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Le désordre des itérations chaotiques et leur utilité en sécurité informatique

Abstract : For the first time, the divergence and disorder properties of ''chaotic iterations'', a tool taken from the discrete mathematics domain, are studied. After having used discrete mathematics to deduce situations of non-convergence, these iterations are modeled as a dynamical system and are topologically studied into the framework of the mathematical theory of chaos. We prove that their adjective ''chaotic'' is well chosen: these iterations are chaotic, according to the definitions of Devaney, Li-Yorke, expansivity, topological entropy, Lyapunov exponent, and so on. These properties have been established for a topology different from the order topology, thus the consequences of this choice are discussed. We show that these chaotic iterations can be computed without any loss of properties, and that it is possible to circumvent the problem of the finiteness of computers to obtain programs that are proven to be chaotic according to Devaney, etc. The procedure proposed in this document is followed to generate a digital watermarking algorithm and a hash function, which are chaotic according to the strongest possible sense. At each time, the advantages of being chaotic as defined in the mathematical theory of chaos is justified, the properties to check are chosen depending on the objectives to reach, and the programs are evaluated. A novel notion of security for steganography is introduced, to address the lack of tool for estimating the strength of an information hiding scheme against certain types of attacks. Finally, two solutions to the problem of secure data aggregation in wireless sensor networks are proposed.
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https://tel.archives-ouvertes.fr/tel-00648148
Contributor : Christophe Guyeux Connect in order to contact the contributor
Submitted on : Monday, December 5, 2011 - 11:19:21 AM
Last modification on : Thursday, January 13, 2022 - 12:00:17 PM
Long-term archiving on: : Monday, December 5, 2016 - 10:33:53 AM

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  • HAL Id : tel-00648148, version 1

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Christophe Guyeux. Le désordre des itérations chaotiques et leur utilité en sécurité informatique. Dynamique Chaotique [nlin.CD]. Université de Franche-Comté, 2010. Français. ⟨NNT : 2010BESA2019⟩. ⟨tel-00648148⟩

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