Evaluating the Randomness of Chaotic Binary Sequences Via a Novel Period Detection Algorithm

Abstract

When chaotic systems are applied to stream ciphers, chaotic real-valued sequences generally need to be converted into binary sequences with the purpose of encrypting data. However, the performance of binary sequences will be degraded under the joint influence of round-off and quantization errors. In this case, the randomness of some chaotic binary sequences may be weakened in a local range. Taking advantage of parallel computing, a fast period detection algorithm is designed to locate all local “periodicities” contained in chaotic binary sequences quickly and accurately. This algorithm evaluates the randomness of a chaotic binary sequence from a new perspective of periodicity which enriches the randomness test methods for binary sequences. Different logistic binary sequences are analyzed to demonstrate the effectiveness and practicability of the proposed algorithm.