Discrete Applied Mathematics - Special issue on Boolean functions and related problems
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
New approaches to the design of self-synchronizing stream ciphers
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Towards a spectral approach for the design of self-synchronizing stream ciphers
Cryptography and Communications
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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.