Re: KA=>OWF
From: Scott Fluhrer (sfluhrer_at_ix.netcom.com)
Date: 11/09/03
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Date: Sun, 09 Nov 2003 17:24:07 GMT
"Tom St Denis" <tomstdenis@iahu.ca> wrote in message
news:eBtrb.1108$HoK.428@news01.bloor.is.net.cable.rogers.com...
>
> "Gelo Ilzi" <geloilzi@hotmail.com> wrote in message
> news:bolneo$p9e$1@news2.netvision.net.il...
> >
> > "Tom St Denis" <tomstdenis@iahu.ca> wrote in message
> > news:rYqrb.1069$HoK.672@news01.bloor.is.net.cable.rogers.com...
> > >
> > > "Gelo Ilzi" <geloilzi@hotmail.com> wrote in message
> > > news:bol74k$bd7$1@news.iucc.ac.il...
> > > > It is well known (at least I know simple proof to this fact), that
key
> > > > agreement implies one-way function. Can somebody give me a reference
> > where
> > > > this claim is proven.
> > >
> > > The fact that it is wrong makes finding a reference moot.
> > >
> > > Key agreement often requires a trapdoor one-way permutation but that
> isn't
> > a
> > > strict requirement.
> >
> > Tom, I'm not looking for a reference OWF=>KA, but KA=>OWF
>
> And I'm telling you that KA =/=> OWF
>
> Take DH over a safe prime. You pick a QR as your generator g. That means
> all g^x will be a QR in a sub-group of prime order. so given a y = g^x I
> can then raise y to say z e.g. w = y^z however provided 0 < z < p [p ==
> order of group] the operation is not one-way [since the inverse of z will
> get you back to y from w]
However, it is one-way, in the sense that the function F(x) = g^x is assumed
to be one-way. This is the important sense, because if it is not one-way,
DH is not secure. In general, over any group, if F(x) = g^x is not one-way,
then DH over that group and generator is not secure. Hence, DH is not a
counter-example to what the OP was asking.
What I don't know if there is some other key agreement protocol that doesn't
assume oneway-ness, so I can't answer the OP's question. However, DH isn't
it.
>
> Therefore KA does not imply OWF and what you are asking for does not
exist.
>
> Get over it, move on, live and let learn, kubayah, etc, etc.
Tom, you *really* should stop assuming that you've learned everything
already...
-- poncho
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