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The Alternating Step(r, s) Generator

A new construction of a pseudo-random generator based on a simple combination of three feedback shift registers (FSRs) is introduced. The main characteristic of its structure is that the output of one of the three FSRs controls the clocking of the other two FSRs. This construction allows users to generate a large family of sequences using the same initial states and the same feedback functions of the three combined FSRs. The construction is related to the Alternating Step Generator that is a special case of this construction. The period, and the lower and upper bound of the linear complexity of the output sequences of the construction whose control FSR generates a de Bruijn sequence and the other two FSRs generate m-sequences are established. Furthermore, it is established that the distribution of short patterns in these output sequences occur equally likely and that they are secure against correlation attacks. All these properties make it a suitable cryptogenerator for stream cipher applications.