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Correlation properties of a general binary combiner with an arbitrary number of memory bits are analyzed. It is shown that there exists a pair of certain linear functions of the output and input, respectively, that produce correlated binary sequences. An efficient procedure, based on a linear sequential circuit approximation, is developed for finding such pairs of linear functions. The result may be a basis for a divide and conquer correlation attack on a stream cipher generator consisting of several linear feedback shift registers combined by a combiner with memory.

Correlation Via Linear Sequential Circuit Approximation of Combiners with Memory