Improvement and Analysis of a Pseudo-Random Bit Generator by Means of Cellular Automata

Abstract

In this paper, we implement a revised pseudo random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix H N with the aim of calculating the pseudo random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix H N is revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST).

Design and Implementation of a Configurable Encryption System for Power-Constrained Devices

“…We define a PRNG of size N = 2 n − 1, for n = 1, 2, 3..., as a module that takes an input of size 2N + 1, and produces a sequence of outputs of size N , with the property that larger modules, that is, those with larger N values, produces higherquality sequences [11].…”

“…Cellular Automata (CA) systems provide simple algo-VOLUME X, 202X rithms owing to their high parallelism, homogeneity, and easy implementation in software and hardware systems [11], [12], making them good candidates for designing cryptosystems. CAs are discrete dynamical systems that evolve in discrete time steps and have been used to simulate biological systems [13], [14], road traffic [15], epidemics [16], surface water flow [17], and cryptography [18], [19], among others.…”

Algoritmo esteganográfico basado en autómatas celulares y en la sustitución de los bits menos significativos

“…En la Ref. [8] se evaluó su desempeño pasando todas las pruebas de NIST (National Institute of Standards and Technology).…”

Discrete Wavelet Analyses for Time Series

“…With the aim of computing the pseudo-random sequences of N bits, in Reference (Mejía & Urías, 2001) an algorithm based on the backward evolution of the CA rule 90 has been proposed. A modification of the generator producing pseudo-random sequences has been recently considered in (Murguía et al, 2010). The latter proposal is implemented and studied in terms of the sequence matrix H N , which was used to generate recursively the pseudo-random sequences.…”