Deterministic chaotic finite-state automata

Abstract

Chaotic dynamics have been widely applied in various domains such as cryptography, watermarking and optimization algorithms. Enhancing chaotic complexity of simple one-dimensional (1D) chaotic maps has been a popular topic of research in recent years. However, most of the proposed methods have low complexity and are not suitable for practical applications. To overcome these issues, this paper introduces a novel approach known as deterministic chaotic finite-state automata (DCFSA). Existing 1D chaotic maps are associated with deterministic finite automata states. Then, a transition rule dynamically selects which 1D chaotic map to compute. DCFSA allows the creation of a large number of possible chaotic configurations with enhanced nonlinearity while retaining the computational complexity comparable to a 1D map. Theoretical and performance analyses show that DCFSA provides a larger chaotic parameter range, higher nonlinearity and chaotic complexity, as well as longer cycle length as compared to its underlying 1D chaotic maps. Moreover, performance comparison against other existing chaotification methods demonstrates DCFSA’s superiority.