Struct ark_ed_on_bn254::FqParameters

pub struct FqParameters;

Trait Implementations

impl FftParameters for FrParameters

type BigInt = BigInteger256

pub const TWO_ADICITY: u32

Let N be the size of the multiplicative group defined by the field. Then TWO_ADICITY is the two-adicity of N, i.e. the integer s such that N = 2^s * t for some odd integer t.

pub const TWO_ADIC_ROOT_OF_UNITY: BigInteger256

2^s root of unity computed by GENERATOR^t

const SMALL_SUBGROUP_BASE: Option<u32>

An integer b such that there exists a multiplicative subgroup of size b^k for some integer k.

const SMALL_SUBGROUP_BASE_ADICITY: Option<u32>

The integer k such that there exists a multiplicative subgroup of size Self::SMALL_SUBGROUP_BASE^k.

const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Self::BigInt>

GENERATOR^((MODULUS-1) / (2^s * SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)) Used for mixed-radix FFT.

impl FpParameters for FrParameters

pub const MODULUS: BigInteger256

MODULUS = 21888242871839275222246405745257275088548364400416034343698204186575808495617

pub const R: BigInteger256

R = pow(2, 320) % MODULUS = 6350874878119819312338956282401532410528162663560392320966563075034087161851

pub const R2: BigInteger256

R2 = R * R % MODULUS = 944936681149208446651664254269745548490766851729442924617792859073125903783

pub const INV: u64

INV = (-MODULUS) ^ {-1} % pow(2, 64) = 14042775128853446655

pub const GENERATOR: BigInteger256

GENERATOR = 5

pub const MODULUS_MINUS_ONE_DIV_TWO: BigInteger256

(MODULUS - 1)/2 = 10944121435919637611123202872628637544274182200208017171849102093287904247808

pub const T: BigInteger256

T = (MODULUS - 1) / 2^s = 81540058820840996586704275553141814055101440848469862132140264610111

pub const T_MINUS_ONE_DIV_TWO: BigInteger256

(T - 1) / 2 = 40770029410420498293352137776570907027550720424234931066070132305055

pub const MODULUS_BITS: u32

The number of bits needed to represent the Self::MODULUS.

pub const CAPACITY: u32

The number of bits that can be reliably stored. (Should equal SELF::MODULUS_BITS - 1)

pub const REPR_SHAVE_BITS: u32

The number of bits that must be shaved from the beginning of the representation when randomly sampling.

impl Fp256Parameters for FrParameters