[Cfrg] Consensus and a way forward

Benjamin Black <b@b3k.us> Thu, 27 November 2014 04:25 UTC

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From: Benjamin Black <b@b3k.us>
Date: Wed, 26 Nov 2014 20:25:29 -0800
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Subject: [Cfrg] Consensus and a way forward
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All,

Over the past couple of weeks we have been working with Adam Langley to see
if we could find a compromise with which we could all live. I'm pleased to
say we have been successful in accommodating our respective performance and
trustworthy generation concerns, and I hope the resulting proposal will be
attractive to others, as well. The generation procedure is document in a
draft I've just posted that can be found at
http://www.ietf.org/id/draft-black-rpgecc-00.txt .

The simplest summary is that we have combined the prime preferred by Adam
and others at the 128-bit security level with the rigid parameter
generation we view as essential for producing the most trustworthy curves.
We have used the generation procedure to produce a new twisted Edwards
curve based on 2^255 - 19 and a new Edwards curve based on 2^384 - 317.
These new curves are given as test vectors in the draft, and are also given
below.

These 2 curves are sufficient for meeting the request from TLS. However, if
there is strong interest in a 3rd curve for the 256-bit security level, the
generation procedure‚Äč‚Äč gives the same curve with p =2^521 - 1 as several
teams produced.


b

--

2^255 - 19

   p = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
         FFFFFFFFFFED
   d = 0x15E93
   r = 0x2000000000000000000000000000000016241E6093B2CE59B6B9
         8FD8849FAF35
x(P) = 0x3B7C1D83A0EF56F1355A0B5471E42537C26115EDE4C948391714
         C0F582AA22E2
y(P) = 0x775BE0DEC362A16E78EFFE0FF4E35DA7E17B31DC1611475CB4BE
         1DA9A3E5A819
   h = 0x4


2^384 - 317

     p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
           FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC3
     d = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
           FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD19F
     r = 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE2471A1
           CB46BE1CF61E4555AAB35C87920B9DCC4E6A3897D
  x(P) = 0x61B111FB45A9266CC0B6A2129AE55DB5B30BF446E5BE4C005763FFA
           8F33163406FF292B16545941350D540E46C206BDE
  y(P) = 0x82983E67B9A6EEB08738B1A423B10DD716AD8274F1425F56830F98F
           7F645964B0072B0F946EC48DC9D8D03E1F0729392
     h = 0x4