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Reducing the calculation of the linear complexity of u2^v-periodic binary sequences to games-chan algorithm

DESIGNS CODES AND CRYPTOGRAPHY 2008年第1期46卷 57-65页

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

We show that the linear complexity of a u2(v)-periodic binary sequence, u odd, can easily be calculated from the linear complexities of certain 2(v)-periodic binary sequences. Since the linear complexity of a 2(v)-periodic binary sequence can efficiently be calculated with the games-chan algorithm, this leads to attractive procedures for the determination of the linear complexity of a u2(v)-periodic binary sequence. Realizations are presented for u = 3, 5, 7, 15.

关键词： linear complexity games-chan algorithm binary sequences stream cipher

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Extended games-chan algorithm for the 2-adic complexity of FCSR-sequences

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THEORETICAL COMPUTER SCIENCE 2003年第3期290卷 2045-2051页

作者： Meidl, W Austrian Acad Sci Inst Discrete Math A-1010 Vienna Austria

Binary sequences generated by feedback shift registers with carry operation (FCSR) share many of the important properties enjoyed by sequences generated by linear feedback shift registers. We present an FCSR analog of the (extended) games-chan algorithm, which efficiently determines the linear complexity of a periodic binary sequence with period length T = 2(n) or p(n), where p is an odd prime and 2 is a primitive element modulo p(2). The algorithm to be presented yields an upper bound for the 2-adic complexity, an FCSR analog of the linear complexity, of a p(n)-periodic binary sequence. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： feedback shift register games-chan algorithm 2-adic complexity periodic binary sequence stream cipher

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On the Error Linear Complexity Spectrum of Binary Sequences with Period of Power of Two

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Chinese Journal of Electronics 2015年第2期24卷 366-372页

作者： chanG Zuling KE Pinhui School of Mathematics and Statistics Zhengzhou University Fujian Provincial Key Laboratory of Network Security and Cryptology Fujian Normal University

The properties of error linear complexity of binary sequences with period of power of two are studied in this paper. Using the games-chan algorithm as main tool, accurate formulas of the minimum value k for which the k-error linear complexity is strictly less than the first and second critical error linear complexity are provided respectively.

关键词： Binary sequences games-chan algorithm Error linear complexity Spectrum

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An algorithm for the k-error linear complexity of sequences over GF( p^m) with period pⁿ, p a prime

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INFORMATION AND COMPUTATION 1999年第1-2期151卷 134-147页

作者： Kaida, T Uehara, S Imamura, K Kyushu Inst Technol Dept Comp Sci & Elect Fukuoka 8208502 Japan Yatsushiro Natl Coll Technol Dept Ingn Elect & Informat Kumamoto 8668501 Japan

An algorithm is given for the k-error linear complexity of sequences over GF(p(m)) with period p(n), p a prime. The algorithm is derived by the generalized games-chan algorithm for the linear complexity of sequences over GF(p(m)) with period p(n) and by using the modified cost different from that used in the Stamp-Martin algorithm for sequences over GF(2) with period 2(n). A method is also given for computing an error vector which gives the k-error linear complexity. (C) 1999 Academic Press.

关键词： k-error linear complexity sequence over GF(p(m)) with period p(n) Stamp-Martin algorithm games-chan algorithm

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Fast algorithms for determining the linear complexity of sequences over GF (p^m) with period 2^tn

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第5期51卷 1854-1856页

作者： Chen, H Fudan Univ Dept Comp & Informat Technol Shanghai 200433 Peoples R China

We prove a result which reduces the computation of the linear complexity of a sequence over GF (p(m)) (p is an odd prime) with period 2n (n is a positive integer such that there exists an element b is an element of GF (p(m)), b(n) = -1) to the computation of the linear complexities of two sequences with period n. By combining with some known algorithms such as the Berlekamp-Massey algorithm and the games-chan algorithm we can determine the linear complexity of any sequence over GF (p(m)) with period 2(t)n (such that 2(t)vertical bar p(m) - 1 and gcd(n, p(m) - 1) = 1) more efficiently.

