70abb60b3eed472edbaeb82675d3f8a3d80bbdd14daf9541f44a3ae86e773d0d076e990e6cd39572884f2634b5ff5a1766f5e33029b371a726dc6366b4b67f059581470b8c8d7f15457054f625ace8bf835f8cc", + "0403c2a6126b9a91a58e607ba45aa60a7a2c1a80dea7ac872bdff898028eeb7d13290361f9f715ec812686ea427a6122c31fb9b7ea497abe2b2e7ff6354afa6c0116e2d1de9694a8a499a9729097887ff858b3ae5fe9c2c16cd5f5e5ad743577310b4fa2835a321aa088d631b7a7f9b831f8c938db2b103b83c3fdd92de3c87960", + "0419d1dd9b5be92493d508494bce8685a6a869dfe320cd6b1e410c1f520b17e1880783391979f9aedb2fa731cb0898b3226e4fb27a8f0da4f72d18491194b11d9605950072a7e2bded197dcc2120f3d47c6e96b3013378e11ce47d78f79d2afbc61ecbbeac04eb8800393cfe2677c19f3f6d3708ddc6d2d71211a4bde59528feb3", + "0414a941598ca06b602ebf60c319103b8f286e6bc5ee468e2a31e9ee9597c474731bdcd6166cca254af4db066d8e9a54c96460cac125c3c62f0bf3db31f6fd5ae32016409ba19cf18bf96a7c5d3218c6d0e94ccc383bd6db7ad3454dea0830d2c41d4c380dc4221fac81e042f0feb90fe76ddbea32a97f3e54eaec56ada0c6bb84", + "040fab9277551d5ef7198febe3071d8a6ced030aac87cb232442abe6bf482f5bbb26726302007d614f10307836d994f35ce404d078293a602581287ed67b2a6bb304a759841a5ea3618726507cda0bb0079570bbbc8610a5bd4506b767c57647e105b2a0b50b70253fac177bc64b20e9efe6fa8bbdc8ff549644f44dd21b067da3", + 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"0406939813f76c28590786b32807f3c90b0bbdea67cc28f59569f04b599a32d5f30a9d0bfdb2654bc4c7be2739a427e73c90070652660cd1f77ac8d5fec5858b6d283e5a075c8c06a7856aa3fb34fd07c7998a80270bb2c86d5fb7cc6cff397f8913571721477148e0a53502c87cdb3686c5e3e965121a44db61dcc9fc3f4a2059", + "0401af82a2af67957bc6f919769303f137e829f6ab4305dc4376e7e76916fd687c1ae2bfe3108173f7d2cc1b489d8e35820de4ca4137a6257f91e3a04f67763843284f8fc6b2ca3c148ca4633c73966d877ddefa808759524bf342e137bd64be5d2f64986c06aae9b8a8614de1fbed123ae4f26c7b096dbe663fd36dcf57287e37", + "041be485f30959702efc92ee4b89c0c8d66961163c2b058da6acd8b19e5fa9fad91df599488e5099df6cdb82fb739e1987f13cccee4b9d7dfd9f51c218f17276ee1cb8b1af5eb41541b657b63f681861868f779b6be673de778d9f0bd5b133822a152a93c8dfccad9ec7c61d8052079cedba736795ec2ba378d6d2f2491fb8d251", + "0419911ca364e492ebe2cd1c4810757b1e072bb3a7e17bae19f61accabffc65a530ad273b59427853637dc215fe262084f5bc7814a6d97e53d684647f8939a1a07110122450e41be0b7635802dc1c1b3cd7d4fab981f1c6773c01ae0613b7991b817236a87c4b4148a2027bc1951e84735662e7b33595f765e3c1010afbaddafde", + "04264c1f5744eba1058129daf595ac3b92abe982daddfe1901ba23bd391e9b62d0272f0a3e10c62838ca0420cab64c05b9f0a870d7de936e9a27de1a93f24885251d8e55de68e34936e547685348bbc72e421addc1b6113b8306743584320c6b640d99fb4769101b668560b509ad380965b58327886a1da5ec863d7ff065e275eb", + "042927b07e722dd540a3e0d7c5cec64a9ede67cb33a967a87ff506d1125a7870070ef80b94950eaa1711cdf27ed6c720db47545a7f82687b9a18398b5ff1afa176274e115a4f4ffc072757146ace63b8f3f63cad1e1b32f8060b6fd174a469d103145eedb6a8d4dfb8bbcc35aae9ca0c7cdac69e64d0b80b31a9ebb12d308591cc" + ]; + + let