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

Recently Bu and Wang [1] 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. [2], Wu et al. [3], and Álvarez et al. [4] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. [3] by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed in [3] 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 scheme proposed in [3] is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.