Improving the security of chaotic encryption by using a simple modulating method

In recent years, synchronization of chaotic systems has aroused much interest due to its potential application to secure communications. However, it is found by Perez and Cerdeira that an intruder, without the knowledge of the parameters of the system or even of the nonlinear system itself, may extract the messages from the carrier signal by producing a return map where the dynamics is attracted to an almost 1D set. To eliminate the weakness, in this letter, a simple but efficient method for synchronizing chaotic systems by modulating the transmitted signal with an appropriately choosing scalar signal is proposed. It turns out that this modulating strategy not only preserves all appropriate information required for synchronizing chaotic systems but also destroys the possibility of the phase space reconstruction of the sender dynamics such as a return map.