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Improved Information Set Decoding Algorithms over galois ring in the Lee Metric

Journal of Systems Science & Complexity 2023年第3期36卷 1319-1335页

作者： LI Yu WANG Li-Ping State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China School of Cyber Security University of Chinese Academy of SciencesBeijing 100049China

The security of most code-based cryptosystems relies on the hardness of the syndrome decoding(SD) problem.The best solvers of the SD problem are known as information set,decoding(ISD) algorithms.Recently,Weger,et al.(2020) described Stern’s ISD algorithm,s-blocks algorithm and partial Gaussian elimination algorithms in the Lee metric over an integer residue ring Z_(pm),where p is a prime number and m is a positive integer,and analyzed the time complexity.In this paper,the authors apply a binary ISD algorithm in the Hamming metric proposed by May,et al.(2011)to solve the SD problem over the galois ring GR(p^(m),k) endowed with the Lee metric and provide a detailed complexity analysis.Compared with Stern’s algorithm over Zpmin the Lee metric,the proposed algorithm has a significant improvement in the time complexity.

关键词： galois ring information set decoding lee metric syndrome decoding

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A formula on linear complexity of highest coordinate sequences from maximal periodic sequences over galois rings

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Progress in Natural Science:Materials International 2006年第9期16卷 998-1001页

作者： HU Lei and SUN Nigang (State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China) State Key Laboratory of Information Security Graduate School of Chinese Academy of Sciences Beijing 100049 China

Using a polynomial expression of the highest coordinate map, we deduce an exact formula on the linear complexity of the highest coordinate sequence derived from a maximal periodic sequence over an arbitrary galois ring of characteristic p2 , where p is a prime. This generalizes the known result of Udaya and Siddiqi for the case that the galois ring is Z4.

关键词： galois ring highest coordinate sequence linear complexity.

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GMW sequences over galois rings and their linear complexities

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Frontiers of Electrical and Electronic Engineering in China 2009年第2期4卷 141-144页

作者： Nigang SUN Lei HU Department of Computer Science and Engineering East China University of Science and TechnologyShanghai 200237China State Key Laboratory of Information Security Graduate University of Chinese Academy of SciencesBeijing 100049China

A new family of GMW sequences over an arbitrary galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representation,we derived an estimate of the linear complexities of this family of GMW sequences.And the result shows that such sequences have large linear complexities.

关键词： cryptography GMW sequence linear complexity galois ring

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Period analysis of the Logistic map for the finite field

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Science China(Information Sciences) 2017年第2期60卷 49-63页

作者： Bo YANG Xiaofeng LIAO College of Electronic and Information Engineering Southwest University

Usually, the security of traditional cryptography which works on integer numbers and chaotic cryptosystem which works on real numbers is worthy of study. But the classical chaotic map over the real domain has a disadvantage that the calculation accuracy of the floating point number can be doubled when the map is implemented by computer. This is a serious drawback for practical application. The Logistic map is a classical chaotic system and it has been used as a chaotic cipher in the real number field. This inevitably leads to the degradation of finite precision under computer environment, and it is also very difficult to guarantee security.To solve these drawbacks, we extend the Logistic map to the finite field. In this paper, we consider the Logistic map for the finite field N = 3~n, and analyze the period property of sequences generated by the Logistic map over ZN. Moreover, we discuss the control parameters which may influence the behavior of the mapping, and show that the Logistic map over ZN may be suitable for application by performance analysis. Ultimately, we find that there exists an automorphic map between two Logistic maps with the different control parameters, which makes them suitable for sequence generator in cryptosystem. The automorphic sequence generated algorithm based on the Logistic map over ZN is designed and analyzed in detail. These sequences can be used in the pseudorandom number generator, the chaotic stream cipher, and the chaotic block cipher, etc.

关键词： chaos Logistic map period analysis sequence generated algorithm galois ring

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