Struct ark_ff::fields::models::fp::MontBackend

pub struct MontBackend<T: MontConfig<N>, const N: usize>(/* private fields */);

Trait Implementations

impl<T: MontConfig<N>, const N: usize> FpConfig<N> for MontBackend<T, N>

const MODULUS: BigInt<N> = T::MODULUS

The modulus of the field.

const GENERATOR: Fp<Self, N> = T::GENERATOR

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

const ZERO: Fp<Self, N> = _

Additive identity of the field, i.e. the element e such that, for all elements f of the field, e + f = f.

const ONE: Fp<Self, N> = _

Multiplicative identity of the field, i.e. the element e such that, for all elements f of the field, e * f = f.

fn mul_assign(a: &mut Fp<Self, N>, b: &Fp<Self, N>)

This modular multiplication algorithm uses Montgomery reduction for efficient implementation. It also additionally uses the “no-carry optimization” outlined here if P::MODULUS has (a) a non-zero MSB, and (b) at least one zero bit in the rest of the modulus.

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.

const TWO_ADIC_ROOT_OF_UNITY: Fp<Self, N> = T::TWO_ADIC_ROOT_OF_UNITY

2^s root of unity computed by GENERATOR^t

const SMALL_SUBGROUP_BASE: Option<u32> = T::SMALL_SUBGROUP_BASE

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> = T::SMALL_SUBGROUP_BASE_ADICITY

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

const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Fp<Self, N>> = T::LARGE_SUBGROUP_ROOT_OF_UNITY

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

const SQRT_PRECOMP: Option<SqrtPrecomputation<Fp<Self, N>>> = T::SQRT_PRECOMP

Precomputed material for use when computing square roots. Currently uses the generic Tonelli-Shanks, which works for every modulus.

fn add_assign(a: &mut Fp<Self, N>, b: &Fp<Self, N>)

Set a += b.

fn sub_assign(a: &mut Fp<Self, N>, b: &Fp<Self, N>)

Set a -= b.

fn double_in_place(a: &mut Fp<Self, N>)

Set a = a + a.

fn neg_in_place(a: &mut Fp<Self, N>)

Set a = -a;

fn sum_of_products<const M: usize>( a: &[Fp<Self, N>; M], b: &[Fp<Self, N>; M] ) -> Fp<Self, N>

Compute the inner product <a, b>.

fn square_in_place(a: &mut Fp<Self, N>)

Set a *= b.

fn inverse(a: &Fp<Self, N>) -> Option<Fp<Self, N>>

Compute a^{-1} if a is not zero.

fn from_bigint(r: BigInt<N>) -> Option<Fp<Self, N>>

Construct a field element from an integer in the range 0..(Self::MODULUS - 1). Returns None if the integer is outside this range.

fn into_bigint(a: Fp<Self, N>) -> BigInt<N>

Convert a field element to an integer in the range 0..(Self::MODULUS - 1).