Struct IsogenyMap

pub struct IsogenyMap<'a, Domain: SWCurveConfig, Codomain: SWCurveConfig<BaseField = <Domain as CurveConfig>::BaseField>> {
    pub x_map_numerator: &'a [<Domain as CurveConfig>::BaseField],
    pub x_map_denominator: &'a [<Codomain as CurveConfig>::BaseField],
    pub y_map_numerator: &'a [<Domain as CurveConfig>::BaseField],
    pub y_map_denominator: &'a [<Codomain as CurveConfig>::BaseField],
}

IsogenyMap defines an isogeny between curves of form Phi(x, y) := (a(x), b(x)*y). The xcoordinate of the codomain point only depends on thex-coordinate of the domain point, and the y-coordinate of the codomain point is a multiple of the y-coordinate of the domain point. The multiplier depends on the x`-coordinate of the domain point. All isogeny maps of curves of short Weierstrass form can be written in this way. See [[Ga18]]. Theorem 9.7.5 for details.

We assume that Domain and Codomain have the same BaseField but we use both BaseField<Domain> and BaseField<Codomain> in our fields’ definitions to avoid using PhantomData

• [[Ga18]] Galbraith, S. D. (2018). Mathematics of public key cryptography.

Fields

x_map_numerator: &'a [<Domain as CurveConfig>::BaseField]

x_map_denominator: &'a [<Codomain as CurveConfig>::BaseField]

y_map_numerator: &'a [<Domain as CurveConfig>::BaseField]

y_map_denominator: &'a [<Codomain as CurveConfig>::BaseField]