In the past there have been several attempts
to apply the field of deterministic chaos to cryptography. In this paper we propose for
cryptographic applications to use maps as state transition function of a discrete
dynamical system which leads to deterministic chaos. More specifically, we make use of
generalized versions of the well-known baker transform, which are discrete and finite.
Since they relate by group-theoretic representation to Bernoulli-shifts, we call them
Bernoulli permutations.
The iteration of Bernoulli permutations on a set of data realizes a repeated
"stretching" and "compressing" which has been compared by the
"rolling" and "folding" in the work of a baker by mixing a dough. The
knowledge of the importance of such operations for cryptography goes back to the
fundamental paper of Claude Shannon, a fact which has been pointed out earlier in a paper
by N.J.A. Sloane.