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Date: Thu, 3 Apr 2014 10:39:55 -0400
From: Bo Zhu <>
Subject: Re: [PHC] Catfish and public key hash

Hi Steve,

Thanks for the recommandation of using RSA-type $x ^ e \mod{N}$.
Actually, we have considered this option before.

But by using $x ^ e$, you may have a big trouble about collision
resistance, if you don't handle its input very well.
You may consider the case where (1) $(x + N) ^ e = x ^ e \mod{N}$, and (2)
$N$ is not a power of 2, so it might be less than $2^n$, where $n$ is the
output bit-length of a hash function, e.g. Keccak.
(It seems Makwa is using RSA-type operations, so hope it doesn't have any
issues with this.)

However, the discrete-log type $g ^ x \mod{N}$ doesn't have all these
It is proven to be collision-resistant if factoring $N$ is hard and $x$ is
simply any positive integer.

For more info, you may read Theorem 2 in our specification paper, and/or
the two following papers.
J.K.  Gibson, Discrete logarithm hash function that is collision free and
one way

Best regards,

On Thu, Apr 3, 2014 at 5:06 AM, Steve Thomas <> wrote:

> > On April 2, 2014 at 6:36 PM wrote:
> >
> >  Hi there
> >
> >  I would say that if the attacker needs more than 2x the amount of
> memory used
> >by the defender to get less than a 2x speed-up, then the attacker is
> wasting
> >resources: he/she could simply use two cores to get the same throughput...
> >Unless the attacker model considers a limitation in number of cores,
> which does
> >not seem to be the most common case.
> >
> But it's "free" if I have 8 GiB of ram and 4 cores and the settings are
> such
> that I need 64 MiB/guess then I have 7.75 GiB doing nothing. Anyway this is
> a non-issue if they just change it from (x is the output of Keccak):
> g ** x (mod N)
> to
> x ** e (mod N)

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