use super::fq2::Fq2;
use ff::{Field, PrimeField, PrimeFieldRepr};
#[derive(PrimeField)]
#[PrimeFieldModulus = "21888242871839275222246405745257275088696311157297823662689037894645226208583"]
#[PrimeFieldGenerator = "2"]
pub struct Fq(FqRepr);
pub const B_COEFF: Fq = Fq(FqRepr([
0x7a17caa950ad28d7,
0x1f6ac17ae15521b9,
0x334bea4e696bd284,
0x2a1f6744ce179d8e,
]));
pub const B_COEFF_FQ2: Fq2 = Fq2 {
c0: Fq(FqRepr([
0x3bf938e377b802a8,
0x020b1b273633535d,
0x26b7edf049755260,
0x2514c6324384a86d,
])),
c1: Fq(FqRepr([
0x38e7ecccd1dcff67,
0x65f0b37d93ce0d3e,
0xd749d0dd22ac00aa,
0x0141b9ce4a688d4d,
])),
};
pub const G1_GENERATOR_X: Fq = Fq(FqRepr([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
]));
pub const G1_GENERATOR_Y: Fq = Fq(FqRepr([
0xa6ba871b8b1e1b3a,
0x14f1d651eb8e167b,
0xccdd46def0f28c58,
0x1c14ef83340fbe5e,
]));
pub const G2_GENERATOR_X_C0: Fq = Fq(FqRepr([
0x8e83b5d102bc2026,
0xdceb1935497b0172,
0xfbb8264797811adf,
0x19573841af96503b,
]));
pub const G2_GENERATOR_X_C1: Fq = Fq(FqRepr([
0xafb4737da84c6140,
0x6043dd5a5802d8c4,
0x09e950fc52a02f86,
0x14fef0833aea7b6b,
]));
pub const G2_GENERATOR_Y_C0: Fq = Fq(FqRepr([
0x619dfa9d886be9f6,
0xfe7fd297f59e9b78,
0xff9e1a62231b7dfe,
0x28fd7eebae9e4206,
]));
pub const G2_GENERATOR_Y_C1: Fq = Fq(FqRepr([
0x64095b56c71856ee,
0xdc57f922327d3cbb,
0x55f935be33351076,
0x0da4a0e693fd6482,
]));
pub const FROBENIUS_COEFF_FQ2_C1: [Fq; 2] = [
Fq(FqRepr([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
])),
Fq(FqRepr([
0x68c3488912edefaa,
0x8d087f6872aabf4f,
0x51e1a24709081231,
0x2259d6b14729c0fa,
])),
];
pub const XI_TO_Q_MINUS_1_OVER_2: Fq2 = Fq2 {
c0: Fq(FqRepr([
0xe4bbdd0c2936b629,
0xbb30f162e133bacb,
0x31a9d1b6f9645366,
0x253570bea500f8dd,
])),
c1: Fq(FqRepr([
0xa1d77ce45ffe77c7,
0x07affd117826d1db,
0x6d16bd27bb7edc6b,
0x2c87200285defecc,
])),
};
pub const FROBENIUS_COEFF_FQ6_C1: [Fq2; 6] = [
Fq2 {
c0: Fq(FqRepr([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0])),
},
Fq2 {
c0: Fq(FqRepr([
0xb5773b104563ab30,
0x347f91c8a9aa6454,
0x7a007127242e0991,
0x1956bcd8118214ec,
])),
c1: Fq(FqRepr([
0x6e849f1ea0aa4757,
0xaa1c7b6d89f89141,
0xb6e713cdfae0ca3a,
0x26694fbb4e82ebc3,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0])),
},
Fq2 {
c0: Fq(FqRepr([
0xc9af22f716ad6bad,
0xb311782a4aa662b2,
0x19eeaf64e248c7f4,
0x20273e77e3439f82,
])),
c1: Fq(FqRepr([
0xacc02860f7ce93ac,
0x3933d5817ba76b4c,
0x69e6188b446c8467,
0x0a46036d4417cc55,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0xf91aba2654e8e3b1,
0x4771cb2fdc92ce12,
0xdcb16ae0fc8bdf35,
0x274aa195cd9d8be4,
])),
c1: Fq(FqRepr([
0x5cfc50ae18811f8b,
0x4bb28433cb43988c,
0x4fd35f13c3b56219,
0x301949bd2fc8883a,
])),
},
];
pub const FROBENIUS_COEFF_FQ6_C2: [Fq2; 6] = [
Fq2 {
