Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

Pseudorandom Number Generators

In this chapter, the author considers existing methods and means of forming pseudo-random sequences of numbers and also are described the main characteristics of random and pseudorandom sequences of numbers. The main theoretical aspects of the construction of pseudo-random number generators are considered. Classification of pseudorandom number generators is presented. The structures and models of the most popular pseudo-random number generators are considered, the main characteristics of generators that affect the quality of the formation of pseudorandom bit sequences are described. The models of the basic mathematical generators of pseudo-random numbers are considered, and also the principles of building hardware generators are presented.

Pseudorandom Number Generators Based on Cellular Automata With the Hexagonal Coverage

The seventh chapter describes approaches to constructing pseudo-random number generators based on cellular automata with a hexagonal coating. Several variants of cellular automata with hexagonal coating are considered. Asynchronous cellular automata with hexagonal coating are used. To simulate such cellular automata with software, a hexagonal coating was formed using an orthogonal coating. At the same time, all odd lines shifted to the cell floor to the right or to the left. The neighborhood of each cell contains six neighboring cells that have one common side with one cell of neighborhood. The chapter considers the behavior of cellular automata for different sizes and different initial settings. The behavior of cellular automata with various local functions is described, as well as the behavior of the cellular automaton with an additional bit inverting the state of the cell in each time step of functioning.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata

The fourth chapter deals with the use of asynchronous cellular automata for constructing high-quality pseudo-random number generators. A model of such a generator is proposed. Asynchronous cellular automata are constructed using the neighborhood of von Neumann and Moore. Each cell of such an asynchronous cellular state can be in two states (information and active states). There is only one active cell at each time step in an asynchronous cellular automaton. The cell performs local functions only when it is active. At each time step, the active cell transmits its active state to one of the neighborhood cells. An algorithm for the operation of a pseudo-random number generator based on an asynchronous cellular automaton is described, as well as an algorithm for working a cell. The hardware implementation of such a generator is proposed. Several variants of cell construction are considered.

Pseudorandom Number Generators Based on Cellular Automata

In this chapter, the author considers the main theoretical solutions for the creation of pseudo-random number generators based on one-dimensional cellular automata. A Wolfram generator is described on the basis of rule 30. The main characteristics of the Wolfram generator is presented. The analysis of hybrid pseudo-random number generators based on cellular automata is carried out. Models of such generators and their realization with various forms of neighborhoods are presented. Also in the chapter is presented the analysis of the basic structures and characteristics of pseudo-random number generators using additional sources of pseudo-random numbers. As such additional sources the LFSR is used.

Fundamental of Cellular Automata Theory

In this chapter, the author reviews the main historical aspects of the development of cellular automata. The basic structures of cellular automata are described. The classification of cellular automata is considered. A definition of a one-dimensional cellular automaton is given and the basic rules for one-dimensional cellular automata are described that allow the implementation of pseudo-random number generators. One-dimensional cellular automata with shift registers with linear feedback are compared. Synchronous two-dimensional cellular automata are considered, as well as their behavior for various using local functions. An analysis of the functioning of synchronous cellular automata for the neighborhoods of von Neumann and Moore is carried out. A lot of attention is paid to asynchronous cellular automata. The necessary definitions and rules for the behavior of asynchronous cellular automata are given.

Analysis of the Quality of Pseudorandom Number Generators Based on Cellular Automata

The eighth chapter describes the studies of the presented generators using the ENT and NIST tests. For a complete description of the experiment, different initial settings were used. Tests were conducted for different sizes and for a different number of cells, which initially had a logical “1” states. Also, bit sequences of different lengths are formed. The results presented in this chapter indicate optimal sizes and optimal initial settings of cells of the cellular automaton. Generators are described on the basis of cellular automata with a Moore neighborhood. The obtained results are compared for all the pseudo-random number generators described earlier. Also, the generators were examined using graphical tests. The results of the graphical tests for the generators described in this manuscript are presented in this chapter. Test results are presented in tabular form and in graphical form.

The Pseudorandom Number Generators Based on Cellular Automata With Inhomogeneous Cells

The fifth chapter deals with the use of hybrid cellular automata for constructing high-quality pseudo-random number generators. A hybrid cellular automaton consists of homogeneous cells and a small number of inhomogeneous cells. Inhomogeneous cells perform a local function that differs from local functions that homogeneous cells realize. The location of inhomogeneous cells and the main cell is chosen in advance. The output of the main cell is the output of a pseudo-random number generator. A hardware implementation of a pseudo-random number generator based on hybrid cellular automata is described. The local function that an inhomogeneous cell realizes is the majority function. The principles of constructing a pseudo-random number generator based on cellular automata with inhomogeneous neighborhoods are described. In such cellular automata, inhomogeneous cells have a neighborhood whose shape differs from that of neighborhoods of homogeneous cells.