Development of a Pseudo-Random Number Generator Using the Logistic Map

Alexey Shekhanov, Irina Polyakova

Abstract


The development of pseudo-random number generators (PRNGs) is a relevant problem today, as PRNGs are widely used in various fields, ranging from scientific research, simulation, and statistical analysis to cryptography, financial systems, and the gaming industry. The quality of such generators directly affects the reliability of computations, the security of information systems, and the validity of simulation results. The main objective of this work is to develop a pseudo-random number generator that provides a high degree of randomness in the generated sequences. This study proposes a method for constructing a PRNG based on the logistic map, which is a nonlinear dynamical system exhibiting chaotic behavior. To evaluate the quality of the generated sequences, an entropy-based testing method using a sliding window is developed, allowing the assessment of randomness in binary sequences. The proposed generator is compared with a linear congruential generator and the Mersenne Twister. Testing is performed using entropy-based analysis and histogram distribution evaluation. The obtained results are visualized using graphs and diagrams, enabling a comparative analysis of the characteristics of the studied generators.


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References


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