Software and Hardware Implementation Sensitivity of Chaotic Systems and Impact on Encryption Applications

This paper discusses the implementation sensitivity of chaotic systems added to their widely discussed sensitivities to initial conditions and parameter variation. This sensitivity can cause mismatches in some applications, which require an exact duplication of the system, e.g., chaos-based cryptography, synchronization and communication. Specifically, different implementation cases of three discretized jerk-based chaotic systems and a discrete-time logistic map are presented corresponding to different orders of additions and multiplications. The cases exhibit roughly similar attractor shapes, bifurcation behavior and Lyapunov exponents. However, mismatches between the time series corresponding to these cases in software double-precision, single-precision floating-point and hardware fixed-point implementations are reported. The number of time units after which the mismatch starts to become noticeable, and the effects of the discretization step and precision are discussed. Experimental results on Artix-7 XC7A100T FPGA and oscilloscope validate the presence of mismatch reported through simulations. The wrong decryption effect of this mismatch is demonstrated for a software image encryption application, where one case is used for encryption and the other(s) for decryption. Pseudo-Random Number Generation and image encryption application using the mismatch signal as a chaotic generator are proposed and show good results using several well-established performance metrics.