On 2013-09-30 03:14, Lodewijk andré de la porte wrote:
2013/9/29 James A. Donald <jam...@echeque.com <mailto:jam...@echeque.com>>

    (..) fact, they are not provably random, selected (...)

fixed that for you

It seems obvious that blatant lying about qualities of procedures must have some malignant intention, yet ignorance is as good an explanation. I don't think lying the other way would solve anything. It's obviously not especially secure.

The NIST ec curves are provably non random, and one can prove that NIST is lying about them, which is circumstantial but compelling evidence that they are backdoored:

   From: Gregory Maxwell<gmaxw...@gmail.com>  <mailto:gmaxw...@gmail.com>
   To: "This mailing list is for all discussion about theory, design, and 
development of Onion Routing."
        <tor-t...@lists.torproject.org>  <mailto:tor-t...@lists.torproject.org>
   Subject: Re: [tor-talk] NIST approved crypto in Tor?

   On Sat, Sep 7, 2013 at 4:08 PM, anonymous coward
   <anonymous.cow...@posteo.de>  <mailto:anonymous.cow...@posteo.de>  wrote:

           Bruce Schneier recommends **not** to use ECC. It is safe to
           assume he knows what he says.

       I believe Schneier was being careless there. The ECC parameter
       sets commonly used on the internet (the NIST P-xxxr ones) were
       chosen using a published deterministically randomized procedure.
       I think the notion that these parameters could have been
       maliciously selected is a remarkable claim which demands
       remarkable evidence.

   On Sat, Sep 7, 2013 at 8:09 PM, Gregory Maxwell<gmaxw...@gmail.com>  
<mailto:gmaxw...@gmail.com>  wrote:

   Okay, I need to eat my words here.

   I went to review the deterministic procedure because I wanted to see
   if I could repoduce the SECP256k1 curve we use in Bitcoin. They
   don’t give a procedure for the Koblitz curves, but they have far
   less design freedom than the non-koblitz so I thought perhaps I’d
   stumble into it with the “most obvious” procedure.

   The deterministic procedure basically computes SHA1 on some seed and
   uses it to assign the parameters then checks the curve order, etc..
   wash rinse repeat.

   Then I looked at the random seed values for the P-xxxr curves. For
   example, P-256r’s seed is c49d360886e704936a6678e1139d26b7819f7e90.

   _No_ justification is given for that value. The stated purpose of
   the “veritably random” procedure “ensures that the parameters cannot
   be predetermined. The parameters are therefore extremely unlikely to
   be susceptible to future special-purpose attacks, and no trapdoors
   can have been placed in the parameters during their generation”.

   Considering the stated purpose I would have expected the seed to be
   some small value like … “6F” and for all smaller values to fail the
   test. Anything else would have suggested that they tested a large
   number of values, and thus the parameters could embody any
   undisclosed mathematical characteristic whos rareness is only
   bounded by how many times they could run sha1 and test.

   I now personally consider this to be smoking evidence that the
   parameters are cooked. Maybe they were only cooked in ways that make
   them stronger? Maybe????

   SECG also makes a somewhat curious remark:

   “The elliptic curve domain parameters over (primes) supplied at each
   security level typically consist of examples of two different types
   of parameters — one type being parameters associated with a Koblitz
   curve and the other type being parameters chosen verifiably at
   random — although only verifiably random parameters are supplied at
   export strength and at extremely high strength.”

   The fact that only “verifiably random” are given for export strength
   would seem to make more sense if you cynically read “verifiably
   random” as backdoored to all heck. (though it could be more
   innocently explained that the performance improvements of Koblitz
   wasn’t so important there, and/or they considered those curves weak
   enough to not bother with the extra effort required to produce the
   Koblitz curves).

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