Study of the robustness of an enhanced CSK system by using the Extended Kalman Filter

This paper focuses on the security of an enhanced CSK system and proposes the study of its robustness based on the identification of chaotic map parameters using the Extended Kalman Filter. Chaotic sequences are used to cipher a message for which the map's initial conditions and parameters are part of the secret key. We therefore estimate these parameters using only sequences generated by this map. The estimation complexity is increased by making a multiplicative shift of sequence terms so that no transmission of consecutive terms occurs. The impact of the shift on the identification process is especially studied by scanning the basin of the chaotic attractor of a two-dimensional cubic map and by gradually increasing the shift until the EKF algorithm diverges. Multiple simulations have been done considering three parameters and various initial condition sets. In all cases, we obtain a necessary minimum shift value from which it is not possible to estimate the parameters. This means that the sequence from which the ciphertext results cannot be reconstructed and the message cannot be deciphered.