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On the linear complexity of Legendre–Sidelnikov sequences

2013
*
Designs, Codes and Cryptography
*

) In

doi:10.1007/s10623-013-9889-1
fatcat:g2cvsghzu5bs7nyctw3lbnktgu
*some*cases by using results*on*certain*cyclotomic*numbers and*the*factorization*of**some**cyclotomic*polynomials •*Generalized**Cyclotomic*binary*sequence**of*order 2 (Ding) By using properties*of**cyclotomic*... ; Kyureghyan, Pott; Meidl, Winterhof) In*some*cases by using results*on*certain*cyclotomic*numbers and*the*factorization*of**some**cyclotomic*polynomials •*Generalized**Cyclotomic*binary*sequence**of*order ... Result*on**the**Linear**Complexity*-Theorem 1 Theorem 1*The**linear**complexity**of*Legendre-Sidelnikov*sequences*L(S) satisfies: Experiments Result*on**the**Linear**Complexity*-Theorem 2 Theorem 2 Let q = 2r ...##
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Binary cyclotomic generators
[chapter]

1995
*
Lecture Notes in Computer Science
*

A

doi:10.1007/3-540-60590-8_4
fatcat:gltnof4a7ffzlefkymtbbiz3eq
*general*approach to control*the**linear**complexity*and its stability for periodic*sequences*over any field is shown. ... In this paper a number*of*binary*cyclotomic**generators*based*on*cyclotomy are described. A number*of*cryptographic properties*of**the**generators*are controlled. ... Acknowledgment: I would like to thank Arto Salomaa for several discussions*on*this topic with me, and*the*reviewers for helpful comments. ...##
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About the Linear Complexity of Ding-Hellesth Generalized Cyclotomic Binary Sequences of Any Period
[article]

2012
*
arXiv
*
pre-print

Also we discuss

arXiv:1207.6380v1
fatcat:2t2ae4bulfbinfccxene7i2iqi
*the*method*of*computing*the**linear**complexity**of*Ding-Helleseth*sequences*in*the**general*case. ... We defined sufficient conditions for designing Ding-Helleseth*sequences*with arbitrary period and high*linear**complexity*for*generalized*cyclotomies. ... ., 0, 1)*the*evaluation*of**the**linear**complexity*given in Theorem 1 is valid also for*generalized**cyclotomic**sequences*built*on*new classes. ...##
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New generalized cyclotomic binary sequences of period $$p^2$$ p 2

2017
*
Designs, Codes and Cryptography
*

New

doi:10.1007/s10623-017-0408-7
fatcat:yqfof3vtafevzgpnrrboqbzxuu
*generalized**cyclotomic*binary*sequences**of*period p^2 are proposed in this paper, where p is an odd prime.*The**sequences*are almost balanced and their*linear**complexity*is determined. ...*The*result shows that*the*proposed*sequences*have very large*linear**complexity*if p is a non-Wieferich prime. ...*Cyclotomic**generators*based*on*cyclotomy can*generate**sequences*with larger*linear**complexity*. ...##
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The linear complexity of new q-ary generalized cyclotomic sequences of period pn

2019
*
MATEC Web of Conferences
*

In this paper, we study

doi:10.1051/matecconf/201929202001
fatcat:c5gf7wglwrg5votq6aambz6c2i
*the**linear**complexity**of*new q-ary*generalized**cyclotomic**sequences**of*length pn over*the*finite field*of*order q. ... We show that these*sequences*have*the*high*linear**complexity*when n ≥ 2. These*sequences*are constructed by new*generalized**cyclotomic*classed prepared by X. Zeng at el. ... Conclusion We studied*the**linear**complexity**of*new q-ary*generalized**cyclotomic**sequences**of*length p n over*the*finite field*of*order q. ...##
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The expected value of the joint linear complexity of periodic multisequences

2003
*
Journal of Complexity
*

Using

doi:10.1016/s0885-064x(02)00009-2
fatcat:vcwrlyatc5hflgzplsv6p5ub6m
*the*concept*of**the**generalized*discrete Fourier transform for multisequences, we compute*the*expected value*of**the*joint*linear**complexity**of*random periodic multisequences, and for*some*types*of*... We extend a well-known relationship between*the**linear**complexity**of*an N-periodic*sequence*and*the*(*generalized*) discrete Fourier transform*of*Ntuples to*the*case*of*multisequences. ... Acknowledgments This research was initiated during a visit*of**the*first author to*the*National University*of*Singapore. ...##
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Note about the linear complexity of new generalized cyclotomic binary sequences of period 2p^n
[article]

2019
*
arXiv
*
pre-print

This paper examines

arXiv:1903.04264v1
fatcat:itgatwhxojdbbibyv6lhjyanfq
*the**linear**complexity**of*new*generalized**cyclotomic*binary*sequences**of*period 2p^n recently proposed by Yi Ouang et al. (arXiv:1808.08019v1 [cs.IT] 24 Aug 2018). ... We*generalize*results obtained by them and discuss author's conjecture*of*this paper. ... First*of*all we will recall*some*basics*of**the**linear**complexity**of*a periodic*sequence*and introduce*the**generalized**cyclotomic**sequences*proposed in [6] . ...##
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New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

