Re: [Cfrg] ECC mod 8^91+5
Dan Brown <danibrown@blackberry.com> Thu, 18 May 2017 19:20 UTC
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From: Dan Brown <danibrown@blackberry.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: ECC mod 8^91+5
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Date: Thu, 18 May 2017 19:14:55 +0000
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Subject: Re: [Cfrg] ECC mod 8^91+5
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Clarifying a few things over my previous message: - 8^91+5 has fast modular reduction mainly due its being close to a power of 2 (in contrast to 7^98-2). - 8^91+5 is a little further than I first thought from the specifics of Koblitz-Menezes Example 5, because the conductor seems to have several more prime factors, rather than the single prime in the KM construction - sorry if I gave the wrong impression. Perhaps portions of the KM example 5 argument might yet apply to 2y^2=x^3+x/GF(8^91+5). - 8^91+5 as a field size might be a little awkward. For ECDH, we take advantage of the endomorphism (x,y)->(-x,iy), to drop a sign bit from x. This fits x into 34 bytes. This is larger than the usual 128-bit secure ECC curves, which can use 32 bytes, so they require extra data to send and store. The byte length is not a multiple of 4, let alone power of two, but I am not sure how much trouble that would be.
- [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 David Jacobson
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Thomas Garcia
- Re: [Cfrg] ECC mod 8^91+5 Ilari Liusvaara
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Ilari Liusvaara
- Re: [Cfrg] ECC mod 8^91+5 D. J. Bernstein
- Re: [Cfrg] ECC mod 8^91+5 Samuel Neves
- Re: [Cfrg] ECC mod 8^91+5 D. J. Bernstein
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown
- Re: [Cfrg] ECC mod 8^91+5 Paterson, Kenny
- Re: [Cfrg] ECC mod 8^91+5 Hanno Böck
- Re: [Cfrg] ECC mod 8^91+5 Salz, Rich
- Re: [Cfrg] ECC mod 8^91+5 Stephen Farrell
- Re: [Cfrg] ECC mod 8^91+5 Dan Brown