mut acc = G2::one(); + let by = Fr::from_str("23938123").unwrap(); + + for i in 0..10000 { + assert!(expected[i] == into_hex(acc).unwrap()); + assert!(from_hex::(expected[i]).unwrap() == acc); + + acc = acc * by + acc; + } +} + +#[test] +fn fr_serialization_and_deserialization() { + let mut a = Fr::one(); + let b = Fr::from_str("17").unwrap(); + + for _ in 0..10000 { + a = a * b; + + assert!(reserialize(a) == a); + } +} + +#[test] +fn fr_test_invalid_representations() { + // modulus - 1 is representable + from_hex::("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000").unwrap(); + + // modulus is not representable + assert!(from_hex::("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none()); + + // ridiculously large numbers + assert!(from_hex::("f0644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none()); + assert!(from_hex::("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none()); +} + +#[test] +fn fr_vectors() { + let expected = vec![ + "0000000000000000000000000000000000000000000000000000000000000001", + "0000000000000000000000000000000000000000000000000000000000000003", + "2042def740cbc01bd03583cf0100e59370229adafbd0f5b62d414e62a000000d", + "1eced988f1c4e0f7f7433f99dc0eb1b89dd2a1b7c00a6e1a5df4900b27c8a6b3", + "02363a20539db6638514cb4ba7ec49c91b2c5d405b7e5c021d3a0bf834f2ef0a", + "09889144b32647e7a6a9ec0646bbabe83d9b7d9188c3bdcd3b002c55c9aa80ef", + "014ced1876c520cc926b880803323cb80b4554f8c2588032f6cb727157371641", + "179da4e61ae3117b9b12f86f5aa4f14e1fc3b46bf05d1423900f9ce6228b6d40", + "067140865d6292881384dc2252b9dd20111c942dc2364e8c98f1da3c28da888f", + "2ca25f36b7b20358489b49421b20f6a10eacf80e7f3d2bfce7593d0777fef418", + "2bf0a17a3fa0670820f4f2469774a98f9bcd6a5e490e97d6e11f361c914cfe8c", + "29a228ca3b4b8ed9cf1c2957a826aaf9cc3d1bdccc99996092b42907e8d763d4", + "296a1aae3b4d8c87257609dba587338419937a3f7a8e37234deca0eb9b761478", + "05c9dd8d3da17bb45967ad595e6440ba84243707a5b2a45568f22731b7f2055c", + "2e99a1f1b911be2b5eae798a1bdb87ec8b6b66015af43114d4c4f0c3081808d8", + "0500c67659a93bcd482ce6e2e198e671bff5e9bf276891b0c7f79200da6dd6b5", + "020a4cdd4381c2c7e2a1885ac88036bbacc0d6aac38ca1113