Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]

Mike Hamburg <mike@shiftleft.org> Thu, 27 November 2014 08:15 UTC

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Date: Thu, 27 Nov 2014 00:14:49 -0800
From: Mike Hamburg <mike@shiftleft.org>
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Subject: Re: [Cfrg] draft-black-rpgecc-00-.txt [was: Consensus and a way forward]
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On 11/26/2014 11:54 PM, Alyssa Rowan wrote:
> Yes,  that's just what I thought.
>
> As the greater value of A used in Curve25519 produces a simpler secure implementation with no weak private keys to check for, and that is the only big difference between Curve25519 and this proposal, I should prefer Curve25519 according to our selection criteria. Why *not* that, then?
>
Ask anyone who's implemented ECDSA on NIST-P160 :-)

Curve25519 has no weak keys because its order is 2^252+O(2^126), i.e. 
slightly over a power of 2.  Many curve generation procedures specify 
that the order must be slightly under a power of 2 rather than slightly 
over, because that also has advantages.  It permits slightly easier 
Barrett reduction mod the order, avoids special cases involving an extra 
bit, and for a few cases (MQV, I think) avoids having to do an extra 
point op in constant time algorithms just in case that bit might be set.

-- Mike