Improving security of a chaotic encryption approach

E. Alvarez et al. presented a new chaotic encryption approach recently. But soon G. Alvarez et al. broke it with four cryptanalytic methods and found some other weaknesses. In this Letter we point out why the original scheme is so vulnerable to the proposed four attacks. The chief reasons are two essential defects existing in the original scheme. Based on such a fact, we present an improved encryption scheme to obtain higher security. The cryptographic properties of the improved scheme are studied theoretically and experimentally in detail.