c10efe9226e5744", + "29329d9432d2146f11a0d9e2578c09f7f1182b9cb20f988c6bad57bcb614e48f", + "09507fcafb26bb82d68228ef5f5ed7b71aab295bbe4cdc759df141917d11d79e", + "00a0ba7dcf0405380408feb28cdeeb784a19d0b9679d1adc005e9f1ab34f251a", + "067517b1a7f50aa3a3c9dd3db988b0e2e87a8e6b3fb1184b8a06cc3529141132", + "13e5c7527050b265295b9739cd2f95312932bfb62ce4c159c0ab92a61f0dcdab", + "2a737c37b6881ca875205b949c313108f54eee116d876d4685a88e77a88a7589", + "1103f082a016eea4c4dde6b7caf6d5f23d45007920eacd4ac8c952a9ece70d33", + "12f45350d4c50366dd0c88a77ce35b802cf1e6929210449ff83a73a627ae8a9b", + "18b04aa529992886a880fbabdcc834a983bf07bfb23cfa7bba660aec0a10a8ae", + "03820dad30db55157ce87fc6812ec0a4e659e7547b18206d5844a6d1f28399e1", + "030dfdd27e4e180392ec965b8bf2586d3203fe8931be034c966c37433625fd9a", + "08a9b73efb3282526bee3e609fb408449503b70f617b3bab42919108852cf44b", + "184b6a8fd93b49422099e5d75090dce92edf553115452635bbc8e623ce312ad3", + "030273cc32bbe84b480930f2313491a19c00e2dd39fbd30993603bb8b5495e95", + "1622dd450399ca70b99e94f60d87490b1078ff0dc3ce82cb32fd7dce0c4a4499", + "0195e53a05f7b95040d27b2819f7b23b40c0871dbc476e3c102e4cb64904483e", + "2910b512191aae4c5f27f90aea2f41b3b0e0f2042d57ebc8dc51901d06b10024", + "2e795bc0783c41c950330abcbd7e92a6d7e558787e7f579b4c2e4aaf9f66630f", + "0c34e777e38a18cb4edc5e9d3f4f07dbb1b074f38347dd53a015be494f24c0b0", + "277348139e45c362741e424e4dc10b94df979bbf14f7c4b6dc144a0a0c593e1c", + "1dff63c029e19454c2360a88baf804cafa60f6a50cbb71a79715c2832cf47408", + "23e84f6518e9bab5af850cf1f38a873fe8be0c2f786d1d4e1fdaf32d46150500", + "211b26970071c65390a8c6d822423ab281aae480a12a6fc836b40884a4337e53", + "296abf4e45cc54ba75225ebac4fe863d5cfe725105cadfc9f9357f791d7ffdd9", + "22cf34de7b862a2c4874a03b7ce9a9ac8e748e4741a7d01ef7e443430a543b33", + "2fca5ad500e198625c9d542e0d4aefdcda28d246edf9a83f34c57ac1cfe98a34", + "2a471ed73102e6918e55b0ef00822a5281ef0e49b4586cce10ab2671ddf95731", + "2210b49819b69ca317b63ccfe3a4fed4fcc9b9b368dee5d988624487f7cd7d99", + "0ac117037c41ac977dfac11e614ff3c1f0604fdf1e934addd96ca426a2d56c45", + "18a0c2a40073a85c4a4cec75dc9e049a18def78960c7429a9c6abc1cde4d1c42", + "229574d27795392985547b551380cda18972a32c2caf87b910746ebda6615ca8", + "1c6f0bc008a80d5d36cf483df553e24ac4f969d7a02f45e93181441d79fb72fc", + "1060b506a53a740169a80954eb5fcfc6b261cfca0c021a8113841bfa2b10d3df", + "23ecc4f3237f76dc81fbbb8e467d253ebb6b4e99b9f2c607daec1bb599a63108", + "2350041950c0d7144e6790f939fa4f2f53165b82e6f5c1c730b7129ff1dd6075", + "179de2653b84e8e5d925b21cf206b9886ffe