Re: [Cfrg] New names for draft-ladd-safecurves

Robert Ransom <rransom.8774@gmail.com> Tue, 21 January 2014 05:06 UTC

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Date: Mon, 20 Jan 2014 21:06:53 -0800
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From: Robert Ransom <rransom.8774@gmail.com>
To: Watson Ladd <watsonbladd@gmail.com>
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Cc: "cfrg@irtf.org" <cfrg@irtf.org>, Jon Callas <jon@callas.org>
Subject: Re: [Cfrg] New names for draft-ladd-safecurves
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On 1/20/14, Watson Ladd <watsonbladd@gmail.com> wrote:

> I also don't see why if you are going to toss in the y coordinate into
> Montgomery form to disambiguate addition you
> would use the Montgomery form as a wire format instead of Edwards
> form. I'm aware you can recalculate the y coordinate
> given the original one after a Montgomery ladder, but with radix-k
> addition algorithms on Edwards this doesn't seem to be a win.
>
> Maybe Montgomery form is just a red herring, but when I think about
> the consequences of a missing square root check in an Edwards
> form implementation for ECDH, I feel Montgomery form has a place here.

I would suggest using the Montgomery-form x coordinate with the sign
bit of the Edwards-form x coordinate.  (In fact, I *did* suggest that:
<http://www.ietf.org/mail-archive/web/cfrg/current/msg03868.html>
<http://www.ietf.org/mail-archive/web/cfrg/current/msg03870.html>)

And yes, the Brier-Joye formulas to recover Montgomery-form y after
the Montgomery ladder would be faster than Brauer's algorithm on
Edwards-form points for variable-base single-scalar multiplication.


Robert Ransom