We show that the synchronization of chaotic systems can be achieved by using the observer design techniques which are widely used in the control of dynamical systems. We show that local synchronization is possible under relatively mild conditions and global synchronization is possible if the chaotic system can be transformed into a special form. We also give some examples including the Lorenz, the Rössler systems, and Chua's oscillator which are known to exhibit chaotic behavior, and show that in these systems synchronization by using observers is possible.

We cryptanalyze Fridrich's chaotic image encryption algorithm. We show that the algebraic weaknesses of the algorithm make it vulnerable against chosen-ciphertext attacks. We propose an attack that reveals the secret permutation that is used to shuffle the pixels of a round input. We demonstrate the effectiveness of our attack with examples and simulation results. We also show that our proposed attack can be generalized to other well-known chaotic image encryption algorithms.

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This paper investigates the weaknesses of cryptosystems that use observer based synchronized chaotic systems. It is shown that known plaintext and chosen plaintext attacks can successfully be launched against such cryptosystems to recover the system parameters and subsequently eavesdrop on the message transmission. The methods employed rely only on the basic mathematical relations that exist between the output sequence and the message sequence of the transmitter system and require very less computations.