9df14dd300ef48341707f3a8e43a", + "16c670be2c945714cf9e5b30cc54b846a86ade34ca2f19e95cb9782cd1a1f4f6", + "2a6ac3b3bd2a3ca35792323fe39384b7ba44fd70b8788bfb9a28f0397e6c58f2", + "27c800eb72d3f1ac091747cedb323b02178e9cab5951f1b1c97b70430bc93f49", + "0acb5953cf1583df3f5be7fc264a01d561642171ed8ad66cb0750ef84637919a", + "239f76d1622590038d64e710422cda6cb6e3e12d1593b07b08faea2dd71848de", + "2dab87d5e027c3aa07b95691cf313088176763b92a1a101142b202224c889319", + "2ebb685e594b7ae133c381606c8fc1c7a07ec46c653b1d5e73734362bc8cc31b", + "238274a880a47a28cec6660f31ca766e7c024fb458f7e1df5cc8d9f1fa49b364", + "27c5e092fa1ee06da63928770d5ecc7931845869260b3966d6523ea526db2789", + "00dcdcb4cc0015ab8b8bfca1d52e335275b6fb39b58d41c2b30367a104dc2fec", + "22c7f9595340b66a5f0781fc8c6856facc2228ef749ebe8f4e26a3c9ab74465c", + "2ea0cafc90188c763ae65f132d3d5c873e4bf9a50ceb079874d1c346ab8fb63d", + "180066c34e34c473953b3e66d98660e733729376074b231198e921d4ae28ac75", + "0cc81637599da9f5b8285737283752575daedabd7b463e02992933126b59e167", + "274ced6e1efb4148e7fb778afdb6e7a41a5af073df6c43b7103f291efac8ca76", + "2dccf0cb2b0c9165392462712673c4075a99d1f1e3118ffb3deadcda415768a6", + "1d0128b4b0f47f814b2fb6491f03654541725612c465267f02b73ed28074fbc1", + "264770a08b4fcfe8dcde0161cb4cfe1d851227fa5538adcdef80827636d95f92", + "08cd18d2188a1b7e7103b95a1b7022cb56f14916b5b5a8b4db2b7305d222fb1c", + "2b0fa450d5c7dda8eb466723cd25e0b762968e52fb8a558225ad2b0b3c9f15e4", + "0fb89c9eb27d7e49d4988722e645714fe5be1fd5d1dd7b9f475a10222aef9fb0", + "2384e79d245f048e6433b04a3c7e527a736c198c67682a23cccc127e0fe341c3", + "240c04ce80bb543b5b9dc19abacc681c8c58778141349e9e3f492515c54dbfdd", + "1b2c3e4505b9325d56c1fe596f839bc3bc023ca08485a3f71f575994e61e4e9a", + "2c341055bdfd39ae1c9012b5456790d9e6bb603a56cd215b8fc7ff5df23babda", + "2a618fada6222167ec179c0d2d5a3db64b07d04a0d8ce903ffcd878708131fc6", + "098505eda76826a820e63e004a19ce3c16fbc465d5c294e4710121781e476016", + "2198b95feb3a29a0bc7439a763caf039448143e464d12c3a5753fa4b4039b97e", + "23e150228a041db5a598c4955ad4b763b2edb6208b5f4caccf790d0a2d927215", + "1806b48868d9900275573f4e57ecc9257f0b8787527a2b96d2e24f1cfd4b6ac1", + "2b7b0225bd8e48a401ab3a10507845bf3110c5959980023d166dc4be0aabdadf", + "1b5d5b3c9f454b4019116206d223c708bba4ee71138fffb32ed8674943c72486", + "2a495d1c7fcaa4f27be5914c7c6fed4fb65ee46e6d7974a55141d9bab30b39b4", + "1fddf00cfacfef6cf8dd5e88e04298fd376934a40938aee523338677258469ca", + "01fd18b9683b1aac8675185d5d06773aaab0e19112ddc9bb63e2c63bcde49db0", + "140899d53f48c9b200a48a8618