Random Number Generator with Long-Range Dependence and Multifractal Behavior Based on Memristor

María Téllez,Cesar Hernández,Hans López,Johan Mejía

doi:10.3390/electronics9101607

Abstract

Random number generators are used in areas such as encryption and system modeling, where some of these exhibit fractal behaviors. For this reason, it is interesting to make use of the memristor characteristics for the random number generation. Accordingly, the objective of this article is to evaluate the performance of a chaotic memristive system as a random number generator with fractal behavior and long-range dependence. To achieve the above, modeling memristor and its corresponding chaotic systems is performed, from which a random number generator is constructed. Subsequently, the Hurst parameter for the detection of long-range dependence is estimated and a fractal analysis of the synthesized data is performed. Finally, a comparison between the model proposed in the research and the β-MWM algorithm is made. The results obtained show that the data synthesized from the proposed generator have a variable Hurst parameter and both monofractal and multifractal behavior. The main contribution of this research is the proposal of a new model for the synthesis of traces with long-range dependence and fractal behavior based on the non-linearity of the memristor.

Highlights

Random number generators (RNGs) are currently used to encrypt information and model natural processes
A random number generator with long range dependence was developed from different input chaotic signals, allowing the variation of H through the parameters of the RNG
Another aspect to consider is that when discarding combinations that had a deterministic behavior or without long range dependence (LRD) it was not possible to model the Hurst parameter through a mathematical expression, and parameterize the generator

Summary

Introduction

Random number generators (RNGs) are currently used to encrypt information and model natural processes. Complex encryption processes are required to decipher the information only through the encryption key In most cases, this encryption key is a combination of a data sequence with the information to be transmitted [1]. The inverse transformation method solves the problem of the type of distribution, it only allows the generation of independent random numbers and, it is not suitable for modeling natural processes that are highly correlated and that show dependencies between the different scales; for example: detection of climate zones [3], market behavior [4] and video traffic in Moving Picture Experts Group 4 (MPEG-4) [5]

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Conclusion