Linear span analysis of a set of periodic sequence generators

Abstract

An algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. Unlike the existing methods, the algorithm here presented is based on the realization of bit wise logic operations. The numerical results obtained are valid for any nonlinear function with a unique term of maximum order and for any maximal-length LFSR. To illustrate the power of this technique, we give some high lower bounds that confirm Rueppel's conclusion about the exponential growth of the linear complexity in filter generators.