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On the linear complexity of Legendre–Sidelnikov sequences

Ming Su
2013 Designs, Codes and Cryptography  
) In 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  ... 
doi:10.1007/s10623-013-9889-1 fatcat:g2cvsghzu5bs7nyctw3lbnktgu

Binary cyclotomic generators [chapter]

Cunsheng Ding
1995 Lecture Notes in Computer Science  
A 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.  ... 
doi:10.1007/3-540-60590-8_4 fatcat:gltnof4a7ffzlefkymtbbiz3eq

About the Linear Complexity of Ding-Hellesth Generalized Cyclotomic Binary Sequences of Any Period [article]

Vladimir Edemskiy
2012 arXiv   pre-print
Also we discuss 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.  ... 
arXiv:1207.6380v1 fatcat:2t2ae4bulfbinfccxene7i2iqi

New generalized cyclotomic binary sequences of period $$p^2$$ p 2

Zibi Xiao, Xiangyong Zeng, Chunlei Li, Tor Helleseth
2017 Designs, Codes and Cryptography  
New 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.  ... 
doi:10.1007/s10623-017-0408-7 fatcat:yqfof3vtafevzgpnrrboqbzxuu

The linear complexity of new q-ary generalized cyclotomic sequences of period pn

Vladimir Edemskiy, Nikita Sokolovskiy, N. Mastorakis, V. Mladenov, A. Bulucea
2019 MATEC Web of Conferences  
In this paper, we study 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.  ... 
doi:10.1051/matecconf/201929202001 fatcat:c5gf7wglwrg5votq6aambz6c2i

The expected value of the joint linear complexity of periodic multisequences

Wilfried Meidl, Harald Niederreiter
2003 Journal of Complexity  
Using 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.  ... 
doi:10.1016/s0885-064x(02)00009-2 fatcat:vcwrlyatc5hflgzplsv6p5ub6m

Note about the linear complexity of new generalized cyclotomic binary sequences of period 2p^n [article]

Vladimir Edemskiy
2019 arXiv   pre-print
This paper examines 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] .  ... 
arXiv:1903.04264v1 fatcat:itgatwhxojdbbibyv6lhjyanfq

New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

Jiang Ma, Wei Zhao, Yanguo Jia, Haiyang Jiang
2021 Information  
In this paper, based 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.  ... 
doi:10.3390/info12050193 fatcat:75kivadnnzcxbal2bgp33r3nxm

Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm

Pinhui Ke, Yan Zhong, Shengyuan Zhang
2020 Complexity  
In this paper, based 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.  ... 
doi:10.1155/2020/6538970 fatcat:2mdhslvwkvev3n26cljiq3eqja

New upper bounds on the linear complexity

P. Caballero-Gil
2000 Computers and Mathematics with Applications  
ln this work, 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.  ... 
doi:10.1016/s0898-1221(99)00331-4 fatcat:nikeyl4qdrgltmpqfsafqdls5q

The linear complexity of new binary cyclotomic sequences of period p^n [article]

Vladimir Edemskiy
2017 arXiv   pre-print
In this paper, we determine 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.  ... 
arXiv:1712.03947v1 fatcat:yezvnlypp5axpm2udrzmy5r3sq

A further study on the linear complexity of new binary cyclotomic sequence of length p^r [article]

Zhifan Ye, Pinhui Ke, Chenhuang Wu
2018 arXiv   pre-print
Recently, a conjecture 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.  ... 
arXiv:1712.08886v2 fatcat:xke4fu6qsrehreb2dbmfm5viee

Linear complexity over 𝔽_q and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation [article]

Yan Wang, Xilin Han, Weiqiong Wang, Ziling Heng
2021 arXiv   pre-print
A class 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.  ... 
arXiv:2109.02095v2 fatcat:icpaibnlajdcxjrp3xlm2cgobm

A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period p^n [article]

Yuhua Sun, Qiang Wang, Tongjiang Yan, Chun'e Zhao
2017 arXiv   pre-print
As an application, we determine a lower bound 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.  ... 
arXiv:1704.05544v2 fatcat:zgoxk2bxzbhxtpukrz7ukuk2fm

Some Notes on the Linear Complexity of Sidel'nikov-Lempel-Cohn-Eastman Sequences

Wilfried Meidl, Arne Winterhof
2006 Designs, Codes and Cryptography  
Moreover, we prove a 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.  ... 
doi:10.1007/s10623-005-6340-2 fatcat:f5j6oqh5fjaqtkmwalxj2sxyje
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