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An efficient lattice reduction method for F₂-linear pseudorandom number generators using Mulders and Storjohann algorithm

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第2期236卷 141-149页

作者： Harase, Shin Univ Tokyo Grad Sch Math Sci Meguro Ku Tokyo 1538914 Japan

Recent simulations often use highly parallel machines with many processors, and they need many pseudorandom number generators with distinct parameter sets, and hence we need an effective fast assessment of the generator with a given parameter set. Linear generators over the two-element field are good candidates, because of the powerful assessment via their dimensions of equidistribution. Some efficient algorithms to compute these dimensions use reduced bases of lattices associated with the generator. In this article, we use a fast lattice reduction algorithm by Mulders and Storjohann instead of Schmidt's algorithm, and show that the order of computational complexity is lessened. Experiments show an improvement in the speed by a factor of three. We also report that just using a sparsest initial state (i.e., consisting of all 0 bits except one) significantly accelerates the lattice computation, in the case of Mersenne Twister generators. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Random number generation Uniformity lattice reduction algorithm

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lattice reduction-ordered successive interference cancellation detection algorithm for multiple-input-multiple-output system

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IET SIGNAL PROCESSING 2015年第7期9卷 553-561页

作者： Song, Yunchao Liu, Chen Lu, Feng Nanjing Univ Posts & Telecommun Sch Elect Sci & Engn Nanjing 210003 Jiangsu Peoples R China

lattice reduction (LR) is a powerful technique for improving the performance of linear multiple-input-multiple-output detection methods. The efficient LR algorithms can largely improve the performance of the linear detectors (LDs). Note that the ordered successive interference cancellation (OSIC) system can decrease the interference between antennas and provide performance gain of the LDs. In this paper, a novel LR-aided algorithm called NLR-OSIC improving the performance of the OSIC system has been proposed. Most existing LR algorithms are designed to improve the orthogonality of channel matrices, which is not directly related to the error performance of the OSIC system. While the authors' algorithm maximises the signal-to-interference-plus-noise ratio (SINR) of the detected symbol in each stage of the OSIC system, thus exhibiting improved error rate than the previous LR-aided LDs and their corresponding OSIC algorithms. In each stage, the authors verify that maximising the SINR of the detected symbol can be formulated as a shortest vector problem which is solved by a suboptimal algorithm in this study. In the end of this study, the error rate performance of the proposed algorithm as well as the required complexity has been demonstrated through extensive computer simulations.

关键词： MIMO communication antenna radiation patterns signal detection interference suppression radiofrequency interference wireless channels matrix algebra rdered successive interference cancellation detection algorithm lattice reduction algorithm multiple input multiple output antenna system linear detector NLR-OSIC system channel matrix orthogonality signal-to-interference-plus-noise ratio LR-aided LD SINR shortest vector problem suboptimal algorithm

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A New Random Sampling Method and Its Application in Improving Progressive BKZ algorithm

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Journal of Systems Science & Complexity 2024年第5期37卷 2262-2292页

作者： SUN Minghao WANG Shixiong CHEN Hao QU Longjiang College of Sciences National University of Defense TechnologyChangsha 410073China Academy of Military Sciences Beijing 100091China College of Information Science and Technology/Cyber Security Jinan UniversityGuangzhou 510632China

Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to *** follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in *** they extended the sampling space compared to Schnorr's work through the natural number representation,they did not show how to sample specifically in practice and what vectors should be sampled,in order to find short enough lattice *** this paper,the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors ***,as an application of this new random sampling algorithm,the authors show that it can improve the performance of progressive BKZ algorithm in ***,the authors solve the Darmstadt's lattice Challenge and get a series of new records in the dimension from 500 to 825,using the improved progressive BKZ algorithm.

关键词： Darmstadt’s lattice challenge lattice lattice reduction algorithm post-quantum cryptography random sampling

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Cooperative transmission schemes for energy-efficient collaborative wireless sensor networks

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2014年第6期8卷 391-398页

作者： Naeem, Muhammad Kamran Patwary, Mohammad Nuruzzaman Soliman, Abdel-Hamid Abdel-Maguid, Mohamed Staffordshire Univ FCES Stafford ST18 0AD Staffs England Univ Campus Suffolk Sch Sci Technol & Hlth Ipswich IP4 1QJ Suffolk England

Energy conservation is one of the prime concerns that leads the researcher to investigate collaborative wireless sensor networks with some application specific challenges. Such challenges include combining distributed data synchronously, performing power aware signal processing, defining communication methods that can provide progressive accuracy and, optimising processing and communication for signal transmission. A cooperative resource selection and transmission scheme is proposed to improve the performance of collaborative wireless sensor networks in terms of maintaining link reliability. A measure of Channel Quality Index (CQI) is also proposed to obtain dynamic adaptivity and to optimise resource usage within wireless sensor networks according to environment conditions. As part of the proposed cooperative nature of transmission, the recently proposed transmit-receive antenna selection scheme and lattice reduction algorithm have also been considered. It is assumed that channel state information (CSI) is estimated at receiver and also there is a feedback link between the wireless sensing nodes and the fusion centre receiver. From the simulation results it is observed that for 99.99% detection reliability, the proposed adaptive transmission scheme and proposed hybrid scheme consume only 15% and 18% of energy respectively as compared to the conventional cooperative transmission.

