diff --git a/Cargo.toml b/Cargo.toml index 3446f46..b6ba134 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -15,11 +15,14 @@ homepage = "https://github.com/ebfull/pairing" repository = "https://github.com/ebfull/pairing" [dependencies] -rand = "0.4" +rand_core = "0.3" byteorder = "1" ff = { path = "../ff", features = ["derive"] } group = { path = "../group" } +[dev-dependencies] +rand = "0.5" + [features] unstable-features = ["expose-arith"] expose-arith = [] diff --git a/src/bls12_381/ec.rs b/src/bls12_381/ec.rs index f5a6d8f..b20dea8 100644 --- a/src/bls12_381/ec.rs +++ b/src/bls12_381/ec.rs @@ -200,11 +200,16 @@ macro_rules! curve_impl { } - impl Rand for $projective { - fn rand(rng: &mut R) -> Self { + impl CurveProjective for $projective { + type Engine = Bls12; + type Scalar = $scalarfield; + type Base = $basefield; + type Affine = $affine; + + fn random(rng: &mut R) -> Self { loop { - let x = rng.gen(); - let greatest = rng.gen(); + let x = $basefield::random(rng); + let greatest = rng.next_u32() % 2 != 0; if let Some(p) = $affine::get_point_from_x(x, greatest) { let p = p.scale_by_cofactor(); @@ -215,13 +220,6 @@ macro_rules! curve_impl { } } } - } - - impl CurveProjective for $projective { - type Engine = Bls12; - type Scalar = $scalarfield; - type Base = $basefield; - type Affine = $affine; // The point at infinity is always represented by // Z = 0. @@ -629,7 +627,7 @@ pub mod g1 { use super::g2::G2Affine; use ff::{BitIterator, Field, PrimeField, PrimeFieldRepr, SqrtField}; use group::{CurveAffine, CurveProjective, EncodedPoint, GroupDecodingError}; - use rand::{Rand, Rng}; + use rand_core::RngCore; use std::fmt; use {Engine, PairingCurveAffine}; @@ -1276,7 +1274,7 @@ pub mod g2 { use super::g1::G1Affine; use ff::{BitIterator, Field, PrimeField, PrimeFieldRepr, SqrtField}; use group::{CurveAffine, CurveProjective, EncodedPoint, GroupDecodingError}; - use rand::{Rand, Rng}; + use rand_core::RngCore; use std::fmt; use {Engine, PairingCurveAffine}; diff --git a/src/bls12_381/fq.rs b/src/bls12_381/fq.rs index fd0d416..b006812 100644 --- a/src/bls12_381/fq.rs +++ b/src/bls12_381/fq.rs @@ -1173,7 +1173,7 @@ fn test_neg_one() { } #[cfg(test)] -use rand::{Rand, SeedableRng, XorShiftRng}; +use rand::{SeedableRng, XorShiftRng}; #[test] fn test_fq_repr_ordering() { @@ -1396,7 +1396,10 @@ fn test_fq_repr_num_bits() { #[test] fn test_fq_repr_sub_noborrow() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let mut t = FqRepr([ 0x827a4a08041ebd9, @@ -1426,7 +1429,7 @@ fn test_fq_repr_sub_noborrow() { ); for _ in 0..1000 { - let mut a = FqRepr::rand(&mut rng); + let mut a = Fq::random(&mut rng).into_repr(); a.0[5] >>= 30; let mut b = a; for _ in 0..10 { @@ -1483,7 +1486,10 @@ fn test_fq_repr_sub_noborrow() { #[test] fn test_fq_repr_add_nocarry() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let mut t = FqRepr([ 0x827a4a08041ebd9, @@ -1514,9 +1520,9 @@ fn test_fq_repr_add_nocarry() { // Test for the associativity of addition. for _ in 0..1000 { - let mut a = FqRepr::rand(&mut rng); - let mut b = FqRepr::rand(&mut rng); - let mut c = FqRepr::rand(&mut rng); + let mut a = Fq::random(&mut rng).into_repr(); + let mut b = Fq::random(&mut rng).into_repr(); + let mut c = Fq::random(&mut rng).into_repr(); // Unset the first few bits, so that overflow won't occur. a.0[5] >>= 3; @@ -1595,10 +1601,13 @@ fn test_fq_is_valid() { ])).is_valid() ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); assert!