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18th International Conference on Information and Communications Security (ICICS)

作者： Pan, Wenlun Bao, Zhenzhen Lin, Dongdai Liu, Feng Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Shanghai Jiao Tong Univ Shanghai 200240 Peoples R China

ISBN: (纸本)9783319500119;9783319500102

The linear complexity and k-error linear complexity of sequences are important measures of the strength of key-streams generated by stream ciphers. Based on the characters of the set of sequences with given linear complexity, people get the characterization of 2(n)-binary sequences with given k-error linear complexity for small k recently. In this paper, we put forward this study to get the distribution of linear complexity and k-error linear complexity of 2(n)-periodic binary sequences with fixed Hamming weight. First, we give the counting function of the number of 2(n)-periodic binary sequences with given linear complexity and fixed Hamming weight. Provide an asymptotic evaluation of this counting function when n gets large. Then we take a step further to study the distribution of 2(n)-periodic binary sequences with given 2-error linear complexity and fixed Hamming weight. Through an asymptotic analysis, we provide an estimate on the number of 2(n)-periodic binary sequences with given 2-error linear complexity and fixed Hamming weight.

关键词： Sequence linear complexity k-error linear complexity Counting function Hamming weight Asymptotic analysis

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On the k-error linear complexity of l-sequences

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FINITE FIELDS AND THEIR APPLICATIONS 2010年第6期16卷 420-435页

作者： Tan, Lin Qi, Wen-Feng Zhengzhou Informat Sci & Technol Inst Dept Appl Math Zhengzhou 450002 Peoples R China Chinese Acad Sci State Key Lab Informat Secur Inst Software Beijing Peoples R China

This paper studies the stability of the linear complexity of l-sequences. Let (s) under bar be an I-sequence with linear complexity attaining the maximum per((s) under bar)/2 + 1. A tight lower bound and an upper bound on minerror((s) under bar), i.e., the minimal value k for which the k-error linear complexity of (s) under bar is strictly less than its linear complexity, are given. In particular, for an I-sequence (s) under bar based on a prime number of the form 2r + 1, where r is an odd prime number with primitive root 2, it is shown that minerror((s) under bar) is very close to r, which implies that this kind of I-sequences have very stable linear complexity. (C) 2010 Published by Elsevier Inc.

关键词： Feedback with carry shift register l-Sequences linear complexity k-error linear complexity

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An Improved Approximation Algorithm for Computing the k-error linear complexity of Sequences Using the Discrete Fourier Transform

An Improved Approximation Algorithm for Computing the k</...

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6th International Conference on Sequences and Their Applications

作者： Salagean, Ana Alecu, Alexandra Univ Loughborough Dept Comp Sci Loughborough Leics England Google Inc Zurich Switzerland

ISBN: (纸本)9783642158735

In our previous work we transformed the optimisation problem of finding the k-error linear complexity of a sequence into an optimisation problem in the DFT (Discrete Fourier Transform) domain, using Blahut's theorem. We then gave an approximation algorithm of polynomial complexity for the transformed problem by restricting the search space to error sequences whose DFT have period up to k. However, when applying the inverse transformation, the error vectors obtained are in general in an extension of the original field. In the present paper we develop our previous approximation algorithm so that now it can be constrained to only obtain errors over the original field. Essentially, we give a polynomial approximation algorithm for the computation of the k-error linear complexity of a sequence. More precisely, the algorithm will find the optimum among a restricted set of errors over the original field. While this restricted search space is still exponential, the complexity of the algorithm is polynomial, O(N-2 log N log log N).

关键词： periodic sequences linear complexity k-error linear complexity discrete Fourier transform

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The cube theory for 2ⁿ-periodic binary sequences 9

The cube theory for 2n-periodic binary seq...

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International Conference on Future Generation Communication and Networking

作者： Zhou, Jianqin Liu, Wanquan Wang, Xifeng Curtin Univ Dept Comp Perth WA 6102 Australia Anhui Univ Technol Sch Comp Sci Maanshan 243002 Peoples R China

ISBN: (纸本)9781467398343

The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength, hence designing a sequence with high linear complexity and k-error linear complexity is a popular research topic in cryptography. In order to study k-error linear complexity of binary sequences with period 2(n), a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2(n) into some disjoint cubes. Second, a counting formula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2(n)-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al..

关键词： Periodic sequence linear complexity k-error linear complexity cube theory

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Research on Excellent Sequence of Period pⁿ Over GF(q) with Genetic Algorithm 12

Research on Excellent Sequence of Period pn Over ...

