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improve: avoid the inversions in iso_map_secp256k1 #124

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Jan 10, 2024
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improve: avoid the inversions in iso_map_secp256k1 #124

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35 changes: 15 additions & 20 deletions src/secp256k1/curve.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -246,31 +246,26 @@ pub(crate) fn iso_map_secp256k1(rp: IsoSecp256k1) -> Secp256k1 {
],
];

// Convert to affine coordinates:
let coords = <IsoSecp256k1 as CurveExt>::AffineExt::coordinates(&rp.into()).unwrap();
let x = coords.x();
let y = coords.y();
let (x, y, z) = rp.jacobian_coordinates();

// iso_map logic
let x_squared = x.square();
let x_cubed = x * x_squared;
let z2 = z.square();
let z3 = z2 * z;
let z4 = z2.square();
let z6 = z3.square();

let x_num = K[1][3] * x_cubed + K[1][2] * x_squared + K[1][1] * x + K[1][0];
let x_den = x_squared + K[2][1] * x + K[2][0];
// iso_map logic (avoid inversion)
// reference: <https://github.com/zcash/pasta_curves/blob/main/src/hashtocurve.rs#L80-L106>
let x_num = ((K[1][3] * x + K[1][2] * z2) * x + K[1][1] * z4) * x + K[1][0] * z6;
let x_den = (z2 * x + K[2][1] * z4) * x + K[2][0] * z6;

let y_num = K[3][3] * x_cubed + K[3][2] * x_squared + K[3][1] * x + K[3][0];
let y_den = x_cubed + K[4][2] * x_squared + K[4][1] * x + K[4][0];
let y_num = (((K[3][3] * x + K[3][2] * z2) * x + K[3][1] * z4) * x + K[3][0] * z6) * y;
let y_den = (((x + K[4][2] * z2) * x + K[4][1] * z4) * x + K[4][0] * z6) * z3;

// exceptional case MUST return identity
// reference: <https://www.rfc-editor.org/rfc/rfc9380.html#name-simplified-swu-for-ab-0>
if x_den.is_zero().into() || y_den.is_zero().into() {
return Secp256k1::identity();
}

let x = x_num * x_den.invert().unwrap();
let y = y * (y_num * y_den.invert().unwrap());
let z = x_den * y_den;
let x = x_num * y_den * z;
let y = y_num * x_den * z.square();

Secp256k1::new_jacobian(x, y, Fp::ONE).unwrap()
Secp256k1::new_jacobian(x, y, z).unwrap()
}

#[cfg(test)]
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