The reversibility of one-dimensional cellular automata

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Recently the reversible cellular automata are increasingly used to build high-performance cryptographic algorithms. The paper establishes a connection between the reversibility of homogeneous one-dimensional binary cellular automata of a finite size and the properties of a structure called «binary filter with input memory» and such finite automata properties as the prohibitions in automata output and loss of information. We show that finding the preimage for an arbitrary configuration of a one-dimensional cellular automaton of length L with a local transition function f is associated with reversibility of a binary filter with input memory. As a fact, the nonlinear filter with an input memory corresponding to our cellular automaton does not depend on the number of memory cells of the cellular automaton. The results obtained make it possible to reduce the complexity of solving massive enumeration problems related to the issues of reversibility of cellular automata. All the results obtained can be transferred to cellular automata with non-binary cell filling and to cellular automata of dimension greater than 1.

About the authors

Alexey E. Zhukov

Bauman Moscow State Technical University (National Research University of Technology); «RusCrypto» Association

Author for correspondence.
ORCID iD: 0000-0002-1663-7773

Associate Professor of the Department of Information Security, BMSTU, Director of the «RusCrypto» Association, Ph.D. (Math.)

5 2-ya Baumanskayа St, bldg 1, Moscow, 105005, Russian Federation; 4A Plekhanov St, Moscow, 111123, Russian Federation


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Copyright (c) 2021 Zhukov A.E.

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