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//! Traits for mapping an isogeny to another curve
//!
//! <https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve>
use core::ops::{AddAssign, Mul};
use ff::Field;
use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
/// The coefficients for mapping from one isogenous curve to another
pub struct IsogenyCoefficients<F: Field + AddAssign + Mul<Output = F>> {
/// The coefficients for the x numerator
pub xnum: &'static [F],
/// The coefficients for the x denominator
pub xden: &'static [F],
/// The coefficients for the y numerator
pub ynum: &'static [F],
/// The coefficients for the x denominator
pub yden: &'static [F],
}
/// The [`Isogeny`] methods to map to another curve.
pub trait Isogeny: Field + AddAssign + Mul<Output = Self> {
/// The maximum number of coefficients
type Degree: ArrayLength<Self>;
/// The isogeny coefficients
const COEFFICIENTS: IsogenyCoefficients<Self>;
/// Map from the isogeny points to the main curve
fn isogeny(x: Self, y: Self) -> (Self, Self) {
let mut xs = GenericArray::<Self, Self::Degree>::default();
xs[0] = Self::ONE;
xs[1] = x;
xs[2] = x.square();
for i in 3..Self::Degree::to_usize() {
xs[i] = xs[i - 1] * x;
}
let x_num = Self::compute_iso(&xs, Self::COEFFICIENTS.xnum);
let x_den = Self::compute_iso(&xs, Self::COEFFICIENTS.xden)
.invert()
.unwrap();
let y_num = Self::compute_iso(&xs, Self::COEFFICIENTS.ynum) * y;
let y_den = Self::compute_iso(&xs, Self::COEFFICIENTS.yden)
.invert()
.unwrap();
(x_num * x_den, y_num * y_den)
}
/// Compute the ISO transform
fn compute_iso(xxs: &[Self], k: &[Self]) -> Self {
let mut xx = Self::ZERO;
for (xi, ki) in xxs.iter().zip(k.iter()) {
xx += *xi * ki;
}
xx
}
}
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