Research On Multisequences In Management Information

Management informatics is an integration of management science and informationtechnology, which is based on information theory. Now the world is in the great era of informationsociety. Information security issues become more prominent in all kind of managementinformation system. The core of information security is cryptographic technique, whose basis iscryptography theory. In term of difference of encrypting mode, cryptology can be divided into twosorts as stream cipher and block cipher. In the case of the efficient operation of the software andresourse-constrained, the stream cipher has more advantages compared with the block cipher. Thesecurity of a stream cipher systerm depends on the stability of the key stream used to encrypt,which is able to largly resit the attack of the existing algorithms. Feedback shift registers areindispensable component parts in cryptographic module. The stability theory of key stream is animportant reseach direction and the central topic of the stream cipher theory.This dissertation investigates the stability theory of multisequences based on LFSRs andFCSRs in stream ciphers. Firstly, we study the joint linear complexity of random periodicmultisequences. By using a generalization of discrete Fourier transform to constructmultisequences from single sequence, we determine the joint minimal polynomial of a randomperiodic multisequence by giving an algorithm. Then by the generalized discrete Fourier transform(GDFT) the constructions of multisequences, which simultaneously possess maximal joint linearcomplexity and large1-error joint linear complexity, large joint linear complexity and large1▏�'-error joint linear complexity, are showed. The number of existing such multisequences is large.Secondly, we study the complexity theory ofp~n-periodic multisequences over finite fieldF_q,which p is a odd prime,2a primitive root modulop~2. A fast algorithm of joint linearcomplexity of such multisequence is given. Subsequently, we give an efficient algorithm ofk-error joint linear complexity, on the basis of which we study the k-error joint linearcomplexity spectrum ofp~n-periodic binary multisequences and completely determine k-errorjoint linear complexity spectrum by giving an algorithm. Moreover, we study the statisticalproperties of k-error joint linear complexity onp~n-periodic binary multisequences. We showthat k-error joint linear complexity take a value only form some specific ranges. The lower boundof the minimum value k for which the k-error joint linear complexity is strictly less than thejoint linear complexity is presented. Futhemore, distribution and expection of k-error joint linearcomplexity forp~n-periodic binary multisequences are presented. Finally, we investigate the N-adic complexity and k-error N-adic complexity of N-FCSR sequences, show a generalupper bound on k-error N-adic complexity of N-FCSR sequences, and estabilish the existenceof periodic N-FCSR sequences with simultaneously maximal N-adic complexity and largek-error N-adiccomplexity. Under some conditions the overwhelming majority of all periodicN-FCSR sequences with maximal N-adic complexity have a k-error N-adic complexityclose the value of maximal N-adic complexity. Furthermore, we generize the results for theN-FCSR sequences to the N-FCSR mltisequences to show the existence of the stable N-FCSRmltisequences for N-adic joint complexity. In order to improve the stability and reliability of thevarious management information systerms, our results provide theretical basis.