The complexity of binary sequences using logistic chaotic maps

摘要

The information sources using logistic maps have been studied in this article. We use a particular symmetric binary function to generate the binary sequences due to the generating partition of the logistic maps, which can reflect the dynamics of chaotic real-valued sequences. Using this binary function, we will establish a binary description of the logistic maps, and prove that this description is equivalent with the logistic maps. The probability of all the possible binary sequences generated by this symmetric binary function has been calculated according to this description. Furthermore, the cryptographic complexity of these binary sequences is evaluated theoretically and experimentally, including the correlation functions, the linear complexity, the nonlinear complexity, the Lempel-Ziv complexity and the approximate entropy. Such results show that the logistic binary sequences have good properties of cryptography. (c) 2015 Wiley Periodicals, Inc. Complexity 21: 121-129, 2016