Discovering Chaos-Based Communications by Recurrence Quantification and Quantified Return Map Analyses

Many studies show the possibility of transmitting messages in a protected and covert manner using a noise-like chaotic waveform as a carrier. Among popular chaotic communication system (CCS) types, one may distinguish chaotic shift keying (CSK) and parameter modulation (PM) which are based on the manipulation of the transmitting chaotic oscillators. With the development of direct digital synthesis (DDS), it became possible to modulate chaotic signals by varying the properties of the numerical method used in digital chaos generators. The symmetry coefficient modulation (SCM) is such an approach potentially able to provide higher secrecy. However, the actual security of chaos-based communications is still a questionable and controversial feature. To quantitatively evaluate the CCS security level, a certain numerical metric reflecting the difficulty of breaking a communication channel is needed. Return maps are commonly used to attack chaotic communication systems, but the standard algorithm does not involve any kind of quantification. In this study, we propose a new method for estimating the differences between two return maps based on a two-dimensional (2D) histogram. Then, we investigate the resistance of chaotic shift keying, parameter modulation, and SCM communication schemes against three types of attacks: the proposed quantified return map analysis (QRMA), recurrence quantification analysis (RQA), which had not been previously reported for attacking chaos-based communications, and the classical approach based on spectral analysis. In our experiments we managed to recover the plain binary message from the waveform in the channel when transmitted using all three chaos-based messaging techniques; among them, SCM appeared to be the most secure communication scheme. The proposed QRMA turned out to be the most efficient technique for message recovery: the sensitivity of the QRMA appeared to be 2-5 times higher than that in the case of spectral analysis. The proposed QRMA method can be efficiently used for evaluating the difficulty of hacking chaos-based communication systems. Moreover, it is suitable for the evaluation of any other secure data transmission channel.