Trait FieldExtension

pub trait FieldExtension<BaseField> {
    type Coeffs: Sized;

    const D: usize;

    // Required methods
    fn from_coeffs(coeffs: Self::Coeffs) -> Self;
    fn from_bytes(bytes: &[u8]) -> Self;
    fn to_coeffs(self) -> Self::Coeffs;
    fn to_bytes(&self) -> Vec<u8>;
    fn embed(base_elem: BaseField) -> Self;
    fn frobenius_map(&self, power: usize) -> Self;
    fn mul_base(&self, rhs: &BaseField) -> Self;
}

Field extension trait. BaseField is the base field of the extension field.

Required Associated Constants

const D: usize

Extension field degree.

Required Associated Types

type Coeffs: Sized

This should be [BaseField; D]. It is an associated type due to rust const generic limitations.

Required Methods

fn from_coeffs(coeffs: Self::Coeffs) -> Self

Create an extension field element from its base field coefficients.

fn from_bytes(bytes: &[u8]) -> Self

Create an extension field element from little-endian bytes.

fn to_coeffs(self) -> Self::Coeffs

Convert an extension field element to its base field coefficients.

fn to_bytes(&self) -> Vec<u8>

Convert an extension field element to little-endian bytes.

fn embed(base_elem: BaseField) -> Self

Embed a base field element into an extension field element.

fn frobenius_map(&self, power: usize) -> Self

Frobenius map: take self to the p^powerth power, where p is the prime characteristic of the field.

fn mul_base(&self, rhs: &BaseField) -> Self

Multiply an extension field element by an element in the 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.

Implementations on Foreign Types

impl FieldExtension<Fp2> for Fq12

Note that halo2curves does not implement Field for Fq6, so we need to implement the intermediate points manually.

FieldExtension for Fq12 with Fq2 as base field since halo2curves does not implement Field for Fq6.

fn frobenius_map(&self, power: usize) -> Self

Raises this element to p^power, where p is prime characteristic of Self.

const D: usize = 6usize

type Coeffs = [Fp2; 6]

fn from_coeffs(coeffs: [Fq2; 6]) -> Self

fn from_bytes(bytes: &[u8]) -> Self

fn to_coeffs(self) -> Self::Coeffs

fn to_bytes(&self) -> Vec<u8>

fn embed(base_elem: Fq2) -> Self

fn mul_base(&self, rhs: &Fq2) -> Self

impl FieldExtension<Fp> for Fq2

FieldExtension for Fq2 with Fq as base field

const D: usize = 2usize

type Coeffs = [Fp; 2]

fn from_coeffs(coeffs: [Fq; 2]) -> Self

fn from_bytes(bytes: &[u8]) -> Self

fn to_coeffs(self) -> Self::Coeffs

fn to_bytes(&self) -> Vec<u8>

fn embed(c0: Fq) -> Self

fn frobenius_map(&self, power: usize) -> Self

fn mul_base(&self, rhs: &Fq) -> Self

impl FieldExtension<Fq2> for Fq12

FieldExtension for Fq12 with Fq6 as base field since halo2curves does not implement Field for Fq6.

const D: usize = 6usize

type Coeffs = [Fq2; 6]

fn from_coeffs(coeffs: Self::Coeffs) -> Self

fn from_bytes(bytes: &[u8]) -> Self

fn to_coeffs(self) -> Self::Coeffs

fn to_bytes(&self) -> Vec<u8>

fn embed(c0: Fq2) -> Self

fn frobenius_map(&self, power: usize) -> Self

fn mul_base(&self, rhs: &Fq2) -> Self

impl FieldExtension<Fq> for Fq2

FieldExtension for Fq2 with Fq as base field

const D: usize = 2usize

type Coeffs = [Fq; 2]

fn from_coeffs(coeffs: Self::Coeffs) -> Self

fn from_bytes(bytes: &[u8]) -> Self

fn to_coeffs(self) -> Self::Coeffs

fn to_bytes(&self) -> Vec<u8>

fn embed(c0: Fq) -> Self

fn frobenius_map(&self, power: usize) -> Self

fn mul_base(&self, rhs: &Fq) -> Self

Implementors