(a.is_valid()); } } @@ -1708,13 +1717,16 @@ fn test_fq_add_assign() { // Test associativity - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Generate a, b, c and ensure (a + b) + c == a + (b + c). - let a = Fq::rand(&mut rng); - let b = Fq::rand(&mut rng); - let c = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); + let b = Fq::random(&mut rng); + let c = Fq::random(&mut rng); let mut tmp1 = a; tmp1.add_assign(&b); @@ -1818,12 +1830,15 @@ fn test_fq_sub_assign() { ); } - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure that (a - b) + (b - a) = 0. - let a = Fq::rand(&mut rng); - let b = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); + let b = Fq::random(&mut rng); let mut tmp1 = a; tmp1.sub_assign(&b); @@ -1865,13 +1880,16 @@ fn test_fq_mul_assign() { ])) ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000000 { // Ensure that (a * b) * c = a * (b * c) - let a = Fq::rand(&mut rng); - let b = Fq::rand(&mut rng); - let c = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); + let b = Fq::random(&mut rng); + let c = Fq::random(&mut rng); let mut tmp1 = a; tmp1.mul_assign(&b); @@ -1887,10 +1905,10 @@ fn test_fq_mul_assign() { for _ in 0..1000000 { // Ensure that r * (a + b + c) = r*a + r*b + r*c - let r = Fq::rand(&mut rng); - let mut a = Fq::rand(&mut rng); - let mut b = Fq::rand(&mut rng); - let mut c = Fq::rand(&mut rng); + let r = Fq::random(&mut rng); + let mut a = Fq::random(&mut rng); + let mut b = Fq::random(&mut rng); + let mut c = Fq::random(&mut rng); let mut tmp1 = a; tmp1.add_assign(&b); @@ -1932,11 +1950,14 @@ fn test_fq_squaring() { ])).unwrap() ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000000 { // Ensure that (a * a) = a^2 - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); let mut tmp = a; tmp.square(); @@ -1952,13 +1973,16 @@ fn test_fq_squaring() { fn test_fq_inverse() { assert!(Fq::zero().inverse().is_none()); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let one = Fq::one(); for _ in 0..1000 { // Ensure that a * a^-1 = 1 - let mut a = Fq::rand(&mut rng); + let mut a = Fq::random(&mut rng); let ainv = a.inverse().unwrap(); a.mul_assign(&ainv); assert_eq!(a, one); @@ -1967,11 +1991,14 @@ fn test_fq_inverse() { #[test] fn test_fq_double() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure doubling a is equivalent to adding a to itself. - let mut a = Fq::rand(&mut rng); + let mut a = Fq::random(&mut rng); let mut b = a; b.add_assign(&a); a.double(); @@ -1988,11 +2015,14 @@ fn test_fq_negate() { assert!(a.is_zero()); } - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure (a - (-a)) = 0. - let mut a = Fq::rand(&mut rng); + let mut a = Fq::random(&mut rng); let mut b = a; b.negate(); a.add_assign(&b); @@ -2003,12 +2033,15 @@ fn test_fq_negate() { #[test] fn test_fq_pow() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for i in 0..1000 { // Exponentiate by various small numbers and ensure it consists with repeated // multiplication. - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); let target = a.pow(&[i]); let mut c = Fq::one(); for _ in 0..i { @@ -2019,7 +2052,7 @@ fn test_fq_pow() { for _ in 0..1000 { // Exponentiating by the modulus should have no effect in a prime field. - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); assert_eq!