Trait ExtensibleField

pub trait ExtensibleField<const N: usize>: StarkField {
    // Required methods
    fn mul(a: [Self; N], b: [Self; N]) -> [Self; N];
    fn mul_base(a: [Self; N], b: Self) -> [Self; N];
    fn frobenius(x: [Self; N]) -> [Self; N];

    // Provided methods
    fn square(a: [Self; N]) -> [Self; N] { ... }
    fn is_supported() -> bool { ... }
}

Defines basic arithmetic in an extension of a StarkField of a given degree.

This trait defines how to perform multiplication and compute a Frobenius automorphisms of an element in an extension of degree N for a given StarkField. It as assumed that an element in degree N extension field can be represented by N field elements in the base field.

Implementation of this trait implicitly defines the irreducible polynomial over which the extension field is defined.

Required Methods

fn mul(a: [Self; N], b: [Self; N]) -> [Self; N]

Returns a product of a and b in the field defined by this extension.

fn mul_base(a: [Self; N], b: Self) -> [Self; N]

Returns a product of a and b in the field defined by this extension. b represents an element in the base field.

fn frobenius(x: [Self; N]) -> [Self; N]

Returns Frobenius automorphisms for x in the field defined by this extension.

Provided Methods

fn square(a: [Self; N]) -> [Self; N]

Returns the square of a in the field defined by this extension.

fn is_supported() -> bool

Returns true if this extension is supported for the underlying base 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 ExtensibleField<2> for winter_math::fields::f62::BaseElement

Defines a quadratic extension of the base field over an irreducible polynomial x² - x - 1. Thus, an extension element is defined as α + β * φ, where φ is a root of this polynomial, and α and β are base field elements.

impl ExtensibleField<2> for winter_math::fields::f64::BaseElement

Defines a quadratic extension of the base field over an irreducible polynomial x² - x + 2. Thus, an extension element is defined as α + β * φ, where φ is a root of this polynomial, and α and β are base field elements.

impl ExtensibleField<2> for winter_math::fields::f128::BaseElement

Defines a quadratic extension of the base field over an irreducible polynomial x² - x - 1. Thus, an extension element is defined as α + β * φ, where φ is a root of this polynomial, and α and β are base field elements.

impl ExtensibleField<3> for winter_math::fields::f62::BaseElement

Defines a cubic extension of the base field over an irreducible polynomial x³ + 2x + 2. Thus, an extension element is defined as α + β * φ + γ * φ^2, where φ is a root of this polynomial, and α, β and γ are base field elements.

impl ExtensibleField<3> for winter_math::fields::f64::BaseElement

Defines a cubic extension of the base field over an irreducible polynomial x³ - x - 1. Thus, an extension element is defined as α + β * φ + γ * φ^2, where φ is a root of this polynomial, and α, β and γ are base field elements.

impl ExtensibleField<3> for winter_math::fields::f128::BaseElement

Cubic extension for this field is not implemented as quadratic extension already provides sufficient security level.