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In stream cipher design pseudo random generators have been proposed which combine the output of one or several LFSRs in order to produce the key stream. For memoryless combiners it is known that the produced sequence has correlation to sums of certain LFSR-sequences whose correlation coefficients ci satisfy the equation 驴i ci2 = 1. It is proved that a corresponding result also holds for combiners with memory.If correlation probabilities are conditioned on side information, e.g. on known output digits, it is shown that new or stronger correlations may occur. This is exemplified for the summation cipher with two LFSRs where such correlations can be exploited in a known plaintext attack. A cryptanalytic algorithm is given which is shown to be successful for LFSRs of considerable length and with arbitrary feedback connection.

Correlation Properties of Combiners with Memory in Stream Ciphers (Extended Abstract)