Trait ark_ff::fields::models::quadratic_extension::QuadExtParameters[−][src]

pub trait QuadExtParameters: '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];

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

    fn mul_base_field_by_nonresidue(fe: &Self::BaseField) -> Self::BaseField { ... }
    fn add_and_mul_base_field_by_nonresidue(
        x: &Self::BaseField, 
        y: &Self::BaseField
    ) -> Self::BaseField { ... }
    fn add_and_mul_base_field_by_nonresidue_plus_one(
        x: &Self::BaseField, 
        y: &Self::BaseField
    ) -> Self::BaseField { ... }
    fn sub_and_mul_base_field_by_nonresidue(
        x: &Self::BaseField, 
        y: &Self::BaseField
    ) -> Self::BaseField { ... }
    fn cyclotomic_exp(
        fe: &QuadExtField<Self>, 
        exponent: impl AsRef<[u64]>
    ) -> QuadExtField<Self> { ... }
}

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

Associated Types

`type BasePrimeField: PrimeField`[src]

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

`type BaseField: Field<BasePrimeField = Self::BasePrimeField>`[src]

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

`type FrobCoeff: Field`[src]

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

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Associated Constants

`const DEGREE_OVER_BASE_PRIME_FIELD: usize`[src]

The degree of the extension over the base prime field.

`const NONRESIDUE: Self::BaseField`[src]

The quadratic non-residue used to construct the extension.

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

Coefficients for the Frobenius automorphism.

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Required methods

`fn mul_base_field_by_frob_coeff(fe: &mut Self::BaseField, power: usize)`[src]

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

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Provided methods

`fn mul_base_field_by_nonresidue(fe: &Self::BaseField) -> Self::BaseField`[src]

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 add_and_mul_base_field_by_nonresidue( x: &Self::BaseField, y: &Self::BaseField ) -> Self::BaseField`[src]

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.

`fn add_and_mul_base_field_by_nonresidue_plus_one( x: &Self::BaseField, y: &Self::BaseField ) -> Self::BaseField`[src]

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( x: &Self::BaseField, y: &Self::BaseField ) -> Self::BaseField`[src]

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.