Design of Self-Synchronizing Stream Ciphers: a New Control-Theoretical Paradigm

Abstract

This paper deals with the use of control theoretical concepts in the context of private communication. It is proposed a new and systematic methodology to design a cryptographic architecture belonging to the special class of ciphers called Self Synchronizing Stream Ciphers (SSSC). Till now, the constructions of SSSC were based on automata with finite input memory involving shifts or triangular functions (T--functions) as state transition functions. Besides, only ad-hoc approaches were available in the literature. The contribution of this paper is to propose not only a general framework to design SSSC, but with potentially more general state transition functions as well. Two control-theoretical issues are treated to this end: as a new paradigm, the construction of flat dynamical systems, and on the other hand, the notion of mortality of a set of matrices, a problem which is in general not decidable.