Time variant chaos encryption

Chaos synchronization was extensively studied the last two decades leading to several synchronization and modulation methods. The main aim of the research was to develop wide bandwidth, spread spectrum like and secure communication systems. Taking into account the high sensitivity of all synchronization and modulation methods to channel noise and parameter mismatch, digital implementations aiming at chaos encryption were preferred lately. Several authors developed, in their studies, different encryption approaches, most of them being successfully cryptanalized, due to the direct influence of the constant system parameters onto their nonlinear dynamics.

The present contribution proposes a time variant approach to chaotic encryption. The proposed method is based on chaos synchronization and plaintext modulation onto the chaotic dynamics of the emitter. In order to improve communication confidentiality, one or several parameters of the emitter system are modulated with pseudo-random digital sequences, thus drastically increasing the length of the encryption key. At the decryption end, the corresponding receiver parameters are also time variant. Exact knowledge of the emitter pseudo-random digital sequence shape and timing are necessary for correct decryption of the cipher-text. It is also worth noting the importance of the modulating sequence amplitude or dynamic range due to its influence on the instantaneous value of the emitter sensitivity and, by consequence, its capacity in hiding the transmitted plaintext. Thus a parametric analysis is presented in order to find a valid parameter range for possible modulation. For the digital implementation of the proposed encryption/decryption systems, although input and output are fixed point, the internal structure of both emitter and receiver must be implemented in floating point to obtain the closest behavior with the chaotic prototype that has analog valued state variables.

Both analog and discrete examples for the encryption/decryption system are analyzed. Presented simulations confirm the theoretical results and highlight the great improvement of the communication security by the proposed approach. The concluding remarks point towards some directions in further research.