2021
*
Information
*

In this paper, based

doi:10.3390/info12050193
fatcat:75kivadnnzcxbal2bgp33r3nxm
*on**the*theory*of*inverse Gray mapping, two classes*of*new*generalized**cyclotomic*quaternary*sequences*with period pq are constructed, where pq is a product*of*two large distinct primes ...*The*results show that these two kinds*of**sequences*have large*linear**complexity*. ... Data Availability Statement:*The*data used to support*the*findings*of*this study are included within*the*article. Conflicts*of*Interest:*The*authors declare that they have no conflict*of*interest. ...##
###
Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm

2020
*
Complexity
*

In this paper, based

doi:10.1155/2020/6538970
fatcat:2mdhslvwkvev3n26cljiq3eqja
*on**the*theory*of**generalized*cyclotomy, new classes*of*quaternary*generalized**cyclotomic**sequences*with order 4 and period 2pm are constructed. ...*Sequences*with high*linear**complexity*property are*of*importance in applications. ...*of*works*on**linear**complexity**of*binary*cyclotomic**sequences*, see [4] [5] [6] [7] , for instance. ...##
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New upper bounds on the linear complexity

2000
*
Computers and Mathematics with Applications
*

ln this work,

doi:10.1016/s0898-1221(99)00331-4
fatcat:nikeyl4qdrgltmpqfsafqdls5q
*the**general*upper bound*on**the**linear**complexity*given by Key is improved for certain families*of*nonlinear filter functions. ... Also, a new class*of**cyclotomic*cosets whose degeneration is relatively easy to prove in several conditions is introduced and analysed. (~) ... bound*on**the**linear**complexity**of*certain*sequences*. ...##
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The linear complexity of new binary cyclotomic sequences of period p^n
[article]

2017
*
arXiv
*
pre-print

In this paper, we determine

arXiv:1712.03947v1
fatcat:yezvnlypp5axpm2udrzmy5r3sq
*the**linear**complexity**of*a class*of*new binary*cyclotomic**sequences**of*period pn constructed by Z. Xiao et al. (Des. Codes Cryptogr. ... DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high*linear**complexity**of*these*sequences*. ... Conclusion In this paper,*the**linear**complexity**of*a class*of*new binary*cyclotomic**sequences**of*period p n was studied. ...##
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A further study on the linear complexity of new binary cyclotomic sequence of length p^r
[article]

2018
*
arXiv
*
pre-print

Recently, a conjecture

arXiv:1712.08886v2
fatcat:xke4fu6qsrehreb2dbmfm5viee
*on**the**linear**complexity**of*a new class*of**generalized**cyclotomic*binary*sequences**of*period p^r was proposed by Z. Xiao et al. (Des. ... a special case, and then an efficient method to compute*the**linear**complexity**of**the**sequence*by*the**generic*construction is presented, based*on*which*the*conjecture proposed by Z. ...*Linear**complexity*is*one**of**the*most important properties*of*a*sequence*for its applications in cryptography. ...##
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Linear complexity over 𝔽_q and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation
[article]

2021
*
arXiv
*
pre-print

A class

arXiv:2109.02095v2
fatcat:icpaibnlajdcxjrp3xlm2cgobm
*of*binary*sequences*with period 2p is constructed using*generalized**cyclotomic*classes, and their*linear**complexity*, minimal polynomial over 𝔽_q as well as 2-adic*complexity*are determined using ...*The*results show that*the**linear**complexity**of*these*sequences*attains*the*maximum when p≡± 1( 8) and is equal to p+1 when p≡± 3( 8) over extension field. ... There are lots*of*work*on**linear**complexity**of*binary*cyclotomic**sequences*based*on*Whiteman*generalized*cyclotomy and Ding-Helleseth*generalized*cyclotomy [3] [4] [5] . Zhang et al. ...##
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A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period p^n
[article]

2017
*
arXiv
*
pre-print

As an application, we determine a lower bound

arXiv:1704.05544v2
fatcat:zgoxk2bxzbhxtpukrz7ukuk2fm
*on**the*2-adic*complexity**of*a class*of*Ding-Helleseth*generalized**cyclotomic**sequences**of*period p^n. ...*The*result shows that*the*2-adic*complexity*is at least p^n-p^n-1-1, which is larger than N+1/2, where N=p^n is*the*period*of**the**sequence*. ... Acknowledgement Parts*of*this work were written during a very pleasant visit*of**the*first author to*the*Carleton University in School*of*Mathematics and Statistics. ...##
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Some Notes on the Linear Complexity of Sidel'nikov-Lempel-Cohn-Eastman Sequences

2006
*
Designs, Codes and Cryptography
*

Moreover, we prove a

doi:10.1007/s10623-005-6340-2
fatcat:f5j6oqh5fjaqtkmwalxj2sxyje
*general*lower bound*on**the**linear**complexity*profile for all*of*these*sequences*. ... We determine*the*exact*linear**complexity**of*several families*of*these*sequences*using well-known results*on**cyclotomic*numbers. ... Acknowledgments*The*first author was supported by DSTA research grant R-394-000-011-422.*The*second author was supported by*the*Austrian Academy*of*Sciences and by*the*FWF research grant S8313. ...
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