Correlation via linear sequential circuit approximation of cominers with memory

Abstract

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.