Re: [Cfrg] Safecurves draft

Watson Ladd <watsonbladd@gmail.com> Thu, 09 January 2014 18:11 UTC

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Date: Thu, 9 Jan 2014 10:10:54 -0800
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From: Watson Ladd <watsonbladd@gmail.com>
To: Mike Hamburg <mike@shiftleft.org>
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Subject: Re: [Cfrg] Safecurves draft
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On Thu, Jan 9, 2014 at 10:07 AM, Mike Hamburg <mike@shiftleft.org> wrote:
> On Jan 9, 2014, at 7:26 AM, Bodo Moeller <bmoeller@acm.org> wrote:
>
> Robert Ransom <rransom.8774@gmail.com>om>:
>
>> > So while the Montgomery-form Curve25519 certainly has its use, allowing
>> > applications to negotiate a different form for ECDH would be beneficial.
>>
>
>>
>> Even if the party which generates a public key uses Edwards-form
>> points internally for that operation, whoever generates the key can
>> put it into Montgomery form for free before scaling, whereas whoever
>> receives it would need to perform an extra coordinate inversion in
>> order to convert from Edwards form to affine Montgomery form.
>
>
> That's a good point.  As I've pointed out (or tried to point out, anyway),
> the receiver might want to do the computations in Edwards form too, but
> there's not that much to be gained from that, so it may not be worth the
> extra complexity.
>
> Bodo
>
>
> I agree.  The sender might well use Edwards internally -- it's about 3x
> faster -- but the point should be sent in Montgomery form.
>
> I wonder, though, if the standard encoding of the spec should have the sign
> of the y-coordinate.  That way if we want to use the format for something
> other than ECDH -- signatures or PAKE or whatever -- we won't have to
> specify a new encoding.
>
> An overly-complicated but cute solution is 1/sqrt(x) chosen with the same
> sign as y.  (x is always square if you're in the q-torsion; 1/x works just
> as well as x in the ladder; 1/x lets you encode the identity.)  But we
> probably don't actually want to spec that.  Maybe just a bit for sign(y)?

This draft doesn't specify an encoding: it's up to whichever standard
uses this draft
to pick one.

Specifying an encoding of an x coordinate, or x coordinate plus sign
is easy enough.

You could upload a draft to specify it in more detail if you want.

I've uploaded a new version.
>
> -- Mike
>
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