Struct Curve 

pub struct Curve {
    pub a: BigInt,
    pub b: BigInt,
    pub p: BigInt,
}

A short Weierstrass curve y² = x³ + a·x + b over the prime field 𝔽_p.

Fields

a: BigInt

b: BigInt

p: BigInt

Implementations

impl Curve

pub fn new(a: BigInt, b: BigInt, p: BigInt) -> Curve

pub fn is_on_curve(&self, pt: &Point) -> bool

Whether pt satisfies the curve equation.

pub fn negate(&self, pt: &Point) -> Point

The group inverse −P.

pub fn add(&self, p1: &Point, p2: &Point) -> Point

The group law P + Q.

pub fn double(&self, pt: &Point) -> Point

Point doubling 2P.

pub fn mul(&self, k: &BigInt, pt: &Point) -> Point

Scalar multiplication k·P by double-and-add (k ≥ 0).

pub fn count_points(&self) -> u64

#E(𝔽_p) by direct point counting (includes the identity). O(p) — small p only.

pub fn point_order(&self, pt: &Point, bound: u64) -> Option<u64>

The order of pt — least k > 0 with k·pt = O, searched up to bound; None if larger.

impl Curve

pub fn j_invariant(&self) -> Option<BigInt>

The j-invariant 1728 · 4a³ / (4a³ + 27b²) — the complete isomorphism invariant of the curve (two curves are isomorphic over the algebraic closure iff their j-invariants agree). None if the curve is singular (4a³ + 27b² ≡ 0).

Trait Implementations

impl Clone for Curve

fn clone(&self) -> Curve

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Curve

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

Formats the value using the given formatter.

impl PartialEq for Curve

fn eq(&self, other: &Curve) -> 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 Curve

impl StructuralPartialEq for Curve