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Remarks on the k-error linear complexity of pⁿ-periodic sequences

DESIGNS CODES AND CRYPTOGRAPHY 2007年第2期42卷 181-193页

作者： Meidl, Wilfried Venkateswarlu, Ayineedi Sabanci Univ TR-34956 Istanbul Turkey Natl Univ Singapore Temasek labs Singapore 117508 Singapore

Recently the first author presented exact formulas for the number of 2(n)-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k >= 2, of a random 2(n)-periodic binary sequence. A crucial role for the analysis played the chan-games algorithm. We use a more sophisticated generalization of the chan-games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p(n)-periodic sequences over F-p,p prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p(n)-periodic sequences over F-p.

关键词： linear complexity k-error linear complexity chan-games algorithm periodic sequences stream cipher

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On the stability of 2ⁿ-periodic binary sequences

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第3期51卷 1151-1155页

作者： Meidl, W Natl Univ Singapore Temasek Labs Singapore Singapore

The k-error linear complexity of a periodic binary sequence is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits per period. This contribution focuses on the case of 2(n)-periodic binary sequences. For k = 1, 2, the exact formula for the expected k-error linear complexity of a sequence having maximal possible linear complexity 2(n), and the exact formula of the expected 1-error linear complexity of a random 2(n)-periodic binary sequence are provided. For k greater than or equal to 2, lower and upper bounds on the expected value of the k-error linear complexity of a random 2(n)-periodic binary sequence are established.

关键词： cryptography chan-games algorithm (k-error) linear complexity periodic sequences stability of stream ciphers

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THE 2-ERROR LINEAR COMPLEXITY OF 2~n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2~n-1

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Journal of Electronics(China) 2007年第3期24卷 390-395页

作者： Zhu Fengxiang Qi Wenfeng Department of Applied Mathematics Zhengzhou Informatin Engineering University Zhengzhou 450002 China

Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.

关键词： Linear complexity k-error linear complexity Periodic binary sequences chan-games algorithm

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