GENERALIZED STATISTICAL ATTACK ON SYNCRONOUS STREAM CIPHERS

Abstract

Nowadays chosen IV attacks on synchronous streamciphers are the most powerful. These include Dinur-Shamir cube attack, statistical Fisher-Khazaei-Meier(FKM) attack, and their different modifications and improvements.The FKM attack is based on statistical approximations(depended only on some key bits) of Booleanfunctions associated with encryption algorithms. Attack’developers suggested a method for finding theseapproximations but didn’t provide a theoretical justificationof such method’ efficiency. Also there is an openquestion: is it possible to increase attack’ efficiency bychoosing approximations from a wider class of Booleanfunctions. We propose a generalization of cube attack andstatistical attack FKM on synchronous stream ciphers.This attack is based on algebraic degenerate approximationsof Boolean functions that provides more opportunitiesfor implementation of FKM attack’ basic idea. Wealso propose a polynomial probabilistic algorithm forconstruction of such approximations from known subspacesacceptable for defined Boolean function. We showthat the proposed algorithm allows us to construct muchmore efficient attacks on synchronous stream cipherscompared with exhaustive search.