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Message-ID: <CAAS2fgT8v4B9KyTdBjdCzQ50wy_XY=VeQTnBQOUaHHePSuM9Mw@mail.gmail.com> 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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