Abstract
A general methodology for designing chaotic and hyperchaotic cryptosystems has been developed using the control systems theory. Grassi et al. proposed a nonlinear-observer-based decrypter for the state of an encrypter. If we can design the decrypter without the knowledge of the parameters of the encrypter, the chaos-based secure communication systems are not secure. In this paper, we have designed an observer-based chaotic communication system, which allows us to assign the relative degree and the zeros of its encrypter system. Moreover, under some conditions, we have designed an adaptive decrypter using the adaptive parameter adjustment law based on a Riccati equation when the transfer function of the encrypter is of minimal-phase type. The simulations via MATLAB/Simulink suggest that the encrypter dynamics should be designed such that its relative degree is more than 2 and its zeros are unstable so as to fail to synchronize the cryptosystem for the intruders.
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