Improvement and analysis of a pseudo random bit generator by means of cellular automata

TL;DR

This paper enhances a pseudo random bit generator based on cellular automata, introduces a sequence matrix for sequence calculation, analyzes its multifractal structure, and evaluates its statistical performance for cryptographic applications.

Contribution

The paper presents a revised cellular automaton-based pseudo random generator, introduces a novel sequence matrix, and analyzes its multifractal properties to improve cryptographic randomness.

Findings

The generator passes all NIST statistical tests.

Multifractal analysis reveals structural properties of the automaton.

Conditions are identified for optimal randomness performance.

Abstract

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)