Abstract
This paper describes a method about how to determine parameters of some double-scroll chaotic systems, including the Lorenz system and the Chua’s circuit, from one of its variables. The geometric properties of the system are exploited firstly to reduce the parameter search space. Then, a synchronization-based approach, with the help of the same geometric properties as coincidence criteria, is implemented to determine the parameter values with the wanted accuracy. The method is not affected by a moderate amount of noise in the waveform. As an example of its effectiveness, the method is applied to cryptanalyze two two-channel chaotic cryptosystems, figuring out how the secret keys can be directly derived from the driving signal z(t).