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12th IEEE Int Conf Ubiquitous Intelligence & Comp/12th IEEE Int Conf Autonom & Trusted Comp/15th IEEE Int Conf Scalable Comp & Commun & Associated Workshops/IEEE Int Conf Cloud & Big Data Comp/IEEE Int Conf Internet People

作者： Niu, Zhihua Ye, Ling Li, Qinqin Shanghai Univ Sch Comp Engn & Sci Shanghai Peoples R China

ISBN: (纸本)9781467372114

The p(n)-periodic q-ary sequence with high linear complexity and high k-error linear complexity is defined as excellent sequence. With appropriate fitness function and parameters, this paper design a genetic algorithm to generate the N-periodic q-ary excellent sequences, where N=27,81,., 2187, and get some laws of k-error linear complexity and linear complexity, here p is an odd prime and q is a primitive root modulo p(2).

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

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New Results on Periodic Sequences With Large k-error linear complexity

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第10期55卷 4687-4694页

作者： Hu, Honggang Gong, Guang Feng, Dengguo Chinese Acad Sci Inst Software State Key Lab Informat Secur Beijing 100080 Peoples R China Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

Niederreiter showed that there is a class of periodic sequences which possess large linear complexity and large k-error linear complexity simultaneously. This result disproved the conjecture that there exists a trade-off between the linear complexity and the k-error linear complexity of a periodic sequence by Ding et al. By considering the orders of the divisors of x(N)-1 over F-q, we obtain three main results which hold for much larger k than those of Niederreiter et al.: a) sequences with maximal linear complexity and almost maximal k-error linear complexity with general periods;b) sequences with maximal linear complexity and maximal k-error linear complexity with special periods;c) sequences with maximal linear complexity and almost maximal k-error linear complexity in the asymptotic case with composite periods. Besides, we also construct some periodic sequences with low correlation and large k-error linear complexity.

关键词： correlation cyclotomy entropy function k-error linear complexity linear complexity periodic sequence

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Multisequences With Large linear and k-error linear complexity From Hermitian Function Fields

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第8期55卷 3858-3863页

作者： Xing, Chaoping Ding, Yang Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 637616 Singapore Southeast Univ Dept Math Nanjing 210096 Peoples R China

In the present paper, by making use of some special properties of the Hermitian function fields, we construct multisequences with both large linear complexity and k-error linear complexity. Moreover, these sequences c... 详细信息

关键词： Automorphisms curves Hermitian function fields k-error linear complexity linear complexity places

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How to determine linear complexity and k-error linear complexity in some classes of linear recurring sequences

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2009年第1期1卷 117-133页

作者： Meidl, Wilfried Sabanci Univ MDBF TR-34956 Istanbul Turkey

Several fast algorithms for the determination of the linear complexity of d-periodic sequences over a finite field F-q, i.e. sequences with characteristic polynomial f(x) = x(d) - 1, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial f(x) = (x - 1)(d) for an arbitrary positive integer d, and f(x) = (x(2) + x + 1)(2v) are presented. The result is then utilized to establish a fast algorithm for determining the k-error linear complexity of binary sequences with characteristic polynomial (x(2) + x + 1)(2v).

关键词： linear complexity k-error linear complexity Algorithm linear recurring sequences Stream cipher

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Counting Functions for the k-error linear complexity of 2ⁿ-Periodic Binary Sequences

Counting Functions for the k-Error Linear Complexity ...

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15th International Workshop on Selected Areas in Cryptography

作者： kavuluru, Ramakanth klapper, Andrew Univ Kentucky Dept Comp Sci Lexington KY 40506 USA

ISBN: (纸本)9783642041587

linear complexity is an important measure of the cryptographic strength of key streams used in stream ciphers. The linear complexity of a sequence can decrease drastically when a few symbols are changed. Hence there has been considerable interest in the k-error linear complexity of sequences which measures this instability in linear complexity. For 2(n)-periodic sequences it is known that minimum number of changes needed per period to lower the linear complexity is the same for sequences with fixed linear complexity. In this paper we derive an expression to enumerate all possible corresponding number of 2(n)-periodic binary sequences with fixed linear equals the minimum number of changes needed to lower the linear complexity below L. For some of these values we derive the expression for the of 2(n)-periodic binary sequences with fixed linear complexity L, when k values for the k-error linear complexity binary sequences with fixed linear complexity and k-error linear complexity when k equals the minimum stability of linear complexity of 2(n)-periodic binary sequences. are of importance to compute some statistical properties concerning.

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

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An algorithm for computing the error sequence of pⁿ-periodic binary sequences

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2014年第3期25卷 197-212页

作者： Tang, Miao Anhui Agr Univ Dept Appl Math Hefei 230036 Anhui Peoples R China

For binary sequences with period , where is an odd prime and 2 is a primitive root modulo , we present an algorithm which computes the minimum number so that the -error linear complexity is not greater than a given co... 详细信息

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

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