From: "Deranged Mutant" <WlkngOwl@UNiX.asb.com>
Date: Fri, 5 Jan 1996 15:49:04 +0800
To: Cypherpunks@toad.com
Subject: Visual Correlations of RNGs useful for cryptanalysis?
Message-ID: <199601050740.CAA26664@UNiX.asb.com>
MIME-Version: 1.0
Content-Type: text/plain


Somebody passed an interesting article to me, "Random number 
generators: pretty good ones are easy to find", Clifford Pickover 
(IBM Watson Research Ctr, NY), The Visual Computer (1995) 11:369-377.

The article does NOT deal with cryptographically secure RNGs, however 
the author discusses some interesting methods for visualizing 
correlations in RNGs that probably can be applied to crypto.

One is the "Noise Sphere", which involves plotting the last three 
numbers generated by the RNG (Xn, Xn+1, Xn+2, where 0<Xn<1, and 
n=0,1,2,3...N) on spherical coordinates (r, theta, phi), where

  theta = 2 * pi * Xn
  phi = pi  * Xn+1         (note, X subscript n+1)
  r = sqrt(Xn+2)            (  "      X subscript n+2)

The article includes some pretty interesting graphics, including a 
couple that demonstrate what crappy RNGs look like.  Also discusses 
some other methods (terrain generation) for visualization.

Advantage is that this type of test is that it can be done on a 
low-end PC, can show some complex correlations even when an RNG is 
statistically good, and one doesn't have to an expert to see when 
something is wrong.

Crypto output (bytes, words, dwords, etc.) can be easily(?) translated into 
binary fractions for this type of test.

Take care,

--Rob
--- "Mutant" Rob <wlkngowl@unix.asb.com>

Send a blank message with the subject "send pgp-key"
(not in quotes) for a copy of my PGP key.