International Association
for Cryptologic Research

In this paper, we study stability and linearization of multi-

valued nonlinear feedback shift registers which are considered as logic

networks. First, the linearization of multi-valued nonlinear feedback shift

registers (NFSRs) is discussed, which is to nd their state transition ma-

trices by considering it as a logical network via a semi-tensor product ap-

proach. For a multi-valued NFSR, the new state transition matrix which

can be simply computed from the truth table of its feedback function is

more explicit. Second, based on the linearization theory of multi-valued

NFSRs, we investigate the stability of multi-valued NFSRs, and some suf-

cient and necessary conditions are provided for globally (locally) stable

multi-valued NFSRs. Finally, some examples are presented to show the

eectiveness of the proposed results.