Abstract : The work deals with the synthesis and the cryptanalysis of chaos-based encryption schemes. These schemes involve, at the transmitter side, nonlinear dynamic systems exhibiting chaotic behavior. The complex sequence thus generated is used to mask an information. Several encryption schemes are studied : the chaotic switching, the parameter modulation and the message-embedding, mostly in the case of chaotic discrete-time systems. For these schemes, the information reconstruction requires the synchronization between the transmitter and the receiver. An observer plays the role of the receiver.
First, the connection between chaos-based encryption and standard encryption is established.
In the case of chaotic switching, we propose, for the decryption, a systematic method to design polytopic observer taking into account the specificity of chaos. In the parameter modulation, at the transmitter side, the parameters are modulated by the plaintext. To achieve the synchronization, a polytopic adaptive observer ensuring the joint state and modulated parameter estimation is proposed.
Finally, the cryptanalysis of the message-embedding scheme is performed. We consider chaotic discrete-time cryptosystems involving only polynomial nonlinearities which include a large number of usual chaotic systems. In this scheme, the security is based on the system parameters expected to act as the secret key. A general formalism based on the identifiability concept is proposed to test the parameters reconstructibility. The different identifiability definitions are summarized and the approaches to test the parametric identifiability are presented. This formalism is applied to usual chaotic message-embedding schemes in order to test their security.