Re: [Cfrg] Formal request from TLS WG to CFRG for new elliptic curves

Nigel Smart <> Sun, 20 July 2014 15:28 UTC

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Date: Sun, 20 Jul 2014 16:27:52 +0100
From: Nigel Smart <>
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Subject: Re: [Cfrg] Formal request from TLS WG to CFRG for new elliptic curves
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It seems there is a lot of noise about new types of curves, curvexxxyy this,
and NUMS that.

Note the request is for new ELLIPTIC CURVES not elliptic curve PROTOCOLS

Thus any curve should be IMHO usable with any STANDARD protocol, in any
STANDARD way of implementing the protocol. Without this constraint one is
bound to get implementation errors.

   - Curve25519 is a combined curve/protocol; so is out of scope IMHO. As
      someone is bound to use the underlying curve with some other protocol
      and make mistakes.

Benjamin Black is correct; having new types of this that and the other for
a marginal security gain, and/or a marginal performance gain is IMHO
inviting problems.

Thus the ONLY response in my view as responsible cryptographers is
to recommend curves which

    i) Whose data format for point transfer/curve definition is in 
           - I dont care if some implementation wants to use some 
             form to do some calculation; the data transfer must enable
  ii) Whose group order is prime
           - Not having prime group order is inviting problems. Thus Edwards
             curves are out as I am sure they require non-prime group order
iii) The "b" coordinate should be generated by a hash value on some
       random string.
  iv) Usual security constraints; base field has 256 and 512 bits of 
        to match AES 128 and AES 256; MOV criteria; SmartASS criteria;
  v) Ignore "esorteric" constrains like twist security etc.

So basically I cannot see what is wrong with the NIST curves. And if people
want something new then they should really come up with a credible
reason for wanting something new. No argument I have seen warrants
the massive change in software and infrastructure that is being proposed.
If people really are that worried about this NIST curves then
    i) They should probably stop using the internet full stop, as that means
       the NSA probably has massive more capability than even Snowden has
   ii) Generate curves as above; and not trust some new fingle-fangled ideas
       which are not supported by all the major cryptographers who have
       worked on ECC.

BTW I still stand by my statement that we should recommend EC-Schnorr
as an extra hash function.
   - Minor change in code needed to support it (compared to some of the 
   - Provides some "hedge" against future collisions in SHA-256 and SHA-3.
   - Has IMHO (and this is purely subjective) better provable security than
But that is not what we have been asked to comment on; as this is a new
"protocol" (i.e. signature scheme).