关键词： Berlekamp-Massey algorithm cryptography games-chan algorithm linear complexity stream cipher

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Reducing the computation of linear complexities of periodic sequences over GF(p^m)

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IEEE TRANSACTIONS ON INFORMATION THEORY 2006年第12期52卷 5537-5539页

作者： Chen, Hao Fudan Univ Sch Informat Sci & Engn Dept Comp & Informat Technol Shanghai 200433 Peoples R China

The linear complexity of a periodic sequence over GF(p(m)) plays an important role in cryptography and communication (see Menezes, van Oorschort, and Vanstone, Handbook of Applied Cryptography. Boca Raton, FL: CRC, 1997). In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of a period un sequence over GF(p(m)) to the computation of the linear complexities and minimal connection polynomials of 4 period n sequences. The conditions u vertical bar p(m) - 1 and gcd(n, p(m) - 1) = 1 are required for the result to hold. Some applications of this reduction in fast algorithms to determine the linear complexities and minimal connection polynomials of sequences over GF(p(m)) are presented.

关键词： Berlekamp-Massey algorithm cryptography games-chan algorithm linear complexity minimal connection polynomial

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Computing the linear complexity for sequences with characteristic polynomial f^ν

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2013年第2期5卷 163-177页

作者： Salagean, Ana Burrage, Alex J. Phan, Raphael C. -W. Univ Loughborough Dept Comp Sci Loughborough Leics England Qualcomm Farnborough Hants England Multimedia Univ Fac Engn Cyberjaya Malaysia

We present several generalisations of the games-chan algorithm. For a fixed monic irreducible polynomial f we consider the sequences s that have as a characteristic polynomial a power of f. We propose an algorithm for computing the linear complexity of s given a full (not necessarily minimal) period of s. We give versions of the algorithm for fields of characteristic 2 and for arbitrary finite characteristic p, the latter generalising an algorithm of Ding et al. We also propose an algorithm which computes the linear complexity given only a finite portion of s (of length greater than or equal to the linear complexity), generalising an algorithm of Meidl. All our algorithms have linear computational complexity. The proposed algorithms can be further generalised to sequences for which it is known a priori that the irreducible factors of the minimal polynomial belong to a given small set of polynomials.

关键词： Linear complexity games-chan algorithm Linear recurrent sequences

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On the generalized Lauder-Paterson algorithm and profiles of the k-error linear complexity for exponent periodic sequences

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3rd International Conference Sequences and Their Applications (SETA 2004)

作者： Kaida, T Yatsushiro Natl Tech Coll Dept Informat & Elect Engn Kumamoto 8668501 Japan

ISBN: (纸本)3540260846

The Lauder-Paterson algorithm gives the profile of the k-error linear complexity for a binary sequence with period 2(n). In this paper a generalization of the Lauder-Paterson algorithm into a sequence over GF(p(m)) with period p(n), where p is a prime and m, n are positive integers, is proposed. We discuss memory and computation complexities of proposed algorithm. Moreover numerical examples of profiles for balanced binary and ternary exponent periodic sequences, and proposed algorithm for a sequence over GF(3) with period 9(= 3(2)) are given.

关键词： exponent periodic sequence games-chan algorithm k-error linear complexity Lauder-Paterson algorithm pseudo-random sequence Stamp-Martin algorithm

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Some Enumeration Results on Binary 2ⁿ-Periodic Sequences

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2017年第2期28卷 171-184页

作者： chang, Zuling Re, Pinhui Zhao, Yongcheng Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China Fujian Normal Univ Fujian Prov Key Lab Network Secur & Cryptol Fuzhou 350117 Peoples R China

This paper studies some enumeration problems of binary sequences with period 2(n) based on the games-chan algorithm and a modified Stamp-Martin algorithm. We provide the exact number of critical error sequences of binary 2(n)-periodic sequences corresponding to the second critical point. The exact formula for the number of binary 2(n)-periodic sequences with exactly three critical points is also derived.

关键词： Binary periodic sequence linear complexity error linear complexity spectrum games-chan algorithm Stamp-Martin algorithm

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On the Error Linear Complexity Spectrum of Binary 2n-periodic Sequences

On the Error Linear Complexity Spectrum of Binary 2n-periodi...

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中国密码学会2012年会

作者： Zu-Ling chang Department of Mathematics Zhengzhou University Zhengzhou 450001 P.R.China

The properties of error linear complexity of binary sequences with period 2n are studied in this *** games-chan algorithm as main tool,accurate formulas of the minimum value k for which the k-error linear complexity i... 详细信息

关键词： Binary sequence games-chan algorithm error linear complexity error linear complexity spectrum

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