A general framework and a systematic methodology for the cryptanalysis of a large class of chaotic cryptosystems are proposed. More precisely, it is tested, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not. Robustness against brute force attacks is first considered. A connection between uniqueness in the parameters and identifiability is pointed out. Two approaches, the outputs equality approach and the input/output relation approach, are presented to test the identifiability of the system parameters. The second approach is constructive in the sense that not only it allows to conclude on the identifiability of the parameters but it also provides a systematic technique to retrieve the parameters in the context of a known plaintext attack. It is shown that cryptosystems involving polynomial nonlinearities, chaotic or not, are weak against this attack, called algebraic attack.
To cite this version:Gilles Millérioux, Floriane Anstett, Gérard Bloch. Considering the attractor structure of chaotic maps for observer-based synchronization problems.
AbstractThe main purpose of this paper is to state some sufficient conditions for global synchronization of chaotic maps. The synchronization is viewed as a state reconstruction problem which is tackled by polytopic observers. Unlike most standard observers, polytopic observers can account for a special property of chaotic dynamics. Indeed, it is shown that many chaotic maps can be described in a so-called convexified form, involving a time-varying parameter which depends on the chaotic state vector. Such a form makes it possible to incorporate knowledge on the structure of the compact set wherein the parameter lies. This set depends implicitly on the structure of the chaotic attractor. It is proved that the conservatism of the polyquadratic stability conditions for the state reconstruction, stated in a companion paper, can be reduced when the corresponding Linear Matrix Inequalities involve the vertices of the minimal convex hull of this set. Theoretical developments along with special emphasis on computational aspects are provided and illustrated in the context of adaptive synchronization.
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