Methods and Models for the Formation of Pseudo-Random Number Sequences Based on Cellular Automata

Pseudorandom Number Generators Based On One-Dimensional Cellular Automata

One-dimensional cellular automata are represented by one row or one column of cells. Such CA are called elementary cellular automata (ECA). Each cell contains a neighborhood of cells. A neighborhood is represented by a set of cells on both sides of each cell for which the neighborhood is considered (Wolfram, 1986a; Wolfram, 2002; Bilan, 2017). At each time step, each cell performs a certain logical function, the arguments of which are the signals of the state of the cells of the neighborhood. A cellular automaton with new conditions is being built. After a certain number of time steps, a two-dimensional picture is formed, which is called the evolution of the CA. The choice of LSF for each CA cell indicates the number of steps at which CA states do not repeat. If we take off the signals from the outputs of the cells and form a bit sequence from them, then we can talk about a pseudo-random bit sequence. From this point of view, a one-dimensional CA can be considered as a PRNG.