Trait QuadExtConfig

pub trait QuadExtConfig:
    'static
    + Send
    + Sync
    + Sized {
    type BasePrimeField: PrimeField;
    type BaseField: Field<BasePrimeField = Self::BasePrimeField>;
    type FrobCoeff: Field;

    const DEGREE_OVER_BASE_PRIME_FIELD: usize;
    const NONRESIDUE: Self::BaseField;
    const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff];

    // Required method
    fn mul_base_field_by_frob_coeff(fe: &mut Self::BaseField, power: usize);

    // Provided methods
    fn mul_base_field_by_nonresidue_in_place(
        fe: &mut Self::BaseField,
    ) -> &mut Self::BaseField { ... }
    fn mul_base_field_by_nonresidue_and_add(
        y: &mut Self::BaseField,
        x: &Self::BaseField,
    ) { ... }
    fn mul_base_field_by_nonresidue_plus_one_and_add(
        y: &mut Self::BaseField,
        x: &Self::BaseField,
    ) { ... }
    fn sub_and_mul_base_field_by_nonresidue(
        y: &mut Self::BaseField,
        x: &Self::BaseField,
    ) { ... }
}

Defines a Quadratic extension field from a quadratic non-residue.

Required Associated Constants

const DEGREE_OVER_BASE_PRIME_FIELD: usize

The degree of the extension over the base prime field.

const NONRESIDUE: Self::BaseField

The quadratic non-residue used to construct the extension.

const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff]

Coefficients for the Frobenius automorphism.

Required Associated Types

type BasePrimeField: PrimeField

The prime field that this quadratic extension is eventually an extension of.

type BaseField: Field<BasePrimeField = Self::BasePrimeField>

The base field that this field is a quadratic extension of.

Note: while for simple instances of quadratic extensions such as Fp2 we might see BaseField == BasePrimeField, it won’t always hold true. E.g. for an extension tower: BasePrimeField == Fp, but BaseField == Fp3.

type FrobCoeff: Field

The type of the coefficients for an efficient implemntation of the Frobenius endomorphism.

Required Methods

fn mul_base_field_by_frob_coeff(fe: &mut Self::BaseField, power: usize)

A specializable method for multiplying an element of the base field by the appropriate Frobenius coefficient.

Provided Methods

fn mul_base_field_by_nonresidue_in_place( fe: &mut Self::BaseField, ) -> &mut Self::BaseField

A specializable method for multiplying an element of the base field by the quadratic non-residue. This is used in Karatsuba multiplication and in complex squaring.

fn mul_base_field_by_nonresidue_and_add( y: &mut Self::BaseField, x: &Self::BaseField, )

A specializable method for setting y = x + NONRESIDUE * y. This allows for optimizations when the non-residue is canonically negative in the field.

fn mul_base_field_by_nonresidue_plus_one_and_add( y: &mut Self::BaseField, x: &Self::BaseField, )

A specializable method for computing x + mul_base_field_by_nonresidue(y) + y This allows for optimizations when the non-residue is not -1.

fn sub_and_mul_base_field_by_nonresidue( y: &mut Self::BaseField, x: &Self::BaseField, )

A specializable method for computing x - mul_base_field_by_nonresidue(y) This allows for optimizations when the non-residue is canonically negative in the field.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<P: Fp2Config> QuadExtConfig for Fp2ConfigWrapper<P>

const DEGREE_OVER_BASE_PRIME_FIELD: usize = 2usize

const NONRESIDUE: Self::BaseField = P::NONRESIDUE

const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff] = P::FROBENIUS_COEFF_FP2_C1

type BasePrimeField = <P as Fp2Config>::Fp

type BaseField = <P as Fp2Config>::Fp

type FrobCoeff = <P as Fp2Config>::Fp

impl<P: Fp4Config> QuadExtConfig for Fp4ConfigWrapper<P>

const DEGREE_OVER_BASE_PRIME_FIELD: usize = 4usize

const NONRESIDUE: Self::BaseField = P::NONRESIDUE

const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff] = P::FROBENIUS_COEFF_FP4_C1

type BasePrimeField = <<P as Fp4Config>::Fp2Config as Fp2Config>::Fp

type BaseField = QuadExtField<Fp2ConfigWrapper<<P as Fp4Config>::Fp2Config>>

type FrobCoeff = <Fp4ConfigWrapper<P> as QuadExtConfig>::BasePrimeField

impl<P: Fp6Config> QuadExtConfig for Fp6ConfigWrapper<P>

const DEGREE_OVER_BASE_PRIME_FIELD: usize = 6usize

const NONRESIDUE: Self::BaseField = P::NONRESIDUE

const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff] = P::FROBENIUS_COEFF_FP6_C1

type BasePrimeField = <<P as Fp6Config>::Fp3Config as Fp3Config>::Fp

type BaseField = CubicExtField<Fp3ConfigWrapper<<P as Fp6Config>::Fp3Config>>

type FrobCoeff = <Fp6ConfigWrapper<P> as QuadExtConfig>::BasePrimeField

impl<P: Fp12Config> QuadExtConfig for Fp12ConfigWrapper<P>

const DEGREE_OVER_BASE_PRIME_FIELD: usize = 12usize

const NONRESIDUE: Self::BaseField = P::NONRESIDUE

const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff] = P::FROBENIUS_COEFF_FP12_C1

type BasePrimeField = <<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config as Fp2Config>::Fp

type BaseField = CubicExtField<Fp6ConfigWrapper<<P as Fp12Config>::Fp6Config>>

type FrobCoeff = QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>