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This commit is contained in:
Pratyush Mishra
2020-10-11 19:50:41 -07:00
commit 43ca2132fd
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bn254/src/fields/fq6.rs Normal file
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use super::*;
use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
pub type Fq6 = Fp6<Fq6Parameters>;
#[derive(Clone, Copy)]
pub struct Fq6Parameters;
impl Fp6Parameters for Fq6Parameters {
type Fp2Params = Fq2Parameters;
/// NONRESIDUE = U+9
#[rustfmt::skip]
const NONRESIDUE: Fq2 = field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xf60647ce410d7ff7,
0x2f3d6f4dd31bd011,
0x2943337e3940c6d1,
0x1d9598e8a7e39857,
])),
field_new!(Fq, BigInteger256([
202099033278250856u64,
8885205928937022213u64,
5545221690922665192u64,
39800542322357402u64,
])),
);
#[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
// Fp2::NONRESIDUE^(((q^0) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0xe0a77c19a07df2f,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^(((q^1) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xb5773b104563ab30,
0x347f91c8a9aa6454,
0x7a007127242e0991,
0x1956bcd8118214ec,
])),
field_new!(Fq, BigInteger256([
0x6e849f1ea0aa4757,
0xaa1c7b6d89f89141,
0xb6e713cdfae0ca3a,
0x26694fbb4e82ebc3,
])),
),
// Fp2::NONRESIDUE^(((q^2) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^(((q^3) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xc9af22f716ad6bad,
0xb311782a4aa662b2,
0x19eeaf64e248c7f4,
0x20273e77e3439f82,
])),
field_new!(Fq, BigInteger256([
0xacc02860f7ce93ac,
0x3933d5817ba76b4c,
0x69e6188b446c8467,
0xa46036d4417cc55,
])),
),
// Fp2::NONRESIDUE^(((q^4) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^(((q^5) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xf91aba2654e8e3b1,
0x4771cb2fdc92ce12,
0xdcb16ae0fc8bdf35,
0x274aa195cd9d8be4,
])),
field_new!(Fq, BigInteger256([
0x5cfc50ae18811f8b,
0x4bb28433cb43988c,
0x4fd35f13c3b56219,
0x301949bd2fc8883a,
])),
),
];
#[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
// Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0xe0a77c19a07df2f,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x7361d77f843abe92,
0xa5bb2bd3273411fb,
0x9c941f314b3e2399,
0x15df9cddbb9fd3ec,
])),
field_new!(Fq, BigInteger256([
0x5dddfd154bd8c949,
0x62cb29a5a4445b60,
0x37bc870a0c7dd2b9,
0x24830a9d3171f0fd,
])),
),
// Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x448a93a57b6762df,
0xbfd62df528fdeadf,
0xd858f5d00e9bd47a,
0x6b03d4d3476ec58,
])),
field_new!(Fq, BigInteger256([
0x2b19daf4bcc936d1,
0xa1a54e7a56f4299f,
0xb533eee05adeaef1,
0x170c812b84dda0b2,
])),
),
// Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
),
// Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x843420f1d8dadbd6,
0x31f010c9183fcdb2,
0x436330b527a76049,
0x13d47447f11adfe4,
])),
field_new!(Fq, BigInteger256([
0xef494023a857fa74,
0x2a925d02d5ab101a,
0x83b015829ba62f10,
0x2539111d0c13aea3,
])),
),
];
#[inline(always)]
fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
// (c0+u*c1)*(9+u) = (9*c0-c1)+u*(9*c1+c0)
let mut f = *fe;
f.double_in_place().double_in_place().double_in_place();
let c0 = f.c0 + fe.c0 + Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
let c1 = f.c1 + fe.c1 + fe.c0;
field_new!(Fq2, c0, c1)
}
}