Trait snarkvm_fields::FieldParameters

pub trait FieldParameters: 'static + Send + Sync + Sized {
    type BigInteger: BigInteger;

    const MODULUS: Self::BigInteger;
    const MODULUS_BITS: u32;
    const REPR_SHAVE_BITS: u32;
    const R: Self::BigInteger;
    const R2: Self::BigInteger;
    const INV: u64;
    const GENERATOR: Self::BigInteger;
    const CAPACITY: u32;
    const TWO_ADICITY: u32;
    const ROOT_OF_UNITY: Self::BigInteger;
    const T: Self::BigInteger;
    const T_MINUS_ONE_DIV_TWO: Self::BigInteger;
    const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInteger;
}

A trait that defines parameters for a prime field.

Associated Types

type BigInteger: BigInteger

Associated Constants

const MODULUS: Self::BigInteger

The modulus of the field.

const MODULUS_BITS: u32

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

const REPR_SHAVE_BITS: u32

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

const R: Self::BigInteger

R = 2^256 % Self::MODULUS

const R2: Self::BigInteger

R2 = R^2 % Self::MODULUS

const INV: u64

INV = -(MODULUS^{-1} mod MODULUS) mod MODULUS

const GENERATOR: Self::BigInteger

A multiplicative generator that is also a quadratic nonresidue. Self::GENERATOR is an element having multiplicative order Self::MODULUS - 1. There also does not exist x such that Self::GENERATOR = x^2 % Self::MODULUS

const CAPACITY: u32

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

const TWO_ADICITY: u32

2^s * t = MODULUS - 1 with t odd. This is the two-adicity of the prime.

const ROOT_OF_UNITY: Self::BigInteger

2^s root of unity computed by GENERATOR^t

const T: Self::BigInteger

t for 2^s * t = MODULUS - 1

const T_MINUS_ONE_DIV_TWO: Self::BigInteger

(t - 1) / 2

const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInteger

(Self::MODULUS - 1) / 2

Implementors