c0: Fq(FqRepr([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0])),
},
Fq2 {
c0: Fq(FqRepr([
0x7361d77f843abe92,
0xa5bb2bd3273411fb,
0x9c941f314b3e2399,
0x15df9cddbb9fd3ec,
])),
c1: Fq(FqRepr([
0x5dddfd154bd8c949,
0x62cb29a5a4445b60,
0x37bc870a0c7dd2b9,
0x24830a9d3171f0fd,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0x448a93a57b6762df,
0xbfd62df528fdeadf,
0xd858f5d00e9bd47a,
0x06b03d4d3476ec58,
])),
c1: Fq(FqRepr([
0x2b19daf4bcc936d1,
0xa1a54e7a56f4299f,
0xb533eee05adeaef1,
0x170c812b84dda0b2,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0x843420f1d8dadbd6,
0x31f010c9183fcdb2,
0x436330b527a76049,
0x13d47447f11adfe4,
])),
c1: Fq(FqRepr([
0xef494023a857fa74,
0x2a925d02d5ab101a,
0x83b015829ba62f10,
0x2539111d0c13aea3,
])),
},
];
pub const FROBENIUS_COEFF_FQ12_C1: [Fq2; 12] = [
Fq2 {
c0: Fq(FqRepr([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0])),
},
Fq2 {
c0: Fq(FqRepr([
0xaf9ba69633144907,
0xca6b1d7387afb78a,
0x11bded5ef08a2087,
0x02f34d751a1f3a7c,
])),
c1: Fq(FqRepr([
0xa222ae234c492d72,
0xd00f02a4565de15b,
0xdc2ff3a253dfc926,
0x10a75716b3899551,
])),
},
Fq2 {
c0: Fq(FqRepr([
0xca8d800500fa1bf2,
0xf0c5d61468b39769,
0x0e201271ad0d4418,
0x04290f65bad856e6,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0])),
},
Fq2 {
c0: Fq(FqRepr([
0x365316184e46d97d,
0x0af7129ed4c96d9f,
0x659da72fca1009b5,
0x08116d8983a20d23,
])),
c1: Fq(FqRepr([
0xb1df4af7c39c1939,
0x3d9f02878a73bf7f,
0x9b2220928caf0ae0,
0x26684515eff054a6,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0x86b76f821b329076,
0x408bf52b4d19b614,
0x53dfb9d0d985e92d,
0x051e20146982d2a7,
])),
c1: Fq(FqRepr([
0x0fbc9cd47752ebc7,
0x6d8fffe33415de24,
0xbef22cf038cf41b9,
0x15c0edff3c66bf54,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x68c3488912edefaa,
0x8d087f6872aabf4f,
0x51e1a24709081231,
0x2259d6b14729c0fa,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0x8c84e580a568b440,
0xcd164d1de0c21302,
0xa692585790f737d5,
0x2d7100fdc71265ad,
])),
c1: Fq(FqRepr([
0x99fdddf38c33cfd5,
0xc77267ed1213e931,
0xdc2052142da18f36,
0x1fbcf75c2da80ad7,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0x05cd75fe8a3623ca,
0x8c8a57f293a85cee,
0x52b29e86b7714ea8,
0x2852e0e95d8f9306,
])),
c1: Fq(FqRepr([
0x8a41411f14e0e40e,
0x59e26809ddfe0b0d,
0x1d2e2523f4d24d7d,
0x09fc095cf1414b83,
])),
},
Fq2 {
c0: Fq(FqRepr([
0x08cfc388c494f1ab,
0x19b315148d1373d4,
0x584e90fdcb6c0213,
0x09e1685bdf2f8849,
])),
c1: Fq(FqRepr([0x0, 0x0, 0x0, 0x0,])),
},
Fq2 {
c0: Fq(FqRepr([
0xb5691c94bd4a6cd1,
0x56f575661b581478,
0x64708be5a7fb6f30,
0x2b462e5e77aecd82,
])),
c1: Fq(FqRepr([
0x2c63ef42612a1180,
0x29f16aae345bec69,
0xf95e18c648b216a4,
0x1aa36073a4cae0d4,
])),
},
];
pub const NEGATIVE_ONE: Fq = Fq(FqRepr([
