On observability of Galois nonlinear feedback shift registers over finite fields

作     者：Zhe GAO Jun’e FENG Yongyuan YU Yanjun CUI Zhe GAO;Jun'e FENG;Yongyuan YU;Yanjun CUI

作者机构：School of MathematicsShandong UniversityJinan 250100China Department of Computer Science&EngineeringUniversity of Minnesota Twin CitiesMinneapolisMN 55455USA 

出 版 物：《Frontiers of Information Technology & Electronic Engineering》 (信息与电子工程前沿（英文版）)

年 卷 期：2022年第23卷第10期

页      面：1533-1545页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China(No.61877036) 

主　　题：Observability Nonlinear feedback shift registers(NFSRs) Galois NFSRs Semi-tensor product Finite fields Logical networks 

摘      要：Observability ensures that any two distinct initial states can be uniquely determined by their outputs,so the stream ciphers can avoid unobservable nonlinear feedback shift registers(NFSRs)to prevent the occurrence of equivalent *** paper discusses the observability of Galois NFSRs over finite *** NFSRs are treated as logical networks using the semi-tensor *** 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 observability of general Galois ***,a new observability matrix is defined,which can derive a matrix method with lower computation ***,the observability of two special types of Galois NFSRs,a full-length Galois NFSR and a nonsingular Galois NFSR,is *** methods are proposed to determine the observability of these two special types of NFSRs,and some numerical examples are provided to support these results.