From: Matthew J Ghio <mg5n+@andrew.cmu.edu>
Date: Fri, 12 Nov 93 16:19:42 PST
To: cypherpunks@toad.com
Subject: Re: Fractal cryptography
In-Reply-To: <9311120740.AA19589@jobe.shell.portal.com>
Message-ID: <ggt2OaK00awKAjSUYi@andrew.cmu.edu>
MIME-Version: 1.0
Content-Type: text/plain


hfinney@shell.portal.com (Hal Finney) wrote:

> There have been some discussions on sci.crypt within the past few months
> on nonlinear/chaotic algorithms and their use in cryptography.  Fractal
> cryptography sounds like it might be related.  The problem is that unless
> an algorithm was SPECIFICALLY DESIGNED to prevent an intelligent
> adversary from defeating it, the chances of it being an effective
> cryptosystem are limited.  Just because nonlinear systems produce
> complex-looking results does not mean that these results are unpredictable
> given enough data.

Yeah, but how much data?  Just because something can be solved given
enough data doesn't help me break it if I need 10^37643254 bytes of data
to do it.

> Now, maybe this particular fractal cryptosystem idea will actually work
> well.  I don't know; I haven't seen it.  But the point is that these
> complex types of systems have not provided a good foundation for crypto-
> graphy in the past.

Well, here's a little test.  The following numbers were generated using
a chaotic function:

568139551155097445567935056793172821494566808655678121156334445567812121480659

Do you see a pattern?  What function did I use to generate it?  :)

(Actually, assuming you knew what function I used, you could probably
solve for the key if you had enuf raw output from the PRNG, so it's
probably not completely impossible to solve the above, but that wouldn't
necessarily help you decrypt a file which had been encoded with such a
pad, unless you knew a lot about the format of the file.)