关键词： wireless sensor networks signal processing antennas cooperative transmission schemes energy-efficient collaborative wireless sensor networks energy conservation cooperative resource selection link reliability channel quality index dynamic adaptivity transmit-receive antenna selection scheme lattice reduction algorithm

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Revisiting orthogonal lattice attacks on approximate common divisor problems

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THEORETICAL COMPUTER SCIENCE 2022年 911卷 55-69页

作者： Xu, Jun Sarkar, Santanu Hu, Lei Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Indian Inst Technol Madras Dept Math Sardar Patel Rd Chennai 600036 Tamil Nadu India

In this paper, we revisit three existing types of orthogonal lattice (OL) attacks and propose optimized cases to solve approximate common divisor (ACD) problems. In order to reduce both space and time costs, we also make an improved lattice using the rounding technique. Further, we present asymptotic formulas of the time complexities on our optimizations as well as three known OL attacks. Besides, we give specific conditions that the optimized OL attacks can work and show how the attack ability depends on the blocksize beta in the BKZ-beta algorithm. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Approximate common divisor problem lattice Orthogonal lattice attack lattice reduction algorithm

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A New Self-dual BKZ algorithm Based on lattice Sieving 6th

A New Self-dual BKZ Algorithm Based on Lattice Sieving

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6th International Conference on Frontiers in Cyber Security (FCS)

作者： Deng, Xixuan Jia, Huiwen Guangzhou Univ Sch Math & Informat Sci Key Lab Informat Secur Guangzhou Peoples R China Guangzhou Univ Guangzhou Ctr Appl Math Guangzhou Peoples R China

ISBN: (纸本)9789819993307;9789819993314

lattice reduction algorithm is an important algorithm for solving lattice Shortest Vector Problem (SVP), which makes it the primary tool for evaluating the security of lattice-based cryptographic schemes. lattice reduction algorithm's running time and memory depend on the SVP-Oracle used as a subroutine. In this work, we use lattice sieving algorithm as the SVP-Oracle, combined with the Self-Dual BKZ algorithm, to design a new lattice reduction algorithm. Compared to the previous implementations based on enumeration algorithm, our new algorithm can produce more accurate results in less time. In addition, our new algorithm maintains the same computational performance as the state-of-the-art, i.e. the pump and jump BKZ.

关键词： lattice reduction algorithm Security evaluation Self-Dual BKZ lattice sieving

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Implementing Attacks on the Approximate Greatest Common Divisor Problem 2nd

Implementing Attacks on the Approximate Greatest Common Divi...

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2nd International Conference on Frontiers in Cyber Security (FCS)

作者： Wang, Leizhang Qu, Quanbo Li, Tuoyan Chen, Yange Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Xidian Univ Cryptog Res Ctr Xian 710071 Peoples R China Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China Xuchang Univ Sch Informat Engn Xuchang 461000 Peoples R China

ISBN: (纸本)9789811508189;9789811508172

The security of many fully homomorphic encryption (FHE) schemes is guaranteed by the difficulty of the approximate greatest common divisor (AGCD) problem. Therefore, the study of AGCD problem is of great significance to the security of the fully homomorphic encryption. This paper surveys three kinds of attacks on the AGCD problem, i.e. exhaustive search attack, simultaneous Diophantine approximation (SDA) attack and the orthogonal lattice (OL) attack. We utilize the Number Theory Library (NTL) to implement the SDA attack and the optimized OL attack on the AGCD problem. Comparisons are performed based on the experimental results to illustrate that the exhaustive search attack can be easily defended just by increasing the size of q. And increasing the length of the public key is the most effective way to defend SDA attack and OL attack. Meanwhile, we concluded that the success rate of SDA attack and OL attack can be improved by increasing the dimension of lattice at the expense of a certain time efficiency. In addition, the analysis and experiments show that the fully homomorphic computing efficiency of FHE scheme can't be improved by simply increasing the private key without appropriately increasing the size of public key. Otherwise, the FHE scheme is vulnerable to OL and SDA attack. Besides, experimental results show that optimized OL attack performs better than both classical OL attack and SDA attack in terms of attack success rate and the time efficiency.

关键词： Approximate greatest common divisor problem Orthogonal lattice attack Simultaneous diophantine approximation attack lattice reduction algorithm

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A Combination reduction algorithm and Its Application 16th

A Combination Reduction Algorithm and Its Application

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16th International Conference on Network and System Security (NSS)

作者： Yang, Wei Yang, Shaojun Wu, Wei Zhao, Yong Fujian Normal Univ Sch Math & Stat Fuzhou 350117 Peoples R China State Key Lab Cryptol Beijing 100878 Peoples R China Fujian Normal Univ Coll Comp & Cyber Secur Fuzhou 350117 Peoples R China

ISBN: (纸本)9783031230196;9783031230202

After the Snowden incident, cryptographic subversion attack has attracted widespread attentions. Subversion attack is an unconventional attack inside machines, which has strong concealment. It will threaten the security of existing cryptography systems and seriously damage the confidentiality and integrity of communication. In this paper, we construct a subversion attack scheme on the multi-bit version of the learning with errors (LWE) encryption scheme proposed by Peikert, Vaikuntanathan andWaters, which is similar to the construction over the single-bit LWE encryption scheme. During the construction, the NTRU encryption scheme proposed by Zhang et al., is used to encrypt and decrypt the underlying message. In addition, the process of embedding underlying message into LWE ciphertext can be transformed into solving the ISIS problem. Therefore, a subversion attack scheme on the multibit version of LWE encryption scheme can be constructed by solving the ISIS problem successfully. With proper parameters selection, we use BKZ algorithm, BKZ algorithm and segment-LLL combined reduction algorithm to solve the ISIS problem, respectively. Finally, our experiments show that the combination reduction algorithm can improve the success rate of solving ISIS problem, and then promote the attack effect of subversion attack.

关键词： lattice reduction algorithm Subversion attack lattice ISIS

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