Re: (newbie) question on modification of polyalphabetic substitution cipher

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 03/30/04 

Date: Tue, 30 Mar 2004 06:17:10 +0200

Gary Shannon wrote:
[snip]
> Not so. Try any function you wish. As long as you take it mod 256 the
> function will have a repeating period of at most 256, possibly after some
> aperiodic part of less than 256 steps in length. Most of the time the
> period will much shorter than 256.

I doubt this is true, though I couldn't give any simple
function like polynomials etc. as counter-example. Anyway,
note that in math a function need not have a 'neat' formula
but could be defined as an arbitrary mapping. So, if one
defines a function f(n) to be the n-th byte of the binary
sequence representing pi, that would have an infinite period,
if I don't err. (Of course, in any subsequence of length
larger than 256, there must be repetitions, but that's
certainly not the issue.)

M. K. Shen