Trait ark_ff::fields::models::quadratic_extension::QuadExtConfig
source · 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
) { ... }
}Expand description
Defines a Quadratic extension field from a quadratic non-residue.
Required Associated Types§
sourcetype BasePrimeField: PrimeField
type BasePrimeField: PrimeField
The prime field that this quadratic extension is eventually an extension of.
sourcetype BaseField: Field<BasePrimeField = Self::BasePrimeField>
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.
Required Associated Constants§
sourceconst DEGREE_OVER_BASE_PRIME_FIELD: usize
const DEGREE_OVER_BASE_PRIME_FIELD: usize
The degree of the extension over the base prime field.
sourceconst NONRESIDUE: Self::BaseField
const NONRESIDUE: Self::BaseField
The quadratic non-residue used to construct the extension.
sourceconst FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff]
const FROBENIUS_COEFF_C1: &'static [Self::FrobCoeff]
Coefficients for the Frobenius automorphism.
Required Methods§
sourcefn mul_base_field_by_frob_coeff(fe: &mut Self::BaseField, power: usize)
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§
sourcefn mul_base_field_by_nonresidue_in_place(
fe: &mut Self::BaseField
) -> &mut Self::BaseField
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.
sourcefn mul_base_field_by_nonresidue_and_add(
y: &mut Self::BaseField,
x: &Self::BaseField
)
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.
sourcefn mul_base_field_by_nonresidue_plus_one_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 )
A specializable method for computing x + mul_base_field_by_nonresidue(y) + y This allows for optimizations when the non-residue is not -1.
sourcefn sub_and_mul_base_field_by_nonresidue(
y: &mut Self::BaseField,
x: &Self::BaseField
)
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.