On Annihilators in Fewer Variables: Basic Theory and Applications

Algebraic attacks on stream ciphers exploit annihilators of low degree. From another point of view, we concentrate on annihilators in fewer variables in this paper. This work consists of two parts. Firstly, the concept of singular annihilators is proposed and the basic theory is established. Secondly, we present two applications of singular annihilators. We propose a variant of the Filter states guessing attack (FSGA) introduced by Pasalic (2009). Our attack outperforms the FSGA in many cases. Moreover, we put forward a probabilistic algorithm, which can screen out a large number of Boolean functions with annihilators of low degree at a lower cost for the resistance against algebraic attacks.