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9th China International Conference on Information Security and Cryptology (Inscrypt)

作者： Zhou, Jianqin Liu, Wanquan Zhou, Guanglu Curtin Univ Dept Comp Perth WA 6102 Australia Curtin Univ Dept Math & Stat Perth WA 6102 Australia Anhui Univ Technol Sch Comp Sci Maanshan 243032 Peoples R China

ISBN: (纸本)9783319120874;9783319120867

The linear complexity of a sequence has been used as an important measure of keystream strength, hence designing a sequence with high linear complexity and k-error linear complexity is a popular research topic in cryptography. In this paper, the concept of stable k-error linear complexity is proposed to study sequences with stable and large k-error linear complexity. In order to study linear complexity of binary sequences with period 2(n), a new tool called cube theory is developed. By using the cube theory, one can easily construct sequences with the maximum stable k-error linear complexity. For such purpose, we first prove that a binary sequence with period 2(n) can be decomposed into some disjoint cubes. Second, it is proved that the maximum k-error linear complexity is 2(n) -(2(l-1)) over all 2(n) -periodic binary sequences, where 2(l-1) <= k < 2(l). Finally, continuing the work of kurosawa et al., a characterization is presented about the minimum number k for which the second decrease occurs in the k-error linear complexity of a 2(n) -periodic binary sequence s.

关键词： Periodic sequence linear complexity k-error linear complexity Stable k-error linear complexity Cube theory

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On the k-error linear complexity of New Generalized Cyclotomic Sequences

On the k-error Linear Complexity of New Generalized Cyclotom...

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第八届中国可信计算与信息安全学术会议

New generalized cyclotomic sequences with length p2 and pq are considered as good *** this paper,two classes of error generalized cyclotomic sequences are constructed by changing the characteristic sets of the above *** show that k-error linear complexity of generalized cyclotomic sequences don't exceed p and p+q-1,which are much less than their(zero-error) linear complexity.

关键词： stream cipher Pseudo-random sequence generalized cyclotomy k-error linear complexity

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On the stability of periodic binary sequences with zone restriction

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2022年第5期33卷 485-504页

作者： Su, Ming Wang, Qiang Nankai Univ Dept Comp Sci Tianjin Peoples R China Carleton Univ Sch Math & Stat Ottawa ON Canada

Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods 2(n), or 2(v)r (r odd prime and 2 is primitive modulo r), or 2(v)p(1)(s1) ... p(n)(sn) (p(i) is an odd prime and 2 is primitive modulo p(i)(2), where 1 <= i <= n) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary 2(n)-periodic binary sequence.

关键词： Stability linear complexity k-error linear complexity Zone restriction Binary sequences

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On error linear complexity of new generalized cyclotomic binary sequences of period p²

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INFORMATION PROCESSING LETTERS 2019年 144卷 9-15页

作者： Wu, Chenhuang Xu, Chunxiang Chen, Zhixiong ke, Pinhui Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611731 Sichuan Peoples R China Putian Univ Prov Key Lab Appl Math Putian 351100 Fujian Peoples R China Fujian Normal Univ Coll Math & Informat Fujian Prov Key Lab Network Secur & Cryptol Fuzhou 350117 Fujian Peoples R China

We consider the k-error linear complexity of a new generalized cyclotomic binary sequence of period p(2) for an odd prime p. The new sequences were introduced recently by Z. Xiao, X. Zeng, C. Li and T. Helleseth by defining a new kind of generalized cyclotomic classes modulo p(2). They proved that the sequences had large linear complexity. In this work, we determine the values of the k-error linear complexity in terms of the theory of Fermat quotients. The results indicate that such sequences have good stability, that is, the linear complexity does not significantly decrease by changing a few terms. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Cryptography Pseudorandom binary sequences k-error linear complexity Generalized cyclotomic classes Fermat quotients

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On the Distribution of p-error linear complexity of p-Ary Sequences with Period pⁿ

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2019年第12期E102D卷 2595-2598页

作者： Tang, Miao Wang, Juxiang Shi, Minjia Liang, Jing Anhui Agr Univ Dept Appl Math Hefei 230036 Anhui Peoples R China Anhui Jianzhu Univ Sch Math & Phys Hefei 230601 Anhui Peoples R China Anhui Univ Sch Math Sci Hefei 230601 Anhui Peoples R China Anhui Xinhua Univ Minist Gen Educ Hefei 230088 Anhui Peoples R China

linear complexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-error linear complexity of p-ary sequences with period p(n). For p-ary sequences of period p(n) with linear complexity p(n) - p + 1, n >= 1, we present all possible values of the p-error linear complexity, and derive the exact formulas to count the number of the sequences with any given p-error linear complexity.

