Irregularly Decimated Chaotic Map(s) for Binary Digits Generations

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a generating subsystem, where each subsystem is based on a single chaotic map. This chaotic map is presented as a 1-D piecewise chaotic map related to the chaotic logistic map. We conduct an analysis of the dynamical behavior of the proposed map to integrate it as a component in the proposed generators subsystems. The output bits of these keystream generators are produced by applying a threshold function to convert the floating-point iterates of the irregularly decimated map into a binary form. The generated keystream bits are demonstrated to exhibit high level of security, long period length, high linear complexity measure and random-like properties at given certain parameter values. Standard statistical tests on the proposed generators, as well as other keystream generators, are performed and compared.