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Re: [Cfrg] Rigidity and performance

Robert Ransom <rransom.8774@gmail.com> Wed, 10 September 2014 09:33 UTC

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References: <D1EFFB24-C4C1-4595-8F5A-A2834BBA8217@shiftleft.org> <CABqy+spkPbZNsEBfxPJHDjHsD7M_yBT19W26EvrnNox-=ED+QA@mail.gmail.com>
Date: Wed, 10 Sep 2014 02:33:29 -0700
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From: Robert Ransom <rransom.8774@gmail.com>
To: Michael Hamburg <mike@shiftleft.org>
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Cc: IRTF Crypto Forum Research Group <cfrg@irtf.org>
Subject: Re: [Cfrg] Rigidity and performance
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On 9/10/14, Robert Ransom <rransom.8774@gmail.com> wrote:
> On 9/9/14, Michael Hamburg <mike@shiftleft.org> wrote:
>
>>  (2^424 - 2^212 - 1) / 11
>>   Faster than the above prime but has a “cofactor"; clearly worse than
>> Goldilocks unless you need 5 mod 8.
>
> But the prime (which determines the multiplicative-group structure,
> and thus the square-root algorithm) is congruent to 3 mod 4.  Using a
> composite modulus for fast coordinate operations doesn't change that.

Er.  Never mind -- the *modulus* is 3 mod 4, which is irrelevant.  The
prime is indeed 5 mod 8.

Sorry about that.


Robert Ransom

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