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

[Mike Hamburg <[e-mail]>]

On Jan 20, 2014, at 7:54 PM, Watson Ladd <[e-mail]> wrote:

> On Mon, Jan 20, 2014 at 7:50 PM, Jon Callas <[e-mail]> wrote:
>> 
>> On Jan 20, 2014, at 7:17 PM, Watson Ladd <[e-mail]> wrote:
>> 
>>> I am proposing that we name the curves with the following scheme: E,
>>> M, TE, indicating
>>> the curve type, followed by a prime designator. The prime designator
>>> will be the concatination
>>> of the numbers a and b such that 2^a-b=p if such a and b exist and are
>>> small. Otherwise I'll think of something (Ed448 Goldilocks I'm looking
>>> at you).
>>> 
>>> Any objections? Or do we have consensus on this change, and I was just
>>> to dense to notice?
>>> 
>>> A new version with significant alterations will be hitting the draft
>>> server in a few days.
>> 
>> I think it's overkill, myself.
>> 
>> Really, there's no reason to designate in the name an Edwards curve from a Montgomery, especially because in the implementation someone's probably going to flip between representations. Only us math weenies really care about the representation, and you're going to confuse the coders.
> 
> If I hand you a string of bytes, what point does that represent and on
> what curve does it fall? Seems to me like that's a representation
> issue we should all care about.

It may depend on whether we expect a curve to be used for both signatures and ECDH, or just one purpose.  If they're only for one thing, then the letters make a difference.

I think Jon wants to use each curve for both purposes, at least potentially, which makes sense to me.  This is why I suggested always using the Montgomery point representation (or even its inverse square root! but maybe that's crazy) even for the Edwards curves.

I suppose in that case we should be using curves with a small A or (A-2)/4 in Montgomery form instead of small d in Edwards form, because you need to multiply by A more often: Edwards representations are probably fastest with Niels+Extended coordinates at that size so they almost never multiply by d.

>> I spent time talking to Dan and Tanja this weekend at ShmooCon about this sort of thing and I think that our agreement was that names like "Curve 255-19" (which covers both Curve25519 and Ed25519) or "Curve 414-17" (for the curve formerly known as Curve3617) made sense.

This is also nice because you could call Ed448-Goldilocks as "Curve 448-224-1".

> This would be great except that we want both Edwards and Montgomery
> wire formats. If there is consensus on only Edwards wire formats, that
> naming will work fine.

If you're going to pick one, it should be Montgomery.  This is because the Montgomery ladder suffers almost a 10% hit from conversion, but Edwards suffers like an 0.2% hit.

-- Mike