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Do not perform inversions when converting from Montgomery to projective extended twisted Edwards.

This commit is contained in:
Sean Bowe 2017-12-06 17:22:35 -07:00
parent 7c48792511
commit c0f5645ab4
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GPG Key ID: 95684257D8F8B031
1 changed files with 38 additions and 12 deletions
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50
src/jubjub/edwards.rs
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@ -193,29 +193,55 @@ impl<E: Engine, Subgroup> Point<E, Subgroup> {
// y^2 = (-1) + A + (-1)
// y^2 = A - 2
// Indeed, A - 2 is nonsquare.
//
// We need to map into (projective) extended twisted
// Edwards coordinates (X, Y, T, Z) which represents
// the point (X/Z, Y/Z) with Z nonzero and T = XY/Z.
//
// Thus, we compute...
//
// u = x(x + 1)
// v = y(x - 1)
// t = x(x - 1)
// z = y(x + 1) (Cannot be nonzero, as above.)
//
// ... which represents the point ( x / y , (x - 1) / (x + 1) )
// as required by the mapping and preserves the property of
// the auxillary coordinate t.
//
// We need to scale the coordinate, so u and t will have
// an extra factor s.
// u = xs
let mut u = x;
u.mul_assign(&y.inverse().expect("y is nonzero"));
let mut v = x;
v.sub_assign(&E::Fr::one());
{
let mut tmp = x;
tmp.add_assign(&E::Fr::one());
v.mul_assign(&tmp.inverse().expect("A - 2 is nonsquare"));
}
// The resulting x-coordinate needs to be scaled.
u.mul_assign(&params.scale);
// v = x - 1
let mut v = x;
v.sub_assign(&E::Fr::one());
// t = xs(x - 1)
let mut t = u;
t.mul_assign(&v);
// z = (x + 1)
let mut z = x;
z.add_assign(&E::Fr::one());
// u = xs(x + 1)
u.mul_assign(&z);
// z = y(x + 1)
z.mul_assign(&y);
// v = y(x - 1)
v.mul_assign(&y);
Point {
x: u,
y: v,
t: t,
z: E::Fr::one(),
z: z,
_marker: PhantomData
}
}