Algebraic attacks on summation generators

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(2)([log)(n]), using [log(2)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 2(k) LFSRs to reduce the effective degree of the algebraic equation.