Scrambling by Reversible Conservative Bit Block Automata

Michael Schreiber

Wolfram Research

Abstract

Bit block automata return blocks of output bits for blocks of input
bits. They are reversible if their rules include all possible input
blocks among their output blocks. Those reversible systems conserve
bit counts immediately if all their rule digits return output bits
which are permutations of their input bits. Formulas for the numbers
of these kinds of bit block automata are given. Scrambling of images
is discussed as an example. Alternating conservation of bit counts is
implemented for byte block automata as an example for models of
reversible and non-reversible bit block systems which maintain zero
total average energy.