Re: [Cfrg] Elliptic Curves - curve form and coordinate systems (ends on March 12th)

[Adam Langley <[e-mail]>]

On Thu, Mar 12, 2015 at 12:19 PM, Andrey Jivsov <[e-mail]> wrote:
> I propose the Montgomery curve representation (u, v), which can be used for
> signatures on the same curve.
>
> "u" is identical to the sec 9 of
> https://tools.ietf.org/html/draft-agl-cfrgcurve-00.
> "v" is calculated (at virtually no additional computational cost) as v = u^3
> + 486662*u^2 + u

I'm going to display my ignorance here, but if "v" can be calculated
from just u with very little cost, why send it at all? The receiver
could equally calculate it if useful, no?

> * The format is friendly for crypto algorithms that need to add points (as
> opposed to ECDH only)

Wouldn't they need to know an extra bit? Given a point on the
Montgomery curve, (u,v), the "v" value is v^2, right? Doesn't that
discard the sign of v?


Cheers

AGL

-- 
Adam Langley [e-mail] https://www.imperialviolet.org