dda9f24ba27a9acdb63dcf633107feae16fe98", + "0a0a0501eb8fbabf040f420ecad8797db587601e3deab6a01ce4b0d306be7cc6", + "2fa5a098db8149032e6bb899bc0b97c6b2ffdd6cfcc955d17ea2afe6a3cc3990", + "26162db3d4a6e6172f0b8d1d7ec1f706f9eeb7c6d3b0c2a510d7d0e04fe4eda6", + "1fc0dbbbbdea0ffaf2864ccca1b7e937efadd6987ad73881c5fd534ce2ae55ff", + "00dc4562c8483647fe1d924d50c574fb00b53973333cf3f42b24cb0412d1949c", + "2fcdf1fcbdfbec79a47715a340effb55d042f522b0b86acbd4c2c286d8afbbc1", + "0b11546ba7759df51528a4b9656d09ab5c2b7423ea82ed36d7acb01fe96cc8b7", + "2f3dc23b191c92d0a582a35f19c25831bc60fe3aa228c3e00e70fd371f72e80b", + "17b160611d7b3fbffd972f516d72b933980f325db9220cb1f953f74d166badfd", + "17e5ddf96d4c64ebb06179a3544afca2bae78fc1089031906aea8afae5610147", + "012ae487cf528b8197e4333b56705d7c31c92545607e6edbb0105717f5e33f66", + "03a07c50c596fe0ebae61d554d46b055a6fb0de2da4a5434e026052292ef06ac", + "27d9bc26fda4e6554de6d29b88934c53cae2eaee241ae7be961598f41118a7cc", + "0a772b263180a8fd6c99db42be795b3d2944d4858fd84d307cc438dd82541cd1", + "1ff90c2b7d3df22a1dd77b407e7f499d7ce6c7d5d3dfe360c485b6c49ccefcad", + "0253973b5ebdc95b42002fb7695d51aeb1410ba1aeb24d98fac263963e527daf", + "29912c9332807ec705d49f06c24b30caa6b9cc764dd223510e0fd21faf1aa1e4", + "2c9482d7500b2eb22073cba5e6793b8bdc684e2b979df3b18e340ac27141b147", + "25ef1f7f3369c7490da551cdee2eb521d4c058ff26c9ce503174f4b776a62134", + "2850f791ce002da71a143489ca75f103cdb06faacf0cc1cb42d3f16f007c6ac8", + "1b2dfc7f783b9a94a2374d632c7f2b9261c64f3384e7879f8777c761a0f38916", + "1dab259a8cd28a888944dc62f0d71f77fbea3cec30777146eee454d8a38862e3", + "0ff237bdb85a4d1d59d1771a372d85bc4c929c13bd11dc5ab547efbdac506d72", + "03ccca3ce8529946b5971cb7b6cee1b7f0603d1a14fdb2399a0b754616881106", + "0ae33319df196d3e6a9d381c5e9216bef5f269ccdd9bea3228bef871ec64a5ce", + 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"0796e72aeac8238d979f6878c0ffa8bf81fdd5223c0fb19ee005d7d17cfc93fa", + "10e297ec13f69da265157f71f56d41507b689b80e15a684a7d3fdae2b4d2e758", + "2f5284398d7fa56a116d581224ea9b82427f4fbefd6a0aa90ec15ffcdfe6ef3a", + "032e7d83353e1909df1b2924dc6925883feb94e14d61847c7f7918aa7f1ecdeb", + "12ecc47b36279fda239b5262b4b1966d9c044500c2300abbf38a5954c3b0dd11", + "14cc1fb590aef7dc954efd3a4c53a4b1e286d09cb2476ce507b601fb82a084e0", + "2cc55c74693f6a65bdf7ade43d1bed32c9d2fd61dc357c9a41adf722be784455", + "05aa5b48bb735799970ccfa1029b4e28f48c3ea6f3410df016c033ed043a68d7", + "0bc0975e876478f57e2a7b031f8ce2a38dee2029959cd536a96af64c650cf304", + "283121e657b0ad713eafcb2503d1c808bb1d51ea82582330999983db93f13198", + "16d5f557f636d7eac66776a87ead7d3957605a4e17839c5f7d32dc452b48ea8a", + "28394c22094dd78bfb942e3bf4e1f305538bd9eed5690715bb4f27c1c0ca5cfb", + "1af54931d760a0661b21cb5985522848d165b47e5260fe6c02b582ac09f1adda", + "28d32bb1e175dc93a86357b6b39e3102f1390a9e6c3934c73de9250b1d6e373b", + "1c8668339c126322317b90c15406a1b2f08475d0cbfbd1320172e3151eaf530f", + "2eddf87dabd2df616e6afcadb6c1dce2c0dcd074d9eb44dd3a670f9b5e081106", + "071f91fef7e3a13e6e98f1d2f4bb3b08973df8c6715f066cb9f70f47db8db3d4", + "0c9462aee892e3b878c67bf9c0a99a0a7dd0302a807bffd347cd76a48106bfe9", + "0d447987f491bf61f15fc0a9f909919a93b2210d624195293fd600a2c9266fe8", + "0e3dadc74b8817b2b4cb32a78a6c910060e5a4cd79cbfd6a1146069a87e420a7", + "278c0bc5addb7303cff9b3570df6176493de54f43f15aae2416d9bc170957333", + "17dfe0688d2afde487cae0e14a01f02384e7b5c61a659c8bf4df4f36cbf6012c", + "08b4dff73178cce114f19cd5d5d665f4811d23913e988af6e2e9848f94dbacb4", + "1ffb1a7bb1827965bf2259c61f4cc3a579c475e00551939e0201486e51fbe0ab", + "1462aafe0e864b2e54e7d62c594059b464ba9a3e4a3a220e28b22bc598d1df83", + "1d52e0faf9391bc44ba1f66fe637e8e95dde8e7eee9491f9471aa8aae5ed133e", + "13246f6065b8696cb848322da363344f1786820d3d1847dd7210c2fec44393d6", + "133d1b51829583b18d2afaa251686a4148f8ca24dce3fc378ba9ddc1a3d66a4c", + "06f5e01c175eb4bbdcfc07728b092480f2cf0d396fd72e7ff7694357b386c575", + "08c5195b776aab95da6ca17eac81849df8785af3373526ae6a76e7fa4fe95673", + "14889763041484601e85d4ff8159336a8793f18d5edb865974538ad5b58db01a", + "0d454faa86f40794dd02f256c1a338c22f3c814c847b4e205cf20082ff1a5827", + "287e7a4cea0baa17d1c3132536df29f057d03abf655feda515cee4bd45001de8", + "1658219d6a2fddc4251f3432bbc8b9e49684fcd79aae97a0e78df0104d060ff0", + "15cb0566bc07a7ff76ce7fb625640816c32716f2fcc031844aafb2f09b3266eb", + "251fba7c2bccc579147461d7caed44ffc4d7aba749f7c480a143fcc52ff6d0d4", + "0f88bd8cbf293e53bd7ea661309647621bf243b07c3010867a71e81d56daa32e", + "2e50739ded1d40ef1faffa7247fb35f3f3d8738bb300053009720f464b245b4a", + "08a860efa3e963177cd69cd935fd4ce61812deb1ef476eba5c18b53a1825f73d", + "02ef0b5bfd2869670ddc1dde1c9a29ac9a93a28633dd55cd543dd93d031a3776", + "00ad678ff09f4f1d62f3eb67a93e95202c4002b4435a3930b2e97fc8a437c860", + "2c53a9ac608631a119e7f57ed5cb0498134671e6f517757546b3ff61dc24ea9d", + "0b262e363290fd3157aa34482f7d3b63e7293e766a34c528fcaeac7b78c669ab", + "2c729367130f7492d6c7fa81d933e572ceb2cae48abff54290364f7ffd98bbe2", + "0c52b752688f7c1231a81213da5d399f0de08127a0410ab6cec26224520a7302", + "015ed07c528f1f75c39013