0x974bc177a0000006,
0xf13771b2da58a367,
0x51e1a2470908122e,
0x2259d6b14729c0fa,
]));
#[cfg(test)]
use rand::{Rand, SeedableRng, XorShiftRng};
#[test]
fn test_fq_repr_from() {
assert_eq!(FqRepr::from(100), FqRepr([100, 0, 0, 0]));
assert_eq!(FqRepr::from(3), FqRepr([3, 0, 0, 0]));
}
#[test]
fn test_fq_repr_is_odd() {
assert!(!FqRepr::from(0).is_odd());
assert!(FqRepr::from(0).is_even());
assert!(FqRepr::from(1).is_odd());
assert!(!FqRepr::from(1).is_even());
assert!(!FqRepr::from(324834872).is_odd());
assert!(FqRepr::from(324834872).is_even());
assert!(FqRepr::from(324834873).is_odd());
assert!(!FqRepr::from(324834873).is_even());
}
#[test]
fn test_fq_repr_num_bits() {
let mut a = FqRepr::from(0);
assert_eq!(0, a.num_bits());
a = FqRepr::from(1);
for i in 1..257 {
assert_eq!(i, a.num_bits());
a.mul2();
}
assert_eq!(0, a.num_bits());
}
#[test]
fn test_fq_is_valid() {
print!("modulus = {}\n", MODULUS);
print!("R = {}\n", R);
let mut a = Fq(MODULUS);
assert!(!a.is_valid());
a.0.sub_noborrow(&FqRepr::from(1));
assert!(a.is_valid());
assert!(Fq(FqRepr::from(0)).is_valid());
assert!(
Fq(FqRepr([
0xdf4671abd14dab3e,
0xe2dc0c9f534fbd33,
0x31ca6c880cc444a6,
0x257a67e70ef33359
])).is_valid()
);
assert!(
!Fq(FqRepr([
0xffffffffffffffff,
0xffffffffffffffff,
0xffffffffffffffff,
0xffffffffffffffff,
])).is_valid()
);
let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
for _ in 0..1000 {
let a = Fq::rand(&mut rng);
assert!(a.is_valid());
}
}
#[test]
fn test_fq_repr_display() {
assert_eq!(
format!("{}", Fq::into_repr(&Fq::one())),
"0x0000000000000000000000000000000000000000000000000000000000000001".to_string()
);
assert_eq!(
format!("{}", FqRepr([0, 0, 0, 0])),
"0x0000000000000000000000000000000000000000000000000000000000000000".to_string()
);
}
#[test]
fn test_fq_num_bits() {
assert_eq!(Fq::NUM_BITS, 254);
assert_eq!(Fq::CAPACITY, 253);
}
#[test]
fn test_fq_sqrt() {
use ff::SqrtField;
let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
for _ in 0..1000 {
let a = Fq::rand(&mut rng);
let mut nega = a;
nega.negate();
let mut b = a;
b.square();
let b = b.sqrt().unwrap();
assert!(a == b || nega == b);
}
for _ in 0..1000 {
let a = Fq::rand(&mut rng);
if let Some(mut tmp) = a.sqrt() {
tmp.square();
assert_eq!(a, tmp);
}
}
}
#[test]
fn test_fq_sqrt_2() {
use ff::SqrtField;
let x = Fq::from_str("4").unwrap();
print!("x = {}\n", x);
if let Some(y) = x.sqrt() {
print!("y = {}\n", y);
let mut y_other = y;
y_other.negate();
print!("y' = {}\n", y_other);
}
}
#[test]
fn fq_field_tests() {
crate::tests::field::random_field_tests::<Fq>();
crate::tests::field::random_sqrt_tests::<Fq>();
crate::tests::field::random_frobenius_tests::<Fq, _>(Fq::char(), 13);
crate::tests::field::from_str_tests::<Fq>();
}