Improved bounds on the linear complexity of keystreams obtained by filter generators

Abstract

Binary sequences generated by nonlinearly filtering maximal length sequences with period 2 n ∈-∈1 are studied in this paper. We focus on the particular class of normal filters and provide improved lower bounds on the linear complexity of generated keystreams. This is achieved by first proving properties of a special class of determinants which are associated to linearized polynomials over finite fields of characteristic 2 and then by applying the above to simplify generalizations of the root presence test. © 2008 Springer-Verlag Berlin Heidelberg.