[TLS] (offline note) Re: Safe ECC usage

Rene Struik <rstruik.ext@gmail.com> Fri, 04 October 2013 13:09 UTC

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Date: Fri, 04 Oct 2013 08:57:44 -0400
From: Rene Struik <rstruik.ext@gmail.com>
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To: Johannes Merkle <johannes.merkle@secunet.com>
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Subject: [TLS] (offline note) Re: Safe ECC usage
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[offline note]

Hi Johannes:

Thanks for your note. I presume you refer to the paper:
Side Channel Analysis - Simple Power Analysis on Fast Modular Reduction 
with ECC over Generalized Mersenne Primes (Yasuyuki Sakai, Kouichi 
Sakurai, IEICE Trans.Fund., 2006)

I am glad you refer to side channel resistance and implementation 
attacks, an often undershed aspect of security discussions (certainly in 
standardization bodies).

The paper suggests the need to weed out conditional branches, as are 
also a problem in other implementation attacks. Do you think that 
modular reductions with NISTp curves are generally hard to secure, or 
just the naive and well-documented approach? I would be curious if you 
have some data that delves on this with Brainpool curves. {As an 
example, if one uses Barrett reduction (Alg. 2.14 of Guide to ECC book), 
one has a conditional branch as well. This being said, this can be 
massaged away.}

As to patents: for basic scalar multiplication, this era should be 
nearly over, if one discards implementation attacks; if one doesn't, it 
does not seem to, though.

Best regards, Rene


On 10/4/2013 8:18 AM, Johannes Merkle wrote:
>> random prime instead of a special one incurs a computational cost.  So, I
>> think I was reasonable to infer that Brainpool was implying that special
>> fields were lacking in security.  (The implication against special values
>> may then be inferred further.)
> The primes used by NIST curves are so special that there is less room for suspicion of a backdoor in the primes than in
> the curve.
>
> Our main concern with the special primes used by NIST curves is that their special form requires more caution to harden
> your arithmetic against side-channel attacks. As a matter of fact, Sakai & Sakurai, for instance, have proposed power
> analysis attacks targeting arithmetic on Pseudo-Mersenne primes. And we don't know, if the NSA has developed improved
> side-channel attacks against ECC over such fields.
>
> As I understand, the Curve25519 papers address side-channel immunity by specifying an eligible arithmetic. No objection
> to that approach, but for the Brainpool curves we had a different one.
>
> Another aspect was that we avoid many patents by not using Pseudo-Mersenne primes.
>
>
>
> Johannes
> _______________________________________________
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> TLS@ietf.org
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