Information Technologies Based on Noise-like Signals: IV. Algorithmic Pseudo-random Number Generators Based on Dynamic Chaos

Abstract

Numerical simulation is used to investigate the statistical, fractal and structural properties of sequences of integers generated by the algorithm with delay. It is shown that the statistical properties of the generated discrete sequences, close to a random process, are provided by such generating coding algorithms, in which both the one-dimensional probability distribution and the distributions of the conditional probabilities of the generated numbers are close to uniform. The structure of the phase space of a discrete coding algorithm with delay defined on a closed interval of integers is studied. It is established that the phase space consists of a finite number of cycles of different periods, the behavior of the system on which is pseudorandom. The possibility of creating generators of this type with more complex circuits is discussed. It is shown that with an appropriate choice of parameter values, the algorithm allows the formation of a non-periodic pseudo-random sequence of arbitrary given length for encoding information in telecommunication systems.