Generation Algorithms of Invertible Linear and Nonlinear Finite Automata with Memory

Abstract

In the context of rapid digital technology development, information security has become one of the key factors for the sustainable functioning of both society and the state. Modern methods of information protection rely on cryptographic algorithms, whose effectiveness is determined not only by their mathematical rigor but also by the degree of innovation in the applied models. One of the promising directions in this field is the use of finite automata models, which possess significant theoretical potential and broad opportunities for practical implementation. This study is devoted to the description of algorithms for generating invertible linear and nonlinear finite automata with input-output memory, applied in the FAPKC cryptosystem series. Unlike previously published works that are limited to purely mathematical descriptions of such models, this paper presents concrete procedures for their construction and implementation. Furthermore, a set of statistical tests was conducted to evaluate the randomness and cryptographic strength of the generated automata. The experimental results confirm their cryptographic robustness and demonstrate the feasibility of applying the proposed algorithms in modern cryptographic protocols.