A New Upper Bound on the Order of Affine Sub-families of NFSRs

Abstract

Nonlinear feedback shift registers (NFSRs) are widely used as building blocks in the design of stream ciphers. Let NFSR(f) be an NFSR with the characteristic function f and let G(f) be the set of output sequences of NFSR(f). For a given NFSR(f), if there exists an affine Boolean function l such that G(l) ⊆ G(f), then G(l) is called an affine sub-family of NFSR(f). In this paper, by skillfully combining previous ideas, the authors give a new upper bound on the order of affine sub-families of NFSR(f). Compared with the four known bounds, the bound is better than three of them, and in some cases is also better than the rest one.