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lattice reduction Aided MMSE Tomlinson-Harashima Precoding Based on VBLAST Algorithm for MIMO Systems

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Journal of Shanghai Jiaotong university(Science) 2008年第1期13卷 12-15页

作者：刘锋蒋铃鸽何晨 Department of Electronic Engineering Shanghai Jiaotong University

A lattice reduction aided (LRA) minimum mean square error (MMSE) Tomlinson-Harashima pre-coding (THP) was proposed based on vertical Bell Labs layered space time (VBLAST) algorithm for multiple input multiple output (MIMO) systems. The extended channel was used to provide optimal tradeoff between residual interference and noise amplification. The processing based on lattice reduction method helps achieve maximal diversity order. The VBLAST algorithm was applied to get the optimal processing ordering for successive interference cancellation (SIC) at transmitter. Simulation results show that the proposed algorithm outperforms conventional THP and the LRA zero-forcing (ZF) THP with full diversity order.

关键词： multiple input multiple output systems lattice reduction vertical Bell Labs layered space time minimum mean square error Tomlinson-Harashima precoding

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A new parallel lattice reduction algorithm for BKZ reduced bases

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Science China(Information Sciences) 2014年第9期57卷 136-145页

作者： LIU XiangHui FANG Xing WANG Zheng XIE XiangHui Department of Applied Mathematics Zhengzhou Information Science and Technology Institute

In order to implement the original BKZ algorithm in parallel,we describe it in terms of parallelism and give its parallel implementation *** we analyze the efficiency of algorithm’s parallel implementation and show that the speedup factor of BKZ algorithm in parallel is extremely *** we present a new parallel lattice reduction algorithm suitable for multiprocessor computer *** new algorithm can obtain a BKZ reduced basis and the parallel speedup is *** with the practical results,although the computational complexity increases compared with the original BKZ algorithm,we still indicate that the new algorithm performs well in parallel and the time cost in parallel is *** the same time,we show that the length of the shortest vector is smaller.

关键词： lattice reduction BKZ algorithm Goldstein-type lattices parallel algorithm multiprocessor computer architecture

On the Successive Minima of Subbases of Low-Dimensional lattices

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Algebra Colloquium 2014年第3期21卷 477-482页

作者： Feng Gao Shikui Shang Department of Electronic Engineering and Information Science The University of Science and Technology of China Hefei 230027 China Department or Mathematics The University of Science and Tebchnology of China Hefei 230026 China

In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.

关键词： lattice reduction successive minima of subbases successive minimal basis,Hermite-redueed basis Minkowski-reduced basis general greedy-reduced basis

On an attack on RSA with small CRT-exponents

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Science China(Information Sciences) 2010年第8期53卷 1511-1518页

作者： HAN LiDong 1,2 , WANG XiaoYun 3 & XU GuangWu 3,4 1 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan 250100, China 2 School of Mathematics, Shandong University, Jinan 250100, China 3 Institute for Advanced Study, Tsinghua University, Beijing 100084, China 4 Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA Key Laboratory of Cryptologic Technology and Information Security Ministry of Education Shandong University Jinan China School of Mathematics Shandong University Jinan China Institute for Advanced Study Tsinghua University Beijing China Department of Electrical Engineering and Computer Science University of Wisconsin-Milwaukee Milwaukee USA

This paper concerns the RSA system with private CRT-exponents. Since Chinese remainder representation provides efficiency in computation, such system is of some practical significance. In this paper, an existing attack to small private CRT-exponents is analyzed. It is indicated that this attack makes nice use of lattice in RSA analysis, but some argument does not hold in general. Several counterexamples are constructed. Refinements and more precise statements of the attack are given.

关键词： RSA CRT cryptanalysis continued fraction lattice reduction

Quantum-safe cryptography:crossroads of coding theory and cryptography

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Science China(Information Sciences) 2022年第1期65卷 95-115页

作者： Jiabo WANG Ling LIU Shanxiang LYU Zheng WANG Mengfan ZHENG Fuchun LIN Zhao CHEN Liuguo YIN Xiaofu WU Cong LING Beijing National Research Center for Information Science and Technology Tsinghua University Department of Software Engineering Shenzhen University College of Cyber Security Jinan University School of Information Science and Engineering Southeast University Department of Electrical and Electronic Engineering Imperial College London National Engineering Research Center of Communications and Networking Nanjing University of Posts and Telecommunications

We present an overview of quantum-safe cryptography(QSC) with a focus on post-quantum cryptography(PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical-and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon's pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

关键词： post-quantum cryptography lattice-based cryptography code-based cryptogarphy information-theoretic security lattice reduction lattice codes linear codes

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