Algebraic Attacks on Summation Generators

Abstract

AbstractWe 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 \(^{\lceil\log_2 n \rceil}\) 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 2k LFSRs to reduce the effective degree of the algebraic equation.Keywordsstream ciphersalgebraic attackssummation generators