(a, a.pow(Fq::char())); } @@ -2029,13 +2062,16 @@ fn test_fq_pow() { fn test_fq_sqrt() { use ff::SqrtField; - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero()); for _ in 0..1000 { // Ensure sqrt(a^2) = a or -a - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); let mut nega = a; nega.negate(); let mut b = a; @@ -2048,7 +2084,7 @@ fn test_fq_sqrt() { for _ in 0..1000 { // Ensure sqrt(a)^2 = a for random a - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); if let Some(mut tmp) = a.sqrt() { tmp.square(); @@ -2108,11 +2144,14 @@ fn test_fq_from_into_repr() { // Zero should be in the field. assert!(Fq::from_repr(FqRepr::from(0)).unwrap().is_zero()); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Try to turn Fq elements into representations and back again, and compare. - let a = Fq::rand(&mut rng); + let a = Fq::random(&mut rng); let a_repr = a.into_repr(); let b_repr = FqRepr::from(a); assert_eq!(a_repr, b_repr); @@ -2205,7 +2244,7 @@ fn test_fq_ordering() { #[test] fn fq_repr_tests() { - ::tests::repr::random_repr_tests::(); + ::tests::repr::random_repr_tests::(); } #[test] diff --git a/src/bls12_381/fq12.rs b/src/bls12_381/fq12.rs index b24fcaa..4f675cf 100644 --- a/src/bls12_381/fq12.rs +++ b/src/bls12_381/fq12.rs @@ -2,7 +2,7 @@ use super::fq::FROBENIUS_COEFF_FQ12_C1; use super::fq2::Fq2; use super::fq6::Fq6; use ff::Field; -use rand::{Rand, Rng}; +use rand_core::{RngCore}; /// An element of Fq12, represented by c0 + c1 * w. #[derive(Copy, Clone, Debug, Eq, PartialEq)] @@ -17,15 +17,6 @@ impl ::std::fmt::Display for Fq12 { } } -impl Rand for Fq12 { - fn rand(rng: &mut R) -> Self { - Fq12 { - c0: rng.gen(), - c1: rng.gen(), - } - } -} - impl Fq12 { pub fn conjugate(&mut self) { self.c1.negate(); @@ -49,6 +40,13 @@ impl Fq12 { } impl Field for Fq12 { + fn random(rng: &mut R) -> Self { + Fq12 { + c0: Fq6::random(rng), + c1: Fq6::random(rng), + } + } + fn zero() -> Self { Fq12 { c0: Fq6::zero(), @@ -153,13 +151,16 @@ use rand::{SeedableRng, XorShiftRng}; #[test] fn test_fq12_mul_by_014() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let c0 = Fq2::rand(&mut rng); - let c1 = Fq2::rand(&mut rng); - let c5 = Fq2::rand(&mut rng); - let mut a = Fq12::rand(&mut rng); + let c0 = Fq2::random(&mut rng); + let c1 = Fq2::random(&mut rng); + let c5 = Fq2::random(&mut rng); + let mut a = Fq12::random(&mut rng); let mut b = a; a.mul_by_014(&c0, &c1, &c5); diff --git a/src/bls12_381/fq2.rs b/src/bls12_381/fq2.rs index 363439a..c69f13c 100644 --- a/src/bls12_381/fq2.rs +++ b/src/bls12_381/fq2.rs @@ -1,6 +1,6 @@ use super::fq::{FROBENIUS_COEFF_FQ2_C1, Fq, NEGATIVE_ONE}; use ff::{Field, SqrtField}; -use rand::{Rand, Rng}; +use rand_core::RngCore; use std::cmp::Ordering; @@ -56,16 +56,14 @@ impl Fq2 { } } -impl Rand for Fq2 { - fn rand(rng: &mut R) -> Self { +impl Field for Fq2 { + fn random(rng: &mut R) -> Self { Fq2 { - c0: rng.gen(), - c1: rng.gen(), + c0: Fq::random(rng), + c1: Fq::random(rng), } } -} -impl Field for Fq2 { fn zero() -> Self { Fq2 { c0: Fq::zero(), @@ -883,7 +881,10 @@ use rand::{SeedableRng, XorShiftRng}; #[test] fn test_fq2_mul_nonresidue() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let nqr = Fq2 { c0: Fq::one(), @@ -891,7 +892,7 @@ fn test_fq2_mul_nonresidue() { }; for _ in 0..1000 { - let mut a = Fq2::rand(&mut rng); + let mut a = Fq2::random(&mut rng); let mut b = a; a.mul_by_nonresidue(); b.mul_assign(&nqr); diff --git a/src/bls12_381/fq6.rs b/src/bls12_381/fq6.rs index 36c6e28..21c8310 100644 --- a/src/bls12_381/fq6.rs +++ b/src/bls12_381/fq6.rs @@ -1,7 +1,7 @@ use super::fq::{FROBENIUS_COEFF_FQ6_C1, FROBENIUS_COEFF_FQ6_C2}; use super::fq2::Fq2; use ff::Field; -use rand::{Rand, Rng}; +use rand_core::RngCore; /// An element of Fq6, represented by c0 + c1 * v + c2 * v^(2). #[derive(Copy, Clone, Debug, Eq, PartialEq)] @@ -17,15 +17,6 @@ impl ::std::fmt::Display for Fq6 { } } -impl Rand for Fq6 { - fn rand(rng: &mut R) -> Self { - Fq6 { - c0: rng.gen(), - c1: rng.gen(), - c2: rng.gen(), - } - } -} impl Fq6 { /// Multiply by quadratic nonresidue v. @@ -110,6 +101,14 @@ impl Fq6 { } impl Field for Fq6 { + fn random(rng: &mut R) -> Self { + Fq6 { + c0: Fq2::random(rng), + c1: Fq2::random(rng), + c2: Fq2::random(rng), + } + } + fn zero() -> Self { Fq6 { c0: Fq2::zero(), @@ -306,7 +305,10 @@ use rand::{SeedableRng, XorShiftRng}; #[test] fn test_fq6_mul_nonresidue() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let nqr = Fq6 { c0: Fq2::zero(), @@ -315,7 +317,7 @@ fn test_fq6_mul_nonresidue() { }; for _ in 0..1000 { - let mut a = Fq6::rand(&mut rng); + let mut a = Fq6::random(&mut rng); let mut b = a; a.mul_by_nonresidue(); b.mul_assign(&nqr); @@ -326,11 +328,14 @@ fn test_fq6_mul_nonresidue() { #[test] fn test_fq6_mul_by_1() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let c1 = Fq2::rand(&mut rng); - let mut a = Fq6::rand(&mut rng); + let c1 = Fq2::random(&mut rng); + let mut a = Fq6::random(&mut rng); let mut b = a; a.mul_by_1(&c1); @@ -346,12 +351,15 @@ fn test_fq6_mul_by_1() { #[test] fn test_fq6_mul_by_01() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let c0 = Fq2::rand(&mut rng); - let c1 = Fq2::rand(&mut rng); - let mut a = Fq6::rand(&mut rng); + let c0 = Fq2::random(&mut rng); + let c1 = Fq2::random(&mut rng); + let mut a = Fq6::random(&mut rng); let mut b = a; a.mul_by_01(&c0, &c1); diff --git a/src/bls12_381/fr.rs b/src/bls12_381/fr.rs index 5e57631..20811cd 100644 --- a/src/bls12_381/fr.rs +++ b/src/bls12_381/fr.rs @@ -6,7 +6,7 @@ use ff::{Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr}; pub struct Fr(FrRepr); #[cfg(test)] -use rand::{Rand, SeedableRng, XorShiftRng}; +use rand::{SeedableRng, XorShiftRng}; #[test] fn test_fr_repr_ordering() { @@ -197,7 +197,10 @@ fn test_fr_repr_num_bits() { #[test] fn test_fr_repr_sub_noborrow() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let mut t = FrRepr([ 0x8e62a7e85264e2c3, @@ -221,7 +224,7 @@ fn test_fr_repr_sub_noborrow() { ); for _ in 0..1000 { - let mut a = FrRepr::rand(&mut rng); + let mut a = Fr::random(&mut rng).into_repr(); a.0[3] >>= 30; let mut b = a; for _ in 0..10 { @@ -296,7 +299,10 @@ fn test_fr_legendre() { #[test] fn test_fr_repr_add_nocarry() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let mut t = FrRepr([ 0xd64f669809cbc6a4, @@ -322,9 +328,9 @@ fn test_fr_repr_add_nocarry() { // Test for the associativity of addition. for _ in 0..1000 { - let mut a = FrRepr::rand(&mut rng); - let mut b = FrRepr::rand(&mut rng); - let mut c = FrRepr::rand(&mut rng); + let mut a = Fr::random(&mut rng).into_repr(); + let mut b = Fr::random(&mut rng).into_repr(); + let mut c = Fr::random(&mut rng).into_repr(); // Unset the first few bits, so that overflow won't occur. a.0[3] >>= 3; @@ -397,10 +403,13 @@ fn test_fr_is_valid() { ])).is_valid() ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); assert!