Re: [Cfrg] Complete additon for cofactor 1 short Weierstrass curve?

Samuel Neves <sneves@dei.uc.pt> Mon, 08 December 2014 21:12 UTC

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Date: Mon, 08 Dec 2014 21:11:26 +0000
From: Samuel Neves <sneves@dei.uc.pt>
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Subject: Re: [Cfrg] Complete additon for cofactor 1 short Weierstrass curve?
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On 08-12-2014 18:46, Dan Brown wrote:
> Regarding that proviso, I wonder how much the second Bosma-Lenstra formula
> (the one I called (G:H:I), which is the one that corresponds to the line
> (0:1:0) in the Bosma-Lenstra paper) would be slower than the standard
> incomplete formula.  That is, has anybody tried to optimize it?  (Naively,
> with a small a_4, I get a cost of 51M, but I expect much better is
> possible.)  Also, there seems to be many k-complete formula per curve, and
> perhaps some are faster than others, is this studied?

Both Arene-Kohel-Ritzenhaler (https://arxiv.org/abs/1102.2349, Remark 4.4) and Bos-Costello-Longa-Naehrig
(https://eprint.iacr.org/2014/130, pg 37) present simplified formulas, both beating 51M. I don't know of other attempts
to optimize complete Weierstrass formulas.