Struct FieldElement

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

P-192 field element representing values in 𝔽ₚ, where p = 2¹⁹² − 2⁶⁴ − 1. Internally stored as 6 little‐endian 32‐bit limbs.

Implementations

impl FieldElement

pub fn from_u32(n: u32) -> Self

Build a field element from a small literal (0 ≤ n < 2³²)

pub fn zero() -> Self

The additive identity: 0

pub fn one() -> Self

The multiplicative identity: 1

pub fn from_bytes(bytes: &[u8; 24]) -> Result<Self>

Create a field element from big‐endian bytes. Validates that the value < p. Returns Err if ≥ p.

pub fn to_bytes(&self) -> [u8; 24]

Convert this field element into big‐endian bytes.

pub fn is_valid(&self) -> bool

Constant‐time check: is self < p ?

pub fn is_zero(&self) -> bool

Check if element is zero

pub fn is_odd(&self) -> bool

Return true if the element is odd (least‐significant bit = 1).

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

Constant‐time addition: (self + other) mod p

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

Constant‐time subtraction: (self - other) mod p

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

Field multiplication: (self * other) mod p Implements schoolbook 6×6 → 12‐limb product, then reduction

pub fn square(&self) -> Self

Field squaring: (self²) mod p

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

Compute multiplicative inverse via Fermat: a^(p-2) mod p

pub fn negate(&self) -> Self

Negate this field element: returns p - self if non-zero, else zero

pub fn sqrt(&self) -> Option<Self>

Compute square root using the fact that p ≡ 3 (mod 4) For such primes, sqrt(x) = x^((p+1)/4)

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 Eq for FieldElement

impl StructuralPartialEq for FieldElement