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

Robert Ransom <rransom.8774@gmail.com> Tue, 21 January 2014 04:54 UTC

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Date: Mon, 20 Jan 2014 20:54:53 -0800
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From: Robert Ransom <rransom.8774@gmail.com>
To: Mike Hamburg <mike@shiftleft.org>
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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, Mike Hamburg <mike@shiftleft.org> wrote:
> On Jan 20, 2014, at 8:25 PM, Robert Ransom <rransom.8774@gmail.com> wrote:

>> The Montgomery-form ladder is as efficient for small-integer
>> Edwards-form d as it is for small-integer Montgomery-form parameter
>> ((A-2)/4 or (A+2)/4).

> So it is.  Do you have a reference for that, BTW?

I don't have a reference for it.  (But I did use it in my Curve1174
implementation last summer, and I'm pretty sure I said it a few days
ago on this list.)

<http://hyperelliptic.org/EFD/g1p/data/twisted/coordinates> gives an
isomorphism to Montgomery form with A = 4a/(a-d) - 2; the parameter
for the formulas given on
<http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html> is a24 =
(A+2)/4 = a/(a-d).  So the fact that when d is a small integer (and a
is 1 or -1, as usual), the Montgomery-form parameter is the reciprocal
of a small integer is fairly obvious from that.

The remaining step is to move the multiplication by 1/a24 into BB.


Robert Ransom