Encryption test of pseudo-aleatory messages embedded on chaotic laser signals: An information theory approach

In this Letter, we make use of two information-theory based indicators to measure the goodness of two encryption schemes commonly used within the context of chaotic communications. In particular, we have shown that the computation of the normalized Shannon entropy and the MPR-Statistical Complexity measure [M.T. Martín, A. Plastino, O.A. Rosso, Phys. Lett. A 311 (2003) 126, P.W. Lamberti, M.T. Martín, A. Plastino, O.A. Rosso, Physica A 334 (2004) 119] for different chaotic laser signals can lead to statistically significant criteria to assess the quality of several encryption techniques. The proposed measures allow, in some cases, to detect the presence of a message embedded within a chaotic carrier. They also reveal that the Chaos Modulation scheme is more reliable from the statistical point of view, when compared with the Chaos Shift Keying.