Struct FieldElement

pub struct FieldElement(/* private fields */);

A field element in GF(2^283) represented by 5 u64 limbs (320 bits).

Implementations

impl FieldElement

pub fn zero() -> Self

The additive identity element (zero).

pub fn one() -> Self

The multiplicative identity element (one).

pub fn from_bytes(bytes: &[u8; 36]) -> Result<Self>

Create a field element from its canonical byte representation.

The bytes are interpreted as a big-endian representation of the field element.

pub fn to_bytes(&self) -> [u8; 36]

Convert this field element to its canonical byte representation.

The bytes are a big-endian representation of the field element.

pub fn is_zero(&self) -> bool

Check if this field element is zero.

pub fn add(&self, other: &Self) -> Self

Add two field elements in GF(2^283).

In binary fields, addition is performed using XOR.

pub fn mul(&self, other: &Self) -> Self

Multiply two field elements in GF(2^283).

Uses the irreducible polynomial for reduction.

pub fn square(&self) -> Self

Square a field element in GF(2^283).

pub fn invert(&self) -> Result<Self>

Compute the multiplicative inverse of a field element.

Uses Fermat’s Little Theorem: a^(2^m - 2) = a^(-1) in GF(2^m). Returns an error if the element is zero.

pub fn sqrt(&self) -> Self

Compute the square root of a field element.

In binary fields of characteristic 2, sqrt(x) = x^(2^(m-1)).

pub fn trace(&self) -> u64

Get the trace of the element.

The trace is Tr(z) = z + z^2 + z^4 + … + z^(2^(m-1)). For compressed points, it’s used to disambiguate the y-coordinate.

Trait Implementations

impl Clone for FieldElement

fn clone(&self) -> FieldElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FieldElement

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

Formats the value using the given formatter.

impl PartialEq for FieldElement

fn eq(&self, other: &FieldElement) -> 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 Copy for FieldElement

impl Eq for FieldElement

impl StructuralPartialEq for FieldElement