Linear Hybrid Cellular Automata Research Articles

Cryptographic Algorithm Based on Hybrid One-Dimensional Cellular Automata

The theory and application of cellular automata (CA) for a stream cipher-based encryption principle are presented in this study. Certain fundamental transformations are developed based on CA theory regarding decentralized computation for modeling different system’s behavior. The changes governing state transitions rely on simple evolution rules, which can easily be translated into functions using logic operators. A class of linear hybrid cellular automata (LHCA) based on rules 90 and 150 is used to implement these functions. Symmetric key systems theory is the foundation of the suggested algorithm. The algorithm functions use the proprieties provided by the LHCA evolution in order to convert plain text into cipher text and vice versa, in each case starting from the same initial state of the system and performing the same number of steps for each operation. Cellular automata’s parallel information processing property, in addition to their regular and dynamical structure, makes hardware implementation of such schemes best suited for VLSI implementation. Testing of the proposed algorithm was performed by developing both software and hardware solutions. Hardware implementation of the presented cryptosystem was developed using VHDL hardware description language and a FPGA device (XILINX Spartan3E XC3S500E). Design and software simulations have been carried out using the C# programming language.

ВАРИАНТ АЛГОРИТМА ГЕНЕРАЦИИ ПСЕВДОСЛУЧАЙНЫХ ДВОИЧНЫХ ПОСЛЕДОВАТЕЛЬНОСТЕЙ, ОСНОВАННЫЙ НА СВОЙСТВАХ ЛИНЕЙНЫХ КЛЕТОЧНЫХ АВТОМАТОВ

The article is devoted to the development of a linear system for generating a pseudo-random sequence based on cellular automata, the development of a model for several generators of nonlinear pseudo-random sequences with practical applications in symmetric data transformation systems. Such a model generates all solutions to linear binary difference equations. It is important to note that many of these solutions are pseudo-random keystream sequences. In the process of developing a linear system based on cellular automata, two main structures are considered: linear difference equations and one-dimensional linear hybrid cellular automata. This article shows that all solutions to linear binary difference equations can be implemented using linear models based on cellular automata using the "rule 90" and "rule 150". A model for generating pseudo-random bit sequences has been developed, which is most applicable in communication systems with a high transmission rate. The main difference of this model is that it is built on an exclusively sequential concatenation of a basic linear automaton, which determines the simplicity of the proposed model. Also, an algorithm for controlling the integrity and authenticity of block data was proposed based on the proposed algorithm for generating a pseudo-random sequence. The practical significance lies in the fact that the proposed model is simple and can be applied in information security systems in practice, including in authentication and data integrity control systems.

Hardware Random Number GeneratorUsing FPGA

Random numbers are employed in wide range of cryptographic applications. Output of an asynchronous sampling of ring oscillators can be used as the source of randomness and Linear Hybrid CellularAutomata is used to improve the quality of random data. FPGA is an ideal platform for the implementation of random number generator for cryptographic applications. The circuit described in this paper has been implemented on a highly efficient FPGA board which generated a 32-bit random number at a frequency of 125 MHz. The generated sequence of random numbers were subjected to Diehard test and NIST test for testing randomness and found to pass these tests. These tests are a battery of statistical tests for measuring the quality of a random number generator.

CellTCS:A Secure Threshold Cryptography Scheme based on Non-linear Hybrid Cellular Automata

This paper presents a secure threshold cryptography scheme, referred here as CellTCS, designed based on the features of non–linear hybrid Cellular Automata. CellTCS generates the secrets to be shared among m number of entities based on a simple logic structure, however, to learn information about the original secret from k or less shares is an extremely difficult task. CellTCS is effective in terms of efficiency, scalability and correctness.

An Explicit Similarity Transform between Cellular Automata and LFSR Matrices

This paper demonstrates a similarity transform between the tridiagonal matrices of one-dimensional linear hybrid cellular automata and the companion matrices of linear feedback shift registers. Such a transform is of interest to the VLSI design community, as it provides an explicit mapping between the states of these two linear finite state machines.

Partial Symmetry in Cellular Automata Rule Vectors

This letter demonstrates a partial symmetry in the rule vectors of one-dimensional linear hybrid cellular automata (CA). The symmetry was discovered in the CA realizations of the minimal cost primitive polynomials published by Bardell (1992). This symmetry turns out to be a simple function of the structure of the polynomial‘s coefficients, though the proof of this seems to be far from trivial. This letter presents the symmetry function, and outlines its proof.

Quantitative analysis for linear hybrid cellular automata and LFSR as built-in self-test generators for sequential faults

This paper presents a combinatorial method of evaluating the effectiveness of linear hybrid cellular automata (LHCA) and linear feedback shift registers (LFSR) as generators for stimulating faults requiring a pair of vectors. We provide a theoretical analysis and empirical comparisons to see why the LHCA are better than the LFSRs as generators for sequential-type faults in a built-in self-test environment. Based on the concept of a partner set, the method derives the number of distinctk-cell substate vectors which have 22k , 1≤k≤[n/2], transition capability for ann-cell LHCA and ann-cell LFSR with maximum length cycles. Simulation studies of the ISCAS85 benchmark circuits provide evidence of the effectiveness of the theoretrical metric.