Performance evaluation of chaotic random numbers generated from responses of integer logistic maps

Abstract

One of the engineering applications of chaotic nonlinear dynamical systems is a pseudorandom number generator. Pseudorandom numbers generated from chaotic dynamical systems are called chaotic random numbers. A logistic map which exhibits a chaotic response can be used as such a chaotic random number. However, an important issue exists when we use such dynamical systems as a pseudorandom number generator by a digital computer: when the chaotic response of a logistic map is reproduced numerically, the number of iterations that the chaotic response is sustained depends on the precision of the numerical calculation, because the precision of the numerical calculation affects the size of the numerical error. In this paper, we extended the logistic map to an integer logistic map to reduce such numerical errors. We investigated the performance of chaotic random numbers obtained from the integer logistic map with varying numerical precisions and transforming them into binary random numbers. We then used NIST SP 800-22 to evaluate the performance of the random numbers. The results show that a numerical precision of 20 orders of magnitude or more is desirable to the generation of a well-performing chaotic random numbers from the response of the integer logistic map.