Breaking a chaos-based secure communication scheme designed by an improved modulation method

Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919-24] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129-34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367-73], and Álvarez et al. [Álvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/0406065] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu-Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.