(a.is_valid()); } } @@ -492,13 +501,16 @@ fn test_fr_add_assign() { // Test associativity - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Generate a, b, c and ensure (a + b) + c == a + (b + c). - let a = Fr::rand(&mut rng); - let b = Fr::rand(&mut rng); - let c = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); + let b = Fr::random(&mut rng); + let c = Fr::random(&mut rng); let mut tmp1 = a; tmp1.add_assign(&b); @@ -586,12 +598,15 @@ fn test_fr_sub_assign() { ); } - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure that (a - b) + (b - a) = 0. - let a = Fr::rand(&mut rng); - let b = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); + let b = Fr::random(&mut rng); let mut tmp1 = a; tmp1.sub_assign(&b); @@ -627,13 +642,16 @@ fn test_fr_mul_assign() { ])) ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000000 { // Ensure that (a * b) * c = a * (b * c) - let a = Fr::rand(&mut rng); - let b = Fr::rand(&mut rng); - let c = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); + let b = Fr::random(&mut rng); + let c = Fr::random(&mut rng); let mut tmp1 = a; tmp1.mul_assign(&b); @@ -649,10 +667,10 @@ fn test_fr_mul_assign() { for _ in 0..1000000 { // Ensure that r * (a + b + c) = r*a + r*b + r*c - let r = Fr::rand(&mut rng); - let mut a = Fr::rand(&mut rng); - let mut b = Fr::rand(&mut rng); - let mut c = Fr::rand(&mut rng); + let r = Fr::random(&mut rng); + let mut a = Fr::random(&mut rng); + let mut b = Fr::random(&mut rng); + let mut c = Fr::random(&mut rng); let mut tmp1 = a; tmp1.add_assign(&b); @@ -690,11 +708,14 @@ fn test_fr_squaring() { ])).unwrap() ); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000000 { // Ensure that (a * a) = a^2 - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); let mut tmp = a; tmp.square(); @@ -710,13 +731,16 @@ fn test_fr_squaring() { fn test_fr_inverse() { assert!(Fr::zero().inverse().is_none()); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); let one = Fr::one(); for _ in 0..1000 { // Ensure that a * a^-1 = 1 - let mut a = Fr::rand(&mut rng); + let mut a = Fr::random(&mut rng); let ainv = a.inverse().unwrap(); a.mul_assign(&ainv); assert_eq!(a, one); @@ -725,11 +749,14 @@ fn test_fr_inverse() { #[test] fn test_fr_double() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure doubling a is equivalent to adding a to itself. - let mut a = Fr::rand(&mut rng); + let mut a = Fr::random(&mut rng); let mut b = a; b.add_assign(&a); a.double(); @@ -746,11 +773,14 @@ fn test_fr_negate() { assert!(a.is_zero()); } - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Ensure (a - (-a)) = 0. - let mut a = Fr::rand(&mut rng); + let mut a = Fr::random(&mut rng); let mut b = a; b.negate(); a.add_assign(&b); @@ -761,12 +791,15 @@ fn test_fr_negate() { #[test] fn test_fr_pow() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for i in 0..1000 { // Exponentiate by various small numbers and ensure it consists with repeated // multiplication. - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); let target = a.pow(&[i]); let mut c = Fr::one(); for _ in 0..i { @@ -777,7 +810,7 @@ fn test_fr_pow() { for _ in 0..1000 { // Exponentiating by the modulus should have no effect in a prime field. - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); assert_eq!