Algebraic attacks on summation generators

Abstract

We apply the algebraic attacks on stream ciphers with memories to the summation generator. For a summation generator that uses n LFSRs, an algebraic equation relating the key stream bits and LFSR output bits can be made to be of degree less than or equal to 2[log2 n], using [log2 n] + 1 consecutive key stream bits. This is much lower than the upper bound given by previous general results. We also show that the techniques of [6, 2] can be applied to summation generators using 2k LFSRs to reduce the effective degree of the algebraic equation. © International Association for Cryptologic Research 2004.