Study on the Pseudorandomness and Complexity of Chaotic Binary Sequences

The pseudorandomness and complexity of binary sequences generated by typical Lorenz chaotic system and Chebyshev map are analyzed and discussed in this paper. The binary sequences are obtained from the chaotic real-valued sequences generated by chaotic systems by using T. Kohda binary quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel-Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudorandomness and complexity of binary sequences. The experimental results show the finite binary sequences generated by chaotic system approach the random sequences of Lempel-Ziv level. They are of good properties in the pseudorandomness, complexity and nonperiodicity. However, their pseudorandomness and complexity don´t enhance with the sequence length increased, but degrade in the criterion of approximate entropy. Furthermore, the results of data statistics analysis show that the Lorenz system is better than Chebyshev map as the source of pseudorandomness.