(a, a.pow(Fr::char())); } @@ -787,13 +820,16 @@ fn test_fr_pow() { fn test_fr_sqrt() { use ff::SqrtField; - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); assert_eq!(Fr::zero().sqrt().unwrap(), Fr::zero()); for _ in 0..1000 { // Ensure sqrt(a^2) = a or -a - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); let mut nega = a; nega.negate(); let mut b = a; @@ -806,7 +842,7 @@ fn test_fr_sqrt() { for _ in 0..1000 { // Ensure sqrt(a)^2 = a for random a - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); if let Some(mut tmp) = a.sqrt() { tmp.square(); @@ -858,11 +894,14 @@ fn test_fr_from_into_repr() { // Zero should be in the field. assert!(Fr::from_repr(FrRepr::from(0)).unwrap().is_zero()); - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { // Try to turn Fr elements into representations and back again, and compare. - let a = Fr::rand(&mut rng); + let a = Fr::random(&mut rng); let a_repr = a.into_repr(); let b_repr = FrRepr::from(a); assert_eq!(a_repr, b_repr); @@ -982,5 +1021,5 @@ fn fr_field_tests() { #[test] fn fr_repr_tests() { - ::tests::repr::random_repr_tests::(); + ::tests::repr::random_repr_tests::(); } diff --git a/src/lib.rs b/src/lib.rs index 686938f..d498c35 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -14,6 +14,9 @@ extern crate byteorder; extern crate ff; extern crate group; +extern crate rand_core; + +#[cfg(test)] extern crate rand; #[cfg(test)] diff --git a/src/tests/engine.rs b/src/tests/engine.rs index 7b1944d..8616129 100644 --- a/src/tests/engine.rs +++ b/src/tests/engine.rs @@ -1,14 +1,17 @@ use group::{CurveAffine, CurveProjective}; -use rand::{Rand, SeedableRng, XorShiftRng}; +use rand::{SeedableRng, XorShiftRng}; use {Engine, Field, PairingCurveAffine, PrimeField}; pub fn engine_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..10 { - let a = E::G1::rand(&mut rng).into_affine(); - let b = E::G2::rand(&mut rng).into_affine(); + let a = E::G1::random(&mut rng).into_affine(); + let b = E::G2::random(&mut rng).into_affine(); assert!(a.pairing_with(&b) == b.pairing_with(&a)); assert!(a.pairing_with(&b) == E::pairing(a, b)); @@ -18,10 +21,10 @@ pub fn engine_tests() { let z1 = E::G1Affine::zero().prepare(); let z2 = E::G2Affine::zero().prepare(); - let a = E::G1::rand(&mut rng).into_affine().prepare(); - let b = E::G2::rand(&mut rng).into_affine().prepare(); - let c = E::G1::rand(&mut rng).into_affine().prepare(); - let d = E::G2::rand(&mut rng).into_affine().prepare(); + let a = E::G1::random(&mut rng).into_affine().prepare(); + let b = E::G2::random(&mut rng).into_affine().prepare(); + let c = E::G1::random(&mut rng).into_affine().prepare(); + let d = E::G2::random(&mut rng).into_affine().prepare(); assert_eq!