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Zbl 1222.94037
Orue, A.B.; Alvarez, G.; Pastor, G.; Romera, M.; Montoya, F.; Li, Shujun
A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 11, 3471-3483 (2010). ISSN 1007-5704

Summary: We describe 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 $z(t)$.

MSC 2000:: *94A60 Cryptography
37N35 Dynamical systems in control
37D45 Strange attractors, chaotic dynamics

Keywords: chaos-based cryptography; Lorenz's attractor; Chua's attractor; cryptanalysis; parameter determination; projective chaos synchronization

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