关键词： periodic sequence k-error linear complexity counting function stream ciphers

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Asymptotic analysis on the normalized k-error linear complexity of binary sequences

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DESIGNS CODES AND CRYPTOGRAPHY 2012年第3期62卷 313-321页

作者： Tan, Lin Qi, Wen-Feng Xu, Hong Zhengzhou Informat Sci & Technol Inst Dept Appl Math Zhengzhou 450002 Peoples R China

linear complexity and k-error linear complexity are the important measures for sequences in stream ciphers. This paper discusses the asymptotic behavior of the normalized k-error linear complexity L-n,L-k(s)/n of random binary sequences s, which is based on one of Niederreiter's open problems. For k = n theta, where 0 <= theta <= 1/2 is a fixed ratio, the lower and upper bounds on accumulation points of L-n,L-k((s)under bar)/n are derived, which holds with probability 1. On the other hand, for any fixed k it is shown that lim(n ->infinity) Ln, k ((s)under bar)/n = 1/2 holds with probability 1. The asymptotic bounds on the expected value of normalized k-error linear complexity of binary sequences are also presented.

关键词： Stream ciphers Binary sequences linear complexity k-error linear complexity

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Computing the k-error linear complexity of q-Ary Sequences with Period 2pⁿ

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2012年第9期E95A卷 1637-1641页

作者： Niu, Zhihua Li, Zhe Chen, Zhixiong Yan, Tongjiang Shanghai Univ Sch Engn & Comp Sci Shanghai 200072 Peoples R China Putian Univ Dept Math Putian 351100 Peoples R China China Univ Petr Coll Sci Qingdao 266555 Peoples R China

The linear complexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linear complexity properly. Recently, Zhou designed an algorithm for computing the k-error linear complexity of 2p(n) periodic sequences over GF(q). In this paper, we develop a genetic algorithm to confirm that one can't get the real k-error linear complexity for some sequenes by the Zhou's algorithm. Analysis indicates that the Zhou's algorithm is unreasonable in some steps. The corrected algorithm is presented. Such algorithm will increase the amount of computation, but is necessary to get the real k-error linear complexity. Here p and q are odd prime, and q is a primitive root (mod p(2)).

关键词： stream cipher periodic sequence linear complexity k-error linear complexity genetic algorithm

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On the linear complexity for multidimensional sequences

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JOURNAL OF complexity 2018年 49卷 46-55页

作者： Gomez-Perez, Domingo Sha, Min Tirkel, Andrew Univ Cantabria Dept Math Stat & Comp Sci E-39005 Santander Spain Macquarie Univ Dept Comp Sydney NSW 2109 Australia Sci Technol Pty Ltd 8 Cecil St East Brighton Vic 3187 Australia

In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and k-error linear complexity of multidimensional periodic sequences. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Multidimensional sequence linear complexity k-error linear complexity

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On the k-error linear complexity of sequences with period 2pⁿ over G F (q)

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DESIGNS CODES AND CRYPTOGRAPHY 2011年第3期58卷 279-296页

作者： Zhou, Jianqin Hangzhou Dianzi Univ Telecommun Sch Hangzhou 310018 Zhejiang Peoples R China

In this paper, we first optimize the structure of the Wei-Xiao-Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2p (n) , where p and q are odd primes, and q is a primitive root modulo p (2). The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p (n) over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p (2). The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e (N) , where the Hamming weight of e (N) is not greater than k, such that the linear complexity of (s + e) (N) reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.

关键词： Stream ciphers Periodic sequence linear complexity k-error linear complexity Algorithm

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linear complexity problems of level sequences of Euler quotients and their related binary sequences

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Science China(Information Sciences) 2016年第3期59卷 75-86页

作者： Zhihua NIU Zhixiong CHEN Xiaoni DU School of Computer Engineering and Science Shanghai University School of Mathematics Putian University College of Mathematics and Information Science Northwest Normal University

The Euler quotient modulo an odd-prime power pr(r > 1) can be uniquely decomposed as a p-adic number of the form(up-1pr-1- 1)/pr≡ a0(u) + a1(u)p + ··· + ar-1(u)pr-1(mod pr), gcd(u, p) = 1, where0≤aj(u) < p for 0≤j≤r- 1 and we set all aj(u) = 0 if gcd(u, p) > 1. We firstly study certain arithmetic properties of the level sequences(aj(u))u≥0over Fp via introducing a new quotient. Then we determine the exact values of linear complexity of(aj(u))u≥0 and values of k-error linear complexity for binary sequences defined by(aj(u))u≥0.

关键词： cryptography Euler quotients Fermat quotients pseudorandom sequences binary sequences lin ear complexity k-error linear complexity

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