Return-Map Cryptanalysis Revisited

Abstract

As a powerful cryptanalysis tool, the scheme of return-map attack can be used to extract secret messages masked by chaos in secure communication schemes. Recently, a simple defensive mechanism was presented to enhance the security of chaotic parameter modulation schemes against return-map attacks. Two techniques are combined in the proposed defensive mechanism: multistep parameter modulation and alternative driving of two different transmitter variables. This paper re-studies the security of this proposed defensive mechanism against return-map attacks, and points out that the security was much over-estimated by the authors for both ciphertext-only attack and known/chosen-plaintext attacks. It is found that a deterministic relationship exists between the shape of the return map and the modulated parameter, and that such a relationship can be used to dramatically enhance the return-map attack thereby making it easy to break the proposed mechanism.

Controlled Parameter Modulations in Secure Digital Signal Transmissions

“…Because of this increase in number of strips in each segment, it was claimed in our earlier paper [Palaniyandi & Lakshmanan, 2001] that it would be difficult to unmask the message from the return map. However, Li et al [Li et al, 2006] have very recently pointed out that the multistep parameter modulation suggested by us may not be so secure as was expected for smaller modulation steps. These authors have also noted that there exists a deterministic relationship between the positions of the 2n strips of a segment and the 2n different values of the modulation parameter 'b', and this relationship will reduce the attack complexity of the return map.…”

“…Thus, it is not possible to extract the original message from the return map unless one knows the rules by which the values of b are switched for transmitting the digital information. As in the case of singlestep parameter modulation, if one assumes that the strips closer to the origin corresponds to '0' bit and the strips away from the origin corresponds to '1' bit or vice versa [Li et al, 2006], then it is possible to obtain two different messages as shown in Fig. 3.…”

“…For example, we have proposed a method called multistep parameter modulation to complicate the patterns in the return map so that the reconstruction of the message by an eavesdropper is almost impossible [Palaniyandi & Lakshmanan, 2001]. However, Li et al [Li et al, 2006] have very recently pointed out that the multistep parameter modulation suggested by us may not be so secure as was expected for smaller modulation steps (n). These authors have also pointed out that the multistep parameter modulation technique is secure only if n > 50, instead of n > 17 expected in our analysis.…”

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

“…Encryption techniques based on chaotic masking or chaotic switching can be circumvented by constructing some return maps of the master system of an analog chaotic cryptosystem [92], as it has been shown in [65,66]. Problem 4.…”

Time Scaling of Chaotic Systems: Application to Secure Communications

“…The receiver determines the bit value according to the success or failure of its synchronization attempt. Many cryptanalysis tools have been developed in order to evaluate the security of these schemes and it has been shown that the realization of secure communications based on chaotic encryption is still a quite difficult and challenging task [Li et al, 2006]. In this paper we study classes of dynamical systems characterized by having the same phase diagram, but a different time response.…”