Struct lambdaworks_math::field::fields::p448_goldilocks_prime_field::P448GoldilocksPrimeField

pub struct P448GoldilocksPrimeField;

Trait Implementations

impl Clone for P448GoldilocksPrimeField

fn clone(&self) -> P448GoldilocksPrimeField

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for P448GoldilocksPrimeField

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl IsField for P448GoldilocksPrimeField

fn mul(a: &U56x8, b: &U56x8) -> U56x8

Implements fast Karatsuba Multiplication optimized for the Godilocks Prime field. Taken from Mike Hamburg’s implemenation: https://sourceforge.net/p/ed448goldilocks/code/ci/master/tree/src/p448/arch_ref64/f_impl.c

fn eq(a: &U56x8, b: &U56x8) -> bool

Taken from https://sourceforge.net/p/ed448goldilocks/code/ci/master/tree/src/per_field/f_generic.tmpl.c

type BaseType = U56x8

fn add(a: &U56x8, b: &U56x8) -> U56x8

Returns the sum of a and b.

fn sub(a: &U56x8, b: &U56x8) -> U56x8

Returns the subtraction of a and b.

fn neg(a: &U56x8) -> U56x8

Returns the additive inverse of a.

fn inv(a: &U56x8) -> Result<U56x8, FieldError>

Returns the multiplicative inverse of a.

fn div(a: &U56x8, b: &U56x8) -> U56x8

Returns the division of a and b.

fn zero() -> U56x8

Returns the additive neutral element.

fn one() -> U56x8

Returns the multiplicative neutral element.

fn from_u64(x: u64) -> U56x8

Returns the element x * 1 where 1 is the multiplicative neutral element.

fn from_base_type(x: U56x8) -> U56x8

Takes as input an element of BaseType and returns the internal representation of that element in the field.

fn double(a: &Self::BaseType) -> Self::BaseType

Returns the double of a.

fn square(a: &Self::BaseType) -> Self::BaseType

Returns the multiplication of a and a.

fn pow<T>(a: &Self::BaseType, exponent: T) -> Self::BaseType

where T: IsUnsignedInteger,

impl IsPrimeField for P448GoldilocksPrimeField

type RepresentativeType = UnsignedInteger<7>

fn representative(a: &U56x8) -> U448

Returns the integer representative in the range [0, p-1], where p the modulus

fn from_hex(hex_string: &str) -> Result<Self::BaseType, CreationError>

Creates a BaseType from a Hex String 0x is optional Returns an CreationError::InvalidHexStringif the value is not a hexstring

fn to_hex(x: &U56x8) -> String

Creates a hexstring from a FieldElement without 0x.

fn field_bit_size() -> usize

Returns the number of bits of the max element of the field, as per field documentation, not internal representation. This is log2(max FE) rounded up

fn modulus_minus_one() -> Self::RepresentativeType

fn legendre_symbol(a: &Self::BaseType) -> LegendreSymbol

fn sqrt(a: &Self::BaseType) -> Option<(Self::BaseType, Self::BaseType)>

Returns the two square roots of self if they exist and None otherwise

impl PartialEq for P448GoldilocksPrimeField

fn eq(&self, other: &P448GoldilocksPrimeField) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Eq for P448GoldilocksPrimeField

impl StructuralPartialEq for P448GoldilocksPrimeField