Struct FieldElement 

pub struct FieldElement {
    limbs: [u64; 4],
    curve: Curve,
}

A 256-bit prime field element stored as four little-endian 64-bit limbs.

Fields

limbs: [u64; 4]

curve: Curve

Implementations

impl FieldElement

pub fn zero(curve: Curve) -> Self

The additive identity (zero) for the given curve.

pub fn one(curve: Curve) -> Self

The multiplicative identity (one) for the given curve.

pub fn from_limbs(limbs: [u64; 4], curve: Curve) -> Result<Self, Error>

Constructs a field element from little-endian limbs.

Errors

Returns Error::OutOfRange if the value is not less than the modulus.

pub fn from_u64(val: u64, curve: Curve) -> Self

Constructs a field element from a single u64, placed in the lowest limb.

pub fn limbs(&self) -> &[u64; 4]

Returns the little-endian limb representation.

pub fn curve(&self) -> Curve

Returns the curve this element belongs to.

pub fn is_zero(&self) -> bool

Returns true if this element is zero.

pub fn sqr(self) -> Self

Modular squaring: self * self mod p.

pub fn pow(self, exp: &[u64; 4], num_bits: usize) -> Self

Modular exponentiation via square-and-multiply.

The exponent is given as little-endian limbs with num_bits significant bits.

pub fn fifth_root(self) -> Self

Computes the fifth root: self^((4p-3)/5) mod p.

pub fn bit(&self, i: usize) -> bool

Extracts bit i from the element (bit 0 is LSB).

Trait Implementations

impl Add for FieldElement

fn add(self, rhs: Self) -> Self

Modular addition: self + rhs mod p.

type Output = FieldElement

The resulting type after applying the + operator.

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 Hash for FieldElement

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for FieldElement

fn mul(self, rhs: Self) -> Self

Modular multiplication: self * rhs mod p.

Uses schoolbook multiplication followed by shift-and-subtract reduction.

type Output = FieldElement

The resulting type after applying the * operator.

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 Sub for FieldElement

fn sub(self, rhs: Self) -> Self

Modular subtraction: self - rhs mod p.

type Output = FieldElement

The resulting type after applying the - operator.

impl Copy for FieldElement

impl Eq for FieldElement

impl StructuralPartialEq for FieldElement