On two reversible cellular automata with two particle species

We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P), and time-reversal (T) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the hydrodynamic prediction for the model with exactly three local charges. Surprisingly, the numerically observed 'sound velocity' does not match the hydrodynamic value. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.

Evolutionary algorithms for designing reversible cellular automata

Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography, and reversible computing. In this work, we formulate the search of a specific class of RCA – namely, those whose local update rules are defined by conserved landscapes – as an optimization problem to be tackled with Genetic Algorithms (GA) and Genetic Programming (GP). In particular, our experimental investigation revolves around three different research questions, which we address through a single-objective, a multi-objective, and a lexicographic approach. In the single-objective approach, we observe that GP can already find an optimal solution in the initial population. This indicates that evolutionary algorithms are not needed when evolving only the reversibility of such CA, and a more efficient method is to generate at random syntactic trees that define the local update rule. On the other hand, GA and GP proved to be quite effective in the multi-objective and lexicographic approach to (1) discover a trade-off between the reversibility and the Hamming weight of conserved landscape rules, and (2) observe that conserved landscape CA cannot be used in symmetric cryptography because their Hamming weight (and thus their nonlinearity) is too low.

The reversibility of one-dimensional cellular automata

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.

Clustering Using Cyclic Spaces of Reversible Cellular Automata

This paper introduces a cycle-based clustering technique using the cyclic spaces of reversible cellular automata (CAs). Traditionally, a cluster consists of close objects, which in the case of CAs necessarily means that the objects belong to the same cycle; that is, they are reachable from each other. Each of the cyclic spaces of a cellular automaton (CA) forms a unique cluster. This paper identifies CA properties based on “reachability” that make the clustering effective. To do that, we first figure out which CA rules contribute to maintaining the minimum intracluster distance. Our CA is then designed with such rules to ensure that a limited number of cycles exist in the configuration space. An iterative strategy is also introduced that can generate a desired number of clusters by merging objects of closely reachable clusters from a previous level in the present level using a unique auxiliary CA. Finally, the performance of our algorithm is measured using some standard benchmark validation indices and compared with existing well-known clustering techniques. It is found that our algorithm is at least on a par with the best algorithms existing today on the metric of these standard validation indices.

On computing the Lyapunov exponents of reversible cellular automata

We consider the problem of computing the Lyapunov exponents of reversible cellular automata (CA). We show that the class of reversible CA with right Lyapunov exponent 2 cannot be separated algorithmically from the class of reversible CA whose right Lyapunov exponents are at most $$2-\delta$$ 2 - δ for some absolute constant $$\delta >0$$ δ > 0 . Therefore there is no algorithm that, given as an input a description of an arbitrary reversible CA F and a positive rational number $$\epsilon >0$$ ϵ > 0 , outputs the Lyapunov exponents of F with accuracy $$\epsilon$$ ϵ . We also compute the average Lyapunov exponents (with respect to the uniform measure) of the reversible CA that perform multiplication by p in base pq for coprime $$p,q>1$$ p , q > 1 .

Construction of Cryptographically Secure AES S-Box using Second-order Reversible Cellular Automata

In cryptography the block ciphers are the mostly used symmetric algorithms. In the existing system the standard S-Box of Advanced Encryption Standard(AES) is performed using the irreducible polynomial equation in table form known as look-up tables(LUTs). For more security purposes, second-order reversible cellular automata based S-box is created. The security aspects of the S-Box used in the AES algorithm are evaluated using cryptographic properties like Strict Avalanche Criteria, Non-Linearity, Entropy, and Common Immunity Bias. The design of S-Box using second-order reversible Cellular Automata is better concerning security and dynamic aspect as compared to the classical S-boxes used Advanced Encryption Standard.

Composite cellular automata based encryption method applied to surveillance videos

This work is part of the research project “Encryption Models Based on Chaotic Attractors” institutionalized in the Research and Scientific Development Center of the Universidad Distrital Francisco José de Caldas. In this paper, a symmetric encryption method for surveillance videos is presented, based on reversible composite cellular automata developed for this purpose. This method takes advantage of reversible cellular automata and elementary rule 30 properties, for efficient regions of interest encryption in surveillance video frames, obtaining an algorithm which experimental results of security and performance are consistent with those reported in current literature. In addition, it allows decryption without loss of information through a fixed size key for each video frame.

BLOCK CIPHERS ON THE BASIS OF REVERSIBLE CELLULAR AUTOMATA

The given paper is devoted to the software development of block cipher based on reversible one-dimensional cellular automata and the study of its statistical properties. The software implementation of the proposed encryption algorithm is performed in C# programming language in Visual Studio 2017. The paper presents specially designed approach for key generation. To ensure desired cryptographic stability, the shared secret parameters can be adjusted to contain information needed for creating substitution tables, defining reversible rules, and hiding final data. For the first time, it is suggested to create substitution tables based on iterations of a cellular automaton that is initialized by the key data.