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Théorie du contrôle et systèmes hybrides dans un contexte cryptographique

Abstract : This manuscript deals with a specific engineering application involving hybrid dynamical systems : secure communications and cryptography. The work is motivated by the following facts. The considerable progress in communication technology during the last decades has led to an increasing need for security in information exchanges. In this context, cryptography plays a major role as information is mostly conveyed through public networks. Among a wide variety of cryptographic techniques, stream ciphers are of special interest for high speed encryption. They are mainly based on generators of complex sequences in the form of dynamical systems, which must be synchronized at the transmitter and receiver sides. The aim of this work is threefold. First, the interest of resorting to hybrid dynamical systems for the design of cryptographic primitives is motivated. Secondly, a connection between chaotic and conventional cryptography is brought out by comparing the respective algorithms proposed in the open literature. The investigation focuses on structural consideration. Control theoretical concepts, in particular left invertibility and flatness, are the central tools to this end. It is shown that the so-called message-embedding technique, consisting in injecting the information to be concealed into a dynamical system, is the most relevant technique. Furthermore, it is shown that, under the flatness condition, the resulting cipher acts as a self-synchronizing stream cipher. Finally, cryptanalytic methodologies for assessing the security of the message-embedded cryptosystem involving a special class of hybrid systems, namely the switched linear systems, are proposed. Again concepts borrowed from control theory, namely identifiability and identification, are considered. Specificities related to the context are taken into account. The variables describing the dynamical systems do not take values in a continuum unlike what usually happens in automatic control when physical models are considered. They rather take values in finite cardinality sets, especially finite fields, since an implementation in finite state machines, say computers or digital electronic devices, is expected
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Phuoc Vo Tan. Théorie du contrôle et systèmes hybrides dans un contexte cryptographique. Autre. Institut National Polytechnique de Lorraine, 2009. Français. ⟨NNT : 2009INPL079N⟩. ⟨tel-01748774⟩



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