Pseudo-randomness and complexity of binary sequences generated by the chaotic system

The pseudo-randomness and complexity of binary sequences generated by chaotic systems are investigated in this paper. These chaotic binary sequences can have the same pseudo-randomness and complexity as the chaotic real sequences that are transformed into them by the use of Kohda’s quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel–Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudo-randomness and complexity of these binary sequences. The experimental results show the finite binary sequences generated by the chaotic systems have good properties with the pseudo-randomness and complexity of sequences. However, the pseudo-randomness and complexity of sequence are not added with the increase of sequence length. On the contrary, they steadily decrease with the increase of sequence length in the criterion of approximate entropy and statistical test. The constraint of computational precision is a fundamental reason resulting in the problem. So only the shorter binary sequences generated by the chaotic systems are suitable for modern cryptography without other way of adding sequence complexity in the existing computer system.