Struct lambdaworks_math::field::extensions::quadratic::QuadraticExtensionField

pub struct QuadraticExtensionField<F, T>
where
    F: IsField,
    T: HasQuadraticNonResidue<F>,
{ /* private fields */ }

A general quadratic extension field over F with quadratic non residue Q::residue()

Trait Implementations

impl<F, T> Clone for QuadraticExtensionField<F, T>

where F: IsField + Clone, T: HasQuadraticNonResidue<F> + Clone,

fn clone(&self) -> QuadraticExtensionField<F, T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F, T> Debug for QuadraticExtensionField<F, T>

where F: IsField + Debug, T: HasQuadraticNonResidue<F> + Debug,

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

Formats the value using the given formatter.

impl HasCubicNonResidue<QuadraticExtensionField<MontgomeryBackendPrimeField<BN254FieldModulus, 4>, BN254Residue>> for LevelTwoResidue

fn residue() -> FieldElement<Degree2ExtensionField>

This function must return an element that is not a cube in Fp, that is, a cubic non-residue.

impl<F, Q> IsField for QuadraticExtensionField<F, Q>

where F: IsField, Q: Clone + Debug + HasQuadraticNonResidue<F>,

fn add( a: &[FieldElement<F>; 2], b: &[FieldElement<F>; 2], ) -> [FieldElement<F>; 2]

Returns the component wise addition of a and b

fn mul( a: &[FieldElement<F>; 2], b: &[FieldElement<F>; 2], ) -> [FieldElement<F>; 2]

Returns the multiplication of a and b using the following equation: (a0 + a1 * t) * (b0 + b1 * t) = a0 * b0 + a1 * b1 * Q::residue() + (a0 * b1 + a1 * b0) * t where t.pow(2) equals Q::residue().

fn sub( a: &[FieldElement<F>; 2], b: &[FieldElement<F>; 2], ) -> [FieldElement<F>; 2]

Returns the component wise subtraction of a and b

fn neg(a: &[FieldElement<F>; 2]) -> [FieldElement<F>; 2]

Returns the component wise negation of a

fn inv(a: &[FieldElement<F>; 2]) -> Result<[FieldElement<F>; 2], FieldError>

Returns the multiplicative inverse of a This uses the equality (a0 + a1 * t) * (a0 - a1 * t) = a0.pow(2) - a1.pow(2) * Q::residue()

fn div( a: &[FieldElement<F>; 2], b: &[FieldElement<F>; 2], ) -> [FieldElement<F>; 2]

Returns the division of a and b

fn eq(a: &[FieldElement<F>; 2], b: &[FieldElement<F>; 2]) -> bool

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

fn zero() -> [FieldElement<F>; 2]

Returns the additive neutral element of the field extension.

fn one() -> [FieldElement<F>; 2]

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: [FieldElement<F>; 2]) -> [FieldElement<F>; 2]

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<F>; 2]

fn square(a: &[FieldElement<F>; 2]) -> [FieldElement<F>; 2]

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,

impl<F, T> PartialEq for QuadraticExtensionField<F, T>

where F: IsField + PartialEq, T: HasQuadraticNonResidue<F> + PartialEq,

fn eq(&self, other: &QuadraticExtensionField<F, T>) -> 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<F, T> Eq for QuadraticExtensionField<F, T>

where F: IsField + Eq, T: HasQuadraticNonResidue<F> + Eq,

impl<F, T> StructuralPartialEq for QuadraticExtensionField<F, T>

where F: IsField, T: HasQuadraticNonResidue<F>,