From: Jim Choate <ravage@ssz.com>
Date: Tue, 9 Sep 1997 20:23:57 +0800
To: cypherpunks@ssz.com (Cypherpunks Distributed Remailer)
Subject: Re: Gao's Chaos Cryptosystem Algorithm (fwd)
Message-ID: <199709091229.HAA04999@einstein.ssz.com>
MIME-Version: 1.0
Content-Type: text



Forwarded message:

> From: "Nobuki Nakatuji" <bd1011@hotmail.com>
> Subject: Re: Gao's Chaos Cryptosystem Algorithm
> Date: Mon, 08 Sep 1997 23:18:33 PDT

> >Nobuki Nakatuji wrote:

> >> >I will just repeat Prof. Choate's question, how do you generate Ch.

I think Igor got a bruised ego...

> >> Ch generate 
> >> 
> >> begin
> >> Xn+1=aXn(1.0-Xn)
> >> return Xn+1
> >> end
> >
> >What does aXn(1.0-Xn) mean? That's what I do not understand.

More explicity it is a weird IFS nomenclature (I believe). What is being
said here near as I can tell is:

Take some function X and takes it's output for the n'th result and use it as
the input for calculating n+1.

We take the n'th value and subtract it from 1, assuming the RNG function
returns 0 <= x <= 1, and feed this into X take the result and multiply by
some scalar, a, producing Xn+1.

Not shure exactly why the subtraction from unity is in there. All it really
does is give you a number > .5 if you are less than .5 and visa versa.
Doesn't enhance the IFS in any meaningful way that I can see.

The scalar multiplier, a, isn't doing anything but scaling the output.
Again it isn't effecting the IFS in a meaningful way that I can tell.

It would be more interesting to know the specific X's since this is
what will determine the 'level' of chaos that results since this is what
will define the strange attractor.

Section 1.3 onward of the reference I mentioned previously goes into some
detail on the various feedback processes and how to describe them somewhat
formaly. It's called a 'One Step Feedback Machine'.


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