LoupVaillant / elligator

Mirror of a website on Elligator by Daniel J. Bernstein, Mike Hamburg, Anna Krasnova, and Tanja Lange
https://elligator.org
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Choice of name for curve point coordinates #7

Closed LoupVaillant closed 3 years ago

LoupVaillant commented 3 years ago

Currently, the text uses x and y to denote the coordinates of a curve point. This is in line with the original Elligator paper, earlier DJB paper on Curve25519, and the Ref10 source code. (Heck, even Monocypher kept that convention.)

The problem with that choice is that convention has since changed. RFCs now tend to refer to Montgomery curve point coordinates as (u, v) instead. I believe they do this to prevent ambiguities with (twisted) Edwards curves, for which they still use (x, y).

I'm personally inclined to follow the most recent convention for the sake of it. More importantly though, we actually Edwards curves to speed up the procedure involving the inverse map. Well need to show the (x, y) to (u, v) conversion at some point, or at least the extended coordinate variant. (And now I don't know what to do about Z, which is now used 3 times: Montgomery extended, Edwards extended, and the non-square. We'll address that later, perhaps…)

I'll do the edit, but I want to make sure we agree on the convention to begin with.

fscoto commented 3 years ago

As long as it's made clear that Montgomery curves use (uv) and (twisted) Edwards curves use (xy), that's alright with me.

LoupVaillant commented 3 years ago

Cool. I'll make the change, and close this when it's done.