Struct ark_vesta::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

The modulus of the field.

pub const R: BigInteger256

Let M be the power of 2^64 nearest to Self::MODULUS_BITS. Then R = M % Self::MODULUS.

pub const R2: BigInteger256

R2 = R^2 % Self::MODULUS

pub const MODULUS_MINUS_ONE_DIV_TWO: BigInteger256

(Self::MODULUS - 1) / 2

pub const T: BigInteger256

t for 2^s * t = MODULUS - 1, and t coprime to 2.

pub const T_MINUS_ONE_DIV_TWO: BigInteger256

(t - 1) / 2

pub const GENERATOR: BigInteger256

A multiplicative generator of the field. Self::GENERATOR is an element having multiplicative order Self::MODULUS - 1.

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.

pub const INV: u64

INV = -MODULUS^{-1} mod 2^64

impl Fp256Parameters for FrParameters