CRYPTANALYZING CHAOTIC SECURE COMMUNICATIONS USING RETURN MAPS

In chaotic secure communications, message signals are scrambled by cha otic dynamical systems. The interaction between the message signals an d the chaotic systems results in changes of different kinds of return maps. In this paper, we use return map based methods to unmask some ch aotic secure communication systems; namely, chaotic shift keying (chao tic switching), chaotic parameter modulation and non-autonomous chaoti c modulation. These methods are used without knowing the accurate know ledge of chaotic transmitters and without reconstructing the dynamics or identifying the parameters of chaotic transmitters. These methods a lso provide a criterion of deciding whether a chaotic secure communica tion scheme is secure or not. The effects of message signals on the ch anges of different return maps are studied. Fuzzy membership functions are used to characterize different kinds of changes of return maps. F uzzy logic rules are used to extract message signals from the transmit ted signal. The computer experimental results are provided. The result s in this paper show that the security of chaotic secure communication not only depends on the complexity of the chaotic system but also dep ends on the way the message is scrambled. A more complex chaotic syste m is not necessary to provide a higher degree of security if the trans mitted signal has simple and concentrated return maps. We also provide examples to show that a chaotic system with complicated return maps c an achieve a higher degree of security to the attacks presented in thi s paper. (C) 1998 Elsevier Science B.V.