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Date: Wed, 17 Dec 2014 18:24:28 +0000
From: Gregory Maxwell <gmaxwell@...il.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Re: Some KDF stumbling blocks, plus Common

On Wed, Dec 17, 2014 at 11:26 AM, Thomas Pornin <pornin@...et.org> wrote:
> On Wed, Dec 17, 2014 at 09:57:15AM +0800, Ben Harris wrote:
>> A naive question based on my limited knowledge of cool terms like abelian
>> groups - if you did this using elliptic curves could you not worry about
>> the security of pq? And just suffer the once off work to calculate y. Or
>> does the math not carry over to elliptic curves?
>
> The math does not carry over to elliptic curves (or, at least, I did not
> find a way to), unless you do something like generating a curve of order
> n where n = pq with p and q unknown (in which case you gained nothing).

Class groups in imaginary quadratic number fields can give you a group
where the counting the order is presumed hard.
( http://grouper.ieee.org/groups/1363/StudyGroup/contributions/iqstandard.pdf )

Sort of gone far afield for the list, sorry about that.

In any case, for some applications the potential of a trapdoor is
fine. ... e.g. if the trapdoor is per service and this system is just
used to authenticate to the service, I see no great concern.

When talking about parameters to be shared by the general public, I am
dubious that any amount of ritual is really sufficient:  Especially
since a good cryptosystem must be able to strongly reject conspiracy
theories that attackers could use to social engineer users out of
using strong cryptographic tools in the first place.

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