Synchronization of Boolean Dynamical Systems: a Spectral Characterization

Jeremy Parriaux (1) , Philippe Guillot (2) , Gilles Millérioux (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper a spectral characterization of the synchronization property of Boolean dynamical systems is provided. Conditions on the spectrum of the next-state function are derived for two systems coupled in a unidirectional way - also called master-slave configuration - to guarantee self-synchronization. Two kinds of self-synchronization are discussed: the statistical one and the finite one. Next, some conditions are stated for a specific input sequence to allow the system to be self-synchronizing. Some of the results are based on the notion of influence of variables, a notion that is extended to vectorial Boolean functions for the purpose of the paper. A potential application to cryptography is finally given.

Mots clés: Walsh Transform; Boolean sequences; self-synchronizing stream ciphers

Domaines: Cryptographie et sécurité [cs.CR]; Systèmes dynamiques [math.DS]; Automatique

Jeremy Parriaux, Philippe Guillot, Gilles Millérioux. Synchronization of Boolean Dynamical Systems: a Spectral Characterization. 6th Conference on Sequences and their applications, SETA 2010, Sep 2010, Paris, France. pp.CDROM. ⟨hal-00540855⟩