Delay-introducing method to improve the dynamical degradation of a digital chaotic map

Abstract

In this paper, a new delay-introducing method is proposed to improve the dynamical degradation of a digital chaotic map. The delayed state is introduced to construct a function that is used to replace the control parameter of an original chaotic map. The numerical experimental results indicate that the delayed digital chaotic maps are more complex, have larger periods, and do not completely disrupt the phase space of an original chaotic map, indicating that our method is effective and can be competitive with other proposed methods. The most significant advantage of this method is that external systems are no longer required, making it easier to implement than the other popular methods. We also propose a type of pseudorandom bit generator (PRBG) based on the delay-introducing method as a simple application.