Struct Isogeny 

pub struct Isogeny {
    pub domain: Curve,
    pub codomain: Curve,
    pub degree: u64,
    /* private fields */
}

A separable isogeny φ: E → E' of odd prime degree ℓ, built from a kernel generator by Vélu’s formulas. Stores the codomain and, for each kernel representative Q (one per ± pair), the Vélu quantities (xQ, vQ = 6xQ²+2a, uQ = 4yQ²) used to evaluate φ.

Fields

domain: Curve

codomain: Curve

degree: u64

Implementations

impl Isogeny

pub fn from_kernel(curve: &Curve, gen: &Point, ell: u64) -> Option<Isogeny>

Build the ℓ-isogeny with kernel ⟨gen⟩ by Vélu’s formulas (ℓ an odd prime, gen of order exactly ℓ). The codomain is y² = x³ + (a − 5v)x + (b − 7w) where v = Σ vQ, w = Σ (uQ + xQ·vQ) over the (ℓ−1)/2 kernel representatives. None unless ℓ is an odd prime and gen has order ℓ.

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

Evaluate φ at a point. Kernel points map to the identity. For P = (x, y) ∉ ker, the x-map is X = x + Σ [ vQ/(x−xQ) + uQ/(x−xQ)² ] and — since a normalized isogeny pulls back the invariant differential (φ*(dX/Y) = dx/y) — the y-coordinate is Y = y · X'(x) = y·[1 − Σ (vQ/(x−xQ)² + 2uQ/(x−xQ)³)].

Trait Implementations

impl Clone for Isogeny

fn clone(&self) -> Isogeny

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Isogeny

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

Formats the value using the given formatter.