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. Martin, A. Plastino, O.A. Rosso, Phys. Lett. A 311 (2003) 126, P.W. Lamberti, M.T. Martin, 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.

[1]  Osvaldo A. Rosso,et al.  Statistical complexity and disequilibrium , 2003 .

[2]  Silvano Donati,et al.  Introduction to the feature section on optical chaos and applications to cryptography , 2002 .

[3]  Karsten Keller,et al.  Symbolic Analysis of High-Dimensional Time Series , 2003, Int. J. Bifurc. Chaos.

[4]  Laurent Larger,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2005, Nature.

[5]  M Garavaglia,et al.  Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[7]  Mathieu Sinn,et al.  Ordinal analysis of time series , 2005 .

[8]  C. Masoller,et al.  Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme , 2002, IEEE Photonics Technology Letters.

[9]  Osvaldo A. Rosso,et al.  Random number generators and causality , 2006 .

[10]  R. Lang,et al.  External optical feedback effects on semiconductor injection laser properties , 1980 .

[11]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[12]  O. A. Rosso,et al.  EEG analysis using wavelet-based information tools , 2006, Journal of Neuroscience Methods.

[13]  Osvaldo A. Rosso,et al.  Generalized statistical complexity measures: Geometrical and analytical properties , 2006 .

[14]  V. M. Kenkre Statistical mechanical considerations in the theory of the spread of the Hantavirus , 2005 .

[15]  Osvaldo A. Rosso,et al.  Intensive entropic non-triviality measure , 2004 .

[16]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[17]  W. Wootters Statistical distance and Hilbert space , 1981 .