The novelty of this work is the statistical perspective of the cryptanalyst being able to perform a chosen plaintext attack on a private communication scheme involving chaos-based algorithms. The attacker finds himself in the position of analyzing the pseudo-random matrix that was used for encryption. The contribution is done in the context of the well-known fields of secret-key cryptology and that of wavelet packet decomposition of images. The analysis is exemplified on the thoroughly investigated, in the existing literature, simplest chaotic system, the logistic map. Kolmogorov-Smirnov tests, histogram testing, autocorrelation functions and nonlinear singular value decomposition are used. In addition, a new enciphering wavelet-based algorithm is proposed and analyzed.
In the context of a hybrid continuous-discrete time chaos-based secret communication scheme, the present work replaces the non-linear element of a known jerk-type chaotic system, with a LED. The circuit is simulated in Matlab-Simulink and its behavior analyzed when switching the control parameter - the value of one of the resistors in the scheme. The cases illustrated are relevant for emphasizing the route towards randomness. This is achieved through period-doubling starting from the initial period of the signal corresponding to the LED’s output power, which depends on the value of the control parameter. This paper also presents an experimental implementation of the proposed modified Sprott’s jerk-type circuit, as well as a comparison between simulation and empirical results. Qualitative and quantitative interpretations of bifurcation diagrams and Lyapunov exponents for the two situations are to be compared in a future research.
The paper presents a steganographic method which hides a secret message in a video flow. The secret message represents the result of a chaos-based encryption scheme. One of the flaws which make the algorithm unpractical for real-time applications is that, while the elements of the plain-message are represented using 8 bits (ASCII characters) the corresponding encrypted values need to be represented using 16 bits. Since the pixels of a typical image are represented using 24 bits (8 bits for each color component), each encrypted character fits in only one pixel. Moreover, since the resolution of today’s video materials is very large, the pixel previously established to carry in its evolution the hidden content will not be obvious to unaware spectators, but only to the one which knows its coordinates. In addition to the steganographic procedure, the work presents preliminary results on the degree of pseudo-randomness of video flows. The study is based upon the idea behind Lyapunov exponents. The evolution of two pixels which initially differ only by the minimum possible value (the color representation’s resolution) is followed for a large number of video frames. The distance between such points, for pseudo-random behavior, is known to evolve over time in a Gaussian manner. A Kolmogorov-Smirnov statistic is computed and illustrated in order to conclude over the provenience of the data series representing the evolution of the distance between the two initially neighboring pixels from a standard normal law.
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