Influence of Neighborhood Forms on the Quality of Pseudorandom Number Generators' Work Based on Cellular Automata

2020 ◽  
pp. 43-78
Author(s):  
Sergii Bilan
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Initial Conditions ◽  
Experimental Studies ◽  
High Quality ◽  
Random Number Generators ◽  
Optimal Dimension ◽  
Pseudo Random Number ◽  
Nist Tests

The chapter analyzes modern methods for constructing pseudo-random number generators based on cellular automata. Also analyzes the influence of neighborhood forms on the evolution of the functioning of cellular automata, as well as on the quality of the formation of pseudo-random bit sequences. Based on the use of various forms of the neighborhood for the XOR function, the quality of generators was analyzed using graphical tests and NIST tests. As a result of experimental studies, the optimal dimension of cellular automata and the number of heterogeneous cells were determined, which make it possible to obtain a high-quality pseudo-random bit sequence. The obtained results allowed to formulate a method for constructing high-quality pseudo-random number generators based on cellular automata, as well as to determine the necessary initial conditions for generators. The proposed generators allow to increase the length of the repetition period of a pseudo-random bit sequence.

A list of tri-state cellular automata which are potential pseudo-random number generators

2018 ◽  
Vol 29 (09) ◽  
pp. 1850088 ◽  
Author(s):  
Kamalika Bhattacharjee ◽  
Sukanta Das
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generators ◽  
Rule Space ◽  
Pseudo Random Number

This paper explores [Formula: see text]-neighborhood [Formula: see text]-state cellular automata (CAs) to find a list of potential pseudo-random number generators (PRNGs). As the rule-space is huge ([Formula: see text]), we have taken two greedy strategies to select the initial set of rules. These CAs are analyzed theoretically and empirically to find the CAs with consistently good randomness properties. Finally, we have listed [Formula: see text] good CAs which qualify as potential PRNGs.

Pseudorandom Number Generators

2017 ◽  
pp. 1-25
Keyword(s):  
Random Number ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Random Number Generators ◽  
Random Sequences ◽  
Pseudorandom Number Generators ◽  
Pseudo Random Number

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.

Maximal length cellular automata in GF(q) and pseudo-random number generation

2020 ◽  
Vol 31 (03) ◽  
pp. 2050037
Author(s):  
Sumit Adak ◽  
Kamalika Bhattacharjee ◽  
Sukanta Das
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Maximal Length ◽  
Number Generator ◽  
Greedy Strategy ◽  
Pseudo Random Number ◽  
Pseudo Random Number Generator

This work explores the randomness quality of maximal length cellular automata (CAs) in GF([Formula: see text]), where [Formula: see text]. A greedy strategy is chosen to select the candidate CAs which satisfy unpredictability criterion essential for a good pseudo-random number generator (PRNG). Then, performance of these CAs as PRNGs is empirically analyzed by using Diehard battery of tests. It is observed that, up to GF(11), increase in [Formula: see text] improves randomness quality of the CAs, but after that, it saturates. Finally, we propose an implementable design of a good PRNG based on a 13-cell maximal length cellular automaton over GF(11) which can compete with the existing well-known PRNGs.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata

2017 ◽  
pp. 66-108
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Number ◽  
Random Number Generator ◽  
Active Cell ◽  
Time Step ◽  
Random Number Generators ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Pseudo Random Number

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

2017 ◽  
pp. 52-65
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Random Number Generators ◽  
One Dimensional ◽  
Pseudorandom Number Generators ◽  
Pseudo Random Number ◽  
The Creation

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.

The lattice structure of pseudo-random number generators

1983 ◽  
Vol 389 (1796) ◽  
pp. 197-204 ◽  
Keyword(s):  
Random Number ◽  
Lattice Structure ◽  
Random Number Generators ◽  
Pseudo Random Number

The pairs, triples, etc. from most congruential pseudo-random number generators are known to lie on a lattice, and the ‘uniformity’ of these lattices is reflected in the quality of the output of the generator. Various characteristics of the lattices have been proposed as summaries of the quality of a generator, including the so-called lattice and spectral tests. This paper exploits the concept of polar lattices to show that these charac­terizations are essentially equivalent, and that they can be found to an approximation sufficient for assessing the quality of the generator without extensive searches. Checking generators is important, for many of those provided on small computers are inadequate for serious work.

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