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Re: [Cfrg] A2 versus A^2 and BB verus AA

Samuel Neves <sneves@dei.uc.pt> Sat, 10 January 2015 20:39 UTC

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From: Samuel Neves <sneves@dei.uc.pt>
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Subject: Re: [Cfrg] A2 versus A^2 and BB verus AA
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On 01/10/2015 07:29 PM, Adam Langley wrote:
> On Sat, Jan 10, 2015 at 11:15 AM, Paul Lambert <paul@marvell.com> wrote:
>> In draft-agl-cfrgcurve-00 it appears that the ŒAA¹ term  is not consistent
>> with the josefsson text or the EFD that both use BB
> Whether it works out or not, it's good to match EFD. I've updated the
> draft in GitHub to match, thanks!

It is not a typo: the formulas present in the draft are taken from Appendix B of the Curve25519 paper, where as the
formulas in EFD are taken from the 1987 Montgomery paper.

These formulas also differ in the particular a24 constant used: Curve25519 uses (A - 2)/4 = 121665, whereas Montgomery
uses (A + 2)/4 = 121666. Your fix is missing this second adjustment, if it is to match Montgomery's formulas.

Best regards,
Samuel Neves

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