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

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.

Stochastic Computing Implementation of Chaotic Systems

“…Notice, in any case, that the energy consumption needed to generate the random bits is not taken into account, since they can be generated in multiple ways. For instance, a 64-bit Mersenne RNG needs a lot of power to perform all the calculations that lead to the pseudorandom sequence of bits, but if we can use memristors for this task [41][42][43] this energy is drastically reduced, as well as the needed area. Additionally, a final ASIC implementation of the design could utilize some improvements, as extensively discussed in [33], that allow for exponential improvement of consumption.…”

“…It is worth noticing that the RNG is actually responsible of a large part of the total energy consumption, due to the large number of computations needed by the algorithm. This energy consumption could be addressed in the future by using memristors to generate the random bits, as proposed in [41][42][43].…”

Stochastic Computing Implementation of Chaotic Systems

“…Notice, in any case, that the energy consumption needed to generate the random bits is not taken into account, since they can be generated in multiple ways. For instance, a 64-bit Mersenne RNG needs a lot of power to perform all the calculations that lead to the pseudo-random sequence of bits, but if we can use memristors for this task [41][42][43] this energy is drastically reduced, as well as the needed area. Additionally, a final ASIC implementation of the design could utilize some improvements, as extensively discussed in [33], that allow for exponential improvement of consumption.…”

Characterization and Identification of Dependence in EMG Signals from Action Potentials and Random Firing Patterns

“…Taking into account the role of second-order stationary auto similarity and taking the autocorrelation function r k k ( ) ( ) / J V 2 , we have equation ( 1) [22].…”

“…Since the second moment of the DWT detail coefficients follows a power law with an exponent 2H -1, the Hurst parameter can be estimated with equation (5), where µ j is the arithmetic mean of the squared magnitude of the detail coefficients at octave j and C is a constant. The plot of y j vs j is known as the (second order) log-scale diagram [22].…”