Struct FpParameters

pub struct FpParameters;

Trait Implementations

impl FftParameters for FpParameters

const TWO_ADICITY: u32 = 32u32

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.

const TWO_ADIC_ROOT_OF_UNITY: BigInteger

2^s root of unity computed by GENERATOR^t

type BigInt = BigInt<4>

const SMALL_SUBGROUP_BASE: Option<u32> = None

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> = None

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> = None

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

impl FpParameters for FpParameters

const MODULUS: BigInteger

The modulus of the field.

const R: BigInteger

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

const R2: BigInteger

R2 = R^2 % Self::MODULUS

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger

(Self::MODULUS - 1) / 2

const T: BigInteger

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

const T_MINUS_ONE_DIV_TWO: BigInteger

(t - 1) / 2

const GENERATOR: BigInteger

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

const MODULUS_BITS: u32 = 255u32

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

const CAPACITY: u32 = 254u32

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

const REPR_SHAVE_BITS: u32 = 1u32

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

const INV: u64 = 11_037_532_056_220_336_127u64

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

impl Fp256Parameters for FpParameters