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linear complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)

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Chinese Journal of Electronics 2019年第3期28卷 529-534页

作者： YE Zhifan KE Pinhui CHEN Zhixiong Fujian Provincial Key Laboratory of Network Security and Cryptology Fujian Normal University Department of Mathematics and Physics Fujian Jiangxia University School of Mathematics Putian University

For an odd prime p and positive integers r,d such that 0 详细信息

For an odd prime p and positive integers r,d such that 0linear complexity of the proposed sequence over prime field GF（q）with the assumption of q;■ mod p;is determined.An algorithm of computing the linear complexity of the sequence is also given.Our results indicate that,with some constrains on the support set,the new sequences possess large linear complexities.

关键词： linear complexity Euler quotient d-ary sequence

linear complexity of Least Significant Bit of Polynomial Quotients

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Chinese Journal of Electronics 2017年第3期26卷 573-578页

作者： ZHAO Chun'e MA Wenping YAN Tongjiang SUN Yuhua State Key Laboratory of Integrated Service Networks Xidian University College of Sciences China University of PetroleumQingdao

Binary sequences with large linear complexity have been found many applications in communication systems.We determine the linear complexity of a family of p;-periodic binary sequences derived from polynomial quotients modulo an odd prime p.Results show that these sequences have high linear complexity,which means they can resist the linear attack method.

关键词： Cryptography Polynomial quotient Fermat quotient Pseudo-random sequences linear complexity

linear complexity of quaternary sequences with odd period and low autocorrelation

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The Journal of China Universities of Posts and Telecommunications 2014年第5期21卷 89-93页

作者： KE Pin-hui LIN Chang-lu ZHANG Sheng-yuan Fujian Provincial Key Laboratory of Network Security and Cryptology Fujian Normal University

Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternar... 详细信息

关键词： quaternary sequences linear complexity cyclotomy

linear complexity of sequences produced by single cycle T-function

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The Journal of China Universities of Posts and Telecommunications 2011年第4期18卷 123-128页

作者： WANG Yan HU Yu-pu LI Shun-bo YANG Yang Key Laboratory of Computer Networks and Information Security Ministry of Education Xidian University Xi'an 710071 China Department of Mathematics Xi'an University of Architecture and Technology Xi'an 710055 China

Four kinds of sequences generated by single cycle triangular function （T-function） are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on the special properties of single cycle T-function and an algorithm due to Wei, linear complexities of these four kinds of sequence are all acquired. The results show that single cycle T-function sequences have high linear complexity. Therefore, T-function satisfies the essential requirements being a basic component of stream cipher.

关键词： stream cipher single cycle T-function linear complexity

linear complexity of New Generalized Cyclotomic Sequences of Length 2pq

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Transactions of Nanjing University of Aeronautics and Astronautics 2014年第6期31卷 710-716页

作者：王宏伟葛武 Civil Construction Engineering Department Hubei Polytechnic University Zhejiang Education Publishing House

The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show ... 详细信息

关键词： generalized cyclotomic sequence linear complexity minimal polynomial

On the k-error linear complexity of binary sequences derived from polynomial quotients

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Science China(Information Sciences) 2015年第9期58卷 83-97页

作者： CHEN ZhiXiong NIU ZhiHua WU ChenHuang School of Mathematics Putian University School of Computer Engineering and Science Shanghai University

The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from the polynomial quotients modulo p, which are the generalizations of the well-studied Fermat quotients.Indeed, first we determine exact values of the k-error linear complexity over the finite field F2 for these binary sequences under the assumption of 2 being a primitive root modulo p2, and then we determine their k-error linear complexity over the finite field Fp. Theoretical results obtained indicate that such sequences possess‘good’ error linear complexity.

关键词： cryptography Fermat quotients polynomial quotients binary sequences linear complexity k-error linear complexity

On the linear complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr

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Tsinghua Science and Technology 2016年第3期21卷 295-301页

作者： Longfei Liu Xiaoyuan Yang Xiaoni Du Bin Wei Key Laboratory of Network & Information Security of APF Engineering College of APF College of Mathematics and Statistics Northwest Normal University

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd（p-1, q-1 ）=gcd（p- 1, r-1）=gcd（q-1, r-1）=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF（2） is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.

关键词： stream cipher pseudorandom sequence generalized cyclotomy linear complexity

linear complexity of Ding generalized cyclotomic sequences

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Journal of Shanghai University(English Edition) 2007年第1期11卷 22-26页

作者：闫统江陈智雄肖国镇 ISN National Key Laboratory Xidian University

Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.

关键词： stream cipher generalized cyclotomic sequence linear complexity minimal polynomial

linear complexity Problem of Binary Jacobi Sequence

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Wuhan University Journal of Natural Sciences 2012年第6期17卷 481-484页

作者： YAN Tongjiang SUN Yuhua College of Sciences China University of PetroleumQingdao 266555ShandongChina State Key Laboratory of Integrated Service Networks Xidian UniversityXi'an 710071ShaanxiChina

This paper contributes to the stability of linear complexity of a binary periodic Jacobi sequence.By employing a pair of reference sequences,we prove that the linear complexity of a binary Jacobi sequence is unstable,namely,by changing its few bits in one-period length,the linear complexity of the modified sequences will become far less than the required value.

关键词： cryptography Jacobi sequence linear complexity stability of linear complexity