Struct Degree2ExtensionField 

pub struct Degree2ExtensionField;

Implementations

impl Degree2ExtensionField

pub fn mul_fp2_by_nonresidue( a: &FieldElement<Degree2ExtensionField>, ) -> FieldElement<Degree2ExtensionField>

Trait Implementations

impl Clone for Degree2ExtensionField

fn clone(&self) -> Degree2ExtensionField

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Degree2ExtensionField

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

Formats the value using the given formatter.

impl IsFFTField for Degree2ExtensionField

const TWO_ADICITY: u64 = 31u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

fn field_name() -> &'static str

Used for searching this field’s implementation in other languages, e.g in MSL for executing parallel operations with the Metal API.

fn get_primitive_root_of_unity( order: u64, ) -> Result<FieldElement<Self>, FieldError>

Returns a primitive root of unity of order $2^{order}$. This is an element w such that w^{2^order} = 1 modulo p and w^k <> 1 modulo p for k not congruent to 2^order

impl IsField for Degree2ExtensionField

fn add(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the component wise addition of a and b

fn mul(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the multiplication of a and b.

fn sub(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the component wise subtraction of a and b

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

Returns the component wise negation of a

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

Returns the multiplicative inverse of a

fn div( a: &Self::BaseType, b: &Self::BaseType, ) -> Result<Self::BaseType, FieldError>

Returns the division of a and b

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

Returns a boolean indicating whether a and b are equal component wise.

fn one() -> Self::BaseType

Returns the multiplicative neutral element of the field extension.

fn from_u64(x: u64) -> Self::BaseType

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

fn from_base_type(x: Self::BaseType) -> Self::BaseType

Takes as input an element of BaseType and returns the internal representation of that element in the field. Note: for this case this is simply the identity, because the components already have correct representations.

type BaseType = [FieldElement<Mersenne31Field>; 2]

The underlying base type for representing elements from the field.

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

Returns the multiplication of a and a.

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

Returns the double of a.

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

where T: IsUnsignedInteger,

Returns the power of a to the T, a^T Uses the square and multiply algorithm, which takes O(log2(T)) steps This is a non-constant time implementation!

fn zero() -> Self::BaseType

Returns the additive neutral element.

impl IsSubFieldOf<Degree2ExtensionField> for Mersenne31Field

fn add( a: &Self::BaseType, b: &<Degree2ExtensionField as IsField>::BaseType, ) -> <Degree2ExtensionField as IsField>::BaseType

fn sub( a: &Self::BaseType, b: &<Degree2ExtensionField as IsField>::BaseType, ) -> <Degree2ExtensionField as IsField>::BaseType

fn mul( a: &Self::BaseType, b: &<Degree2ExtensionField as IsField>::BaseType, ) -> <Degree2ExtensionField as IsField>::BaseType

fn div( a: &Self::BaseType, b: &<Degree2ExtensionField as IsField>::BaseType, ) -> Result<<Degree2ExtensionField as IsField>::BaseType, FieldError>

fn embed(a: Self::BaseType) -> <Degree2ExtensionField as IsField>::BaseType

fn to_subfield_vec( b: <Degree2ExtensionField as IsField>::BaseType, ) -> Vec<Self::BaseType>