( E::Fqk::one(), @@ -49,12 +52,15 @@ pub fn engine_tests() { } fn random_miller_loop_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); // Exercise the miller loop for a reduced pairing for _ in 0..1000 { - let a = E::G1::rand(&mut rng); - let b = E::G2::rand(&mut rng); + let a = E::G1::random(&mut rng); + let b = E::G2::random(&mut rng); let p2 = E::pairing(a, b); @@ -68,10 +74,10 @@ fn random_miller_loop_tests() { // Exercise a double miller loop for _ in 0..1000 { - let a = E::G1::rand(&mut rng); - let b = E::G2::rand(&mut rng); - let c = E::G1::rand(&mut rng); - let d = E::G2::rand(&mut rng); + let a = E::G1::random(&mut rng); + let b = E::G2::random(&mut rng); + let c = E::G1::random(&mut rng); + let d = E::G2::random(&mut rng); let ab = E::pairing(a, b); let cd = E::pairing(c, d); @@ -92,14 +98,17 @@ fn random_miller_loop_tests() { } fn random_bilinearity_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let a = E::G1::rand(&mut rng); - let b = E::G2::rand(&mut rng); + let a = E::G1::random(&mut rng); + let b = E::G2::random(&mut rng); - let c = E::Fr::rand(&mut rng); - let d = E::Fr::rand(&mut rng); + let c = E::Fr::random(&mut rng); + let d = E::Fr::random(&mut rng); let mut ac = a; ac.mul_assign(c); diff --git a/src/tests/field.rs b/src/tests/field.rs index 55396a7..0f2f1b2 100644 --- a/src/tests/field.rs +++ b/src/tests/field.rs @@ -2,11 +2,14 @@ use ff::{Field, LegendreSymbol, PrimeField, SqrtField}; use rand::{Rng, SeedableRng, XorShiftRng}; pub fn random_frobenius_tests>(characteristic: C, maxpower: usize) { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..100 { for i in 0..(maxpower + 1) { - let mut a = F::rand(&mut rng); + let mut a = F::random(&mut rng); let mut b = a; for _ in 0..i { @@ -20,10 +23,13 @@ pub fn random_frobenius_tests>(characteristic: C, maxp } pub fn random_sqrt_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..10000 { - let a = F::rand(&mut rng); + let a = F::random(&mut rng); let mut b = a; b.square(); assert_eq!(b.legendre(), LegendreSymbol::QuadraticResidue); @@ -54,7 +60,10 @@ pub fn random_sqrt_tests() { } pub fn random_field_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); random_multiplication_tests::(&mut rng); random_addition_tests::(&mut rng); @@ -76,14 +85,14 @@ pub fn random_field_tests() { // Multiplication by zero { - let mut a = F::rand(&mut rng); + let mut a = F::random(&mut rng); a.mul_assign(&F::zero()); assert!(a.is_zero()); } // Addition by zero { - let mut a = F::rand(&mut rng); + let mut a = F::random(&mut rng); let copy = a; a.add_assign(&F::zero()); assert_eq!(a, copy); @@ -106,7 +115,10 @@ pub fn from_str_tests() { } { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { let n: u64 = rng.gen(); @@ -126,9 +138,9 @@ pub fn from_str_tests() { fn random_multiplication_tests(rng: &mut R) { for _ in 0..10000 { - let a = F::rand(rng); - let b = F::rand(rng); - let c = F::rand(rng); + let a = F::random(rng); + let b = F::random(rng); + let c = F::random(rng); let mut t0 = a; // (a * b) * c t0.mul_assign(&b); @@ -149,9 +161,9 @@ fn random_multiplication_tests(rng: &mut R) { fn random_addition_tests(rng: &mut R) { for _ in 0..10000 { - let a = F::rand(rng); - let b = F::rand(rng); - let c = F::rand(rng); + let a = F::random(rng); + let b = F::random(rng); + let c = F::random(rng); let mut t0 = a; // (a + b) + c t0.add_assign(&b); @@ -172,8 +184,8 @@ fn random_addition_tests(rng: &mut R) { fn random_subtraction_tests(rng: &mut R) { for _ in 0..10000 { - let a = F::rand(rng); - let b = F::rand(rng); + let b = F::random(rng); + let a = F::random(rng); let mut t0 = a; // (a - b) t0.sub_assign(&b); @@ -190,7 +202,7 @@ fn random_subtraction_tests(rng: &mut R) { fn random_negation_tests(rng: &mut R) { for _ in 0..10000 { - let a = F::rand(rng); + let a = F::random(rng); let mut b = a; b.negate(); b.add_assign(&a); @@ -201,7 +213,7 @@ fn random_negation_tests(rng: &mut R) { fn random_doubling_tests(rng: &mut R) { for _ in 0..10000 { - let mut a = F::rand(rng); + let mut a = F::random(rng); let mut b = a; a.add_assign(&b); b.double(); @@ -212,7 +224,7 @@ fn random_doubling_tests(rng: &mut R) { fn random_squaring_tests(rng: &mut R) { for _ in 0..10000 { - let mut a = F::rand(rng); + let mut a = F::random(rng); let mut b = a; a.mul_assign(&b); b.square(); @@ -225,7 +237,7 @@ fn random_inversion_tests(rng: &mut R) { assert!(F::zero().inverse().is_none()); for _ in 0..10000 { - let mut a = F::rand(rng); + let mut a = F::random(rng); let b = a.inverse().unwrap(); // probablistically nonzero a.mul_assign(&b); @@ -237,10 +249,10 @@ fn random_expansion_tests(rng: &mut R) { for _ in 0..10000 { // Compare (a + b)(c + d) and (a*c + b*c + a*d + b*d) - let a = F::rand(rng); - let b = F::rand(rng); - let c = F::rand(rng); - let d = F::rand(rng); + let a = F::random(rng); + let b = F::random(rng); + let c = F::random(rng); + let d = F::random(rng); let mut t0 = a; t0.add_assign(&b); diff --git a/src/tests/repr.rs b/src/tests/repr.rs index 09dd441..692c4d3 100644 --- a/src/tests/repr.rs +++ b/src/tests/repr.rs @@ -1,21 +1,24 @@ -use ff::PrimeFieldRepr; +use ff::{PrimeField, PrimeFieldRepr}; use rand::{SeedableRng, XorShiftRng}; -pub fn random_repr_tests() { - random_encoding_tests::(); - random_shl_tests::(); - random_shr_tests::(); +pub fn random_repr_tests() { + random_encoding_tests::

(); + random_shl_tests::

(); + random_shr_tests::

(); } -fn random_encoding_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); +fn random_encoding_tests() { + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..1000 { - let r = R::rand(&mut rng); + let r = P::random(&mut rng).into_repr(); // Big endian { - let mut rdecoded = R::default(); + let mut rdecoded =

::Repr::default(); let mut v: Vec = vec![]; r.write_be(&mut v).unwrap(); @@ -26,7 +29,7 @@ fn random_encoding_tests() { // Little endian { - let mut rdecoded = R::default(); + let mut rdecoded =

::Repr::default(); let mut v: Vec = vec![]; r.write_le(&mut v).unwrap(); @@ -36,8 +39,8 @@ fn random_encoding_tests() { } { - let mut rdecoded_le = R::default(); - let mut rdecoded_be_flip = R::default(); + let mut rdecoded_le =

::Repr::default(); + let mut rdecoded_be_flip =

::Repr::default(); let mut v: Vec = vec![]; r.write_le(&mut v).unwrap(); @@ -55,11 +58,14 @@ fn random_encoding_tests() { } } -fn random_shl_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); +fn random_shl_tests() { + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..100 { - let r = R::rand(&mut rng); + let r = P::random(&mut rng).into_repr(); for shift in 0..(r.num_bits() + 1) { let mut r1 = r; @@ -76,11 +82,14 @@ fn random_shl_tests() { } } -fn random_shr_tests() { - let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]); +fn random_shr_tests() { + let mut rng = XorShiftRng::from_seed([ + 0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc, + 0xe5, + ]); for _ in 0..100 { - let r = R::rand(&mut rng); + let r = P::random(&mut rng).into_repr(); for shift in 0..(r.num_bits() + 1) { let mut r1 = r;