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 ^{élog₂ n ù}^{\lceil\log_2 n \rceil} 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 2 ^k LFSRs to reduce the effective degree of the algebraic equation.