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Control, synchronization and encryption

Abstract : This thesis deals with the synchronization of dynamical systems. The synchronization considered is called master-slave, that is, the dynamical systems are connected in a unidirectional way. This configuration is of interest because it corresponds to an architecture encountered in secured communications of type one-to-one or one-to-many. A special attention is paid to self-synchronization, the behaviour that characterizes synchronization achieved with a simple master-slave coupling and so, without any external control. It is a central feature of self-synchronizing stream ciphers. The study of self-synchronization in the cryptographic context relies on control theory. An original connection between self-synchronization and encryption/decryption is provided. It is based on the flatness property of dynamical systems, a property borrowed from automatic control. It is shown that flat dynamical systems completely define the set of all self-synchronizing systems and thus, enlarge the existing structures of self-synchronizing stream ciphers. Flatness is first of all studied for the case of two nonlinear systems: switched linear systems and linear parameter-varying (LPV) systems. Flatness characterization is based on the concept of nilpotent semigroups and an efficient algorithm is provided. A constructive approach for self-synchronizing master-slave structures is proposed. It relies on the construction of flat systems as well as on left and right invertibility also borrowed from control theory. Then, self-synchronization is studied in the Boolean context which is preferred in cryptography. Self-synchronization is characterized through the notion of influence. Several matrix representations of Boolean functions are proposed. These representations are especially interesting for security analysis. A connection between self-synchronization and the eigenstructures of these matrices is established. Then, a graph oriented approach is provided. New self-synchronizing constructions are deduced and security elements are discussed. Eventually, the description of the FPGA based test platform that we have designed is provided.
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https://theses.hal.science/tel-01749323
Contributor : Jérémy Parriaux Connect in order to contact the contributor
Submitted on : Tuesday, November 6, 2012 - 5:43:14 PM
Last modification on : Saturday, October 16, 2021 - 11:14:12 AM
Long-term archiving on: : Thursday, February 7, 2013 - 3:47:49 AM

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  • HAL Id : tel-01749323, version 2

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Jeremy Parriaux. Control, synchronization and encryption. Optimization and Control [math.OC]. Université de Lorraine, 2012. English. ⟨NNT : 2012LORR0129⟩. ⟨tel-01749323v2⟩

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