2022, Volume 23, Issue 10
Frontiers of Information Technology & Electronic Engineering >> 2022, Volume 23, Issue 10 doi: 10.1631/FITEE.2200228
On observability of Galois nonlinear feedback shift registers over finite fields
Affiliation(s): School of Mathematics, Shandong University, Jinan 250100, China; Department of Computer Science & Engineering, University of Minnesota Twin Cities, Minneapolis, MN 55455, USA; less
Next Previous
Abstract
ensures that any two distinct initial states can be uniquely determined by their outputs, so the stream ciphers can avoid unobservable to prevent the occurrence of equivalent keys. This paper discusses the of over . are treated as using the . The vector form of the state transition matrix is introduced, by which a necessary and sufficient condition is proposed, as well as an algorithm for determining the of general . Moreover, a new matrix is defined, which can derive a matrix method with lower computation complexity. Furthermore, the of two special types of , a full-length Galois NFSR and a nonsingular Galois NFSR, is investigated. Two methods are proposed to determine the of these two special types of NFSRs, and some numerical examples are provided to support these results.
京公网安备 11010502051620号
