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

Paul Lambert <> Tue, 21 January 2014 18:30 UTC

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From: Paul Lambert <>
To: Watson Ladd <>, Bodo Moeller <>
Date: Tue, 21 Jan 2014 10:30:41 -0800
Thread-Topic: [Cfrg] New names for draft-ladd-safecurves
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Cc: "" <>, Jon Callas <>
Subject: Re: [Cfrg] New names for draft-ladd-safecurves
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On 1/21/14, 8:33 AM, "Watson Ladd" <> wrote:

>On Tue, Jan 21, 2014 at 7:28 AM, Bodo Moeller <> wrote:
>> Jon Callas <>rg>:
>>> I spent time talking to Dan and Tanja this weekend at ShmooCon about
>>> 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"
>>> the curve formerly known as Curve3617) made sense.

Two names would be better to differentiate between a Edwards or Montgomery
based point representation for the same curve.

WE also are working on the assumption that there are just one curve choice
for a particular field size. We should provide a extensible naming scheme
that would allow the later introduction additional options (e.g. Ed255
would be #1 of that size and flavor).


>My one concern which I've stated before is that we would then need a
>single wire format for Curve25519 and Ed25519.
>Robert Ransom's idea (sorry for the hijack) is the following: Suppose
>Bv^2=u^3+Au^2+u is isogenous to ax^2+y^2=1+dx^2y^2, with the isogenies
>u=(1+y)/(1-y), v=(1+y)/(1-y)x=ux. Then we represent points as u and
>the sign of x.
>An implementation using the Montgomery ladder to multiply proceeds as
>usual, using the fact that A is the reciprocal of a small integer
>to rewrite the equations. It then reconstructs v (there is a fast
>formula), and uses that to compute the sign of x. One using the
>Edwards curves proceeds as usual, then inverts the isogeny to get u,
>and uses x to get the sign bit.
>The argument for this is we can specify all our curves in twisted
>Edwards form with d small, a=+/-1, and life is nice for everyone.
>Unfortunately Curve25519 doesn't fit this nice pattern, and people
>want to use that exact curve. This form also involves a bit of extra
>field math for everyone, even if they are all going to do ECDH or
>Edwards addition afterwards, and so will want that form anyway. There
>is also a problem of exceptional cases if a and d are nonsquares
>modulo p for example.
>Have I rendered correctly the arguments for and against?
>> Yes, it does. This would fix the single major flaw of Curve25519 --
>> concatenating base-10 numbers to spell out a tuple just doesn't make
>> (except as a trap, so that if anyone reads it out as "twenty-five
>> ..." you'll know they don't know what they're saying).  I also don't
>> like having whitespace in those names, so I'd prefer "Curve-255-19" over
>> "Curve 255-19".
>> ("Curve" isn't very descriptive, but I've yet to see a more descriptive
>> for this curve that is actually helpful.)
>NIST isn't useful either as a prefix, but we live with it.
>Anyway, my view is whatever people want to call these they can call
>them, bobo and kiki aside.
>> Bodo
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