233daae79023c9a10051e272b2a0a5596745b50def", + "054c68de3da880b3efd04d6dd592070402cd24056b7c170657335e9ccfb45ed9", + "0653a2625249ca142027b136af44aa3bea7ce98801ab7964102b20385ed3e38f", + "128265fbcf4f8dc26f44e5de2ccbd57ac858b7a1a3d955a1cafe98de79d239ef", + "290a90817d105423426ab71c2b097df309086c3cc0b83ccb1bf90486cbce4114", + "0ec81adacd88f9f1401c42ceb56348bbf36181a0c03f2512e34fdef39f23859b", + "0059843dff350356ce8db94fc588542dcd43c7621d326a56c7de9126548a84ef", + "05f1d7d0fc3a5e6bfc55ce75e7688236e879a7f60cb52f138f52069b048f05a9", + "2dadc5fa46bbc50df63dadfc9b4fa72bd344e26e93f0fbc184f03bf4a76b51e1", + "1bf5f44265a2400afe65e220ed0c8b49306770e192cfcbe06c8c28206a42cd78", + "0f484d2249c289e95f4c1b2fa0330572037b157ae41187aebf92468d617dacd5", + "1a4dd8999a4847cb26d5cc32ac2b94ff7f5e4e6a37263e34cb18dd53d8be1b75", + "2fbf545602120abfff0a56316d9143d152d43816ef782a67780e1b8f9252a4ff", + "1835d89422d3d824fad14501a3f3c8a6ae474df2b5a29011b5c36030c2b8bdfe", + "18c215d302d89a958d8d9cdad60b5010024e91b510bcab7ffbb384cd21b625da", + "0179533ed710624344ced7dd685ab4dbce139efd5ea097e8adbd02c32aaac947", + "07b91c56dd39dd5d5de474540858aa9b5cd0d91cad2099bd14befb060f4f3b96", + "2a79af347cb1fa3996755c7f68ad83f86b86ba81bd2b9fa98948cfcef63cce23", + "0c38e0161d3e3d317108e518dc74150f8205fb74083fd47b3b88aafc9d0130cf", + "0d65129efa0b7fe99f91e540166753bbbff12cdaa9b5777208f26ba72a87b52a", + "065923e0aa248690099aa247581f481061d9243cedec15a538c6f3dabc54ed3f", + "209749a7661b281882cd713683824ed6122820968a9552ed27f208a45c2837ec", + "0567e0493586c14d0ef128252f9a20c74602ec56626b5c2f3644fc79a7983a16", + "2a3746ab2d1fd023c90559abcb8c36d3273b3685b7da3332b3162e894a6cbcea", + "2fe83a4aa399397b998bc1bf32a322b69e58244d60ccfb546c013ec9818e1355", + "2cba41b38555075f0caa9773c8f358d018620c4fec64c15142e33bae27ff07be", + "262d890f3c3d9ebe6eb150754a0677d94a64f645ddc813eb87f82418160376bc", + "184043dc9ed8d23817f34010c7689116620fb892ebe7b92e7afeb2dff8203bb0", + "16150e6cd627f1aab252d573c715c3e132d63d714e232c200a86db5279dc24f9", + "1aa1be02875b4dd93beaa0841dc74dd43b2f69accd3c3625cd28e720fc3077be", + "0870eb40106c6c25725f4e303741257e730098d7d4f7c07155bc89c805f3e573", + "2c174e5eaedc48a0f83b0638038d79d5ce719a7ba41a974f68dc307a4d7df27e", + "1c5f8c2978c5db3c6483e6c59ecfa4b4591f81c346f882166fe1395f09067c01", + "25a5229df981407d38b35494facd5d3be74835427a084bc796046ee533804256", + "14198c56049b0bafe24c1e58227a15dfdc1730f7570a0425cc3f5175078d3b46", + "06f649866a0de8a7127623c9a87e528dea9d7df9a761fd1bbce65bc1dccc06aa", + "1164c0172f7edcf878d89bec7c593dbac32f366f7c26136c219c9ff79fb4ba8f", + "1d57c7d112c7559eef860394ffa55686dc4addc269e1f4763a3a329d85b9203c", + "29c8787c8830fac709c646dbfda04db6ecf9f508e056fb42d9a7efd3bb0a0360", + "23ef9d9c4a48657f835f302dd6f6efa94f21f7d65fd188fe53c540bc7fbb48f2", + "259ff75fdd8a23943f9d9e91e335395223a11bde135182fc543af4763a9c491b", + "1b14061e2f2c468feb62b9ce08729d60a700aad2f37e7aefdcd977243a50f02f", + "2a79870f9070251178edd6c30596db17a75375b7bc163d39cfa97f42bea1e487", + "2920015344e43aa0e279bb8bbd180ad00f80a2d88d7ee3d75f794ea94f788c5c", + "262f785087e1fb1873a803e55d7f1b6e1d31ae6ce6c25ad0a1ce39f3dc870765", + "2f34183f18efd7f36cf92ef3310ea2b5fcbdc68a08ec1246f86ec7821bdd3593", + "24976ddc28c17b43f06aff004f5237fdf5216bcc98656c4cbfd80d2ceb28f5b4", + "1c75ba32a127cae227f83616357be97ccf95559f4e10a202f6f073f6615708a2", + "29a2d25cbda9f5b67fa860e6d42bd3408a8538b9c6879851db68d2a6bcafc02d", + "0aa84212e380e99137636932c0aadb021c2ecd448bfde7f9bba46dbfae9847c5", + "21f78689e3e2585bd2fa23848df576d8ca6a20c1e22ad912ba5e9bd9317f072c", + "293a1159d1c02a6429adbb0da020a819a687ee7047679c3c60d58c3ff98ae3ea", + "1a7d485f430c376e12fc7d1b3613a511822193599e15e0b30d214cb989edd72d", + "148f89c16be581d1dde28de8b229a14509505effd37e672e3f47a90515f0767d", + "03c2411a03c742bb60b08116a2fd8ea86e1cbaa1f6f82b45951801caab0a6448", + "05b054684c6e494317541efe51da10ca76fb31a10452b442e4993814a08b6bf1", + "1ca534bb0ce1f2ae8149ababf167c5491f00edb4b144f6ea92a7d7918b6d4cd3", + "1c2740412825060b5f2a80d387fd83d5023d1be26ba6eb2b0a5d8e90ecf98f44", + "15832c8f5667b380e31a84435232af18e685d784d201faf7b9bbae68c20aca82", + "14d6fefe0a848db15e0baddc508b71614642dc5dca6e267a4c082eedb7f22f3e", + "0c0a1384c660a036ad581bcce6af24ca06f7b647be7fea648cef6355901fadb1", + "24d5243e9dfd338ac19c7a01a6edb2ddfafb256e6b84964d3c50cb3fd8dca48e", + "0a4d7c32d85fe6458c9b48597aa03087ff6ad9a766ae6e3db65e2b23b6d7dd52", + "1db213ff1511c1dbd7f764afcafb3d1ac5811e7a5795fe61f00ab8abad903bdd", + "1665a557b4a74548ceec6f598ab5684f32bcaa867c12e8d1abdd6acee1285792", + "2fd5d39615c3cfbe8ccc5e362e635cfe06c588e9bc0cb1d95c1df71dad1c0b7d", + "100e6f9483e9c38ce0a7fe26cfd8bd1d915a967ef85e9c3126b6f97b8c67ab0f", + "02f04bc9ea7e55f3901d844e427bc348f934f48551eb0b60051f9ee756a6aa3c", + "18bf6a3dc3320590adae58baf410b4367785d21d0a38e1fd8ad0b5ac73ecf609" + ]; + + let mut acc = Fr::one(); + for i in 0..10000 { + assert!(expected[i] == into_hex(acc).unwrap()); + assert!(from_hex::(expected[i]).unwrap() == acc); + + acc = acc * acc + acc + acc.inverse().unwrap(); + } +}