The main components of an encryption system based on rule 90 cellular automata, i.e., two indexed families of permutations and a pseudo-random bit generator are implemented in a very flexible way through a convenient matrix approach.

In this paper, we implement a revised pseudo random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix H N with the aim of calculating the pseudo random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix H N is revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST).