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Computation-Efficient Decoding of LDPC Codes for High-Speed Space Laser Communications
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作者 Hu Zhuojun Chen Zhao +1 位作者 Kuang Linling Yin Liuguo 《China Communications》 2025年第12期108-123,共16页
Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementa... Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementation of low-density paritycheck(LDPC)decoding under resource-restricted space platforms.Particularly,due to the supply restriction and cost issues of high-speed on-board devices such as analog-to-digital converters(ADCs),the input of LDPC decoding will be usually constrained by hard-decision channel output.To tackle this challenge,density-evolution-based theoretical analysis is firstly performed to identify the cause of performance degradation in the conventional binaryinitialized iterative decoding(BIID)algorithm.Then,a computation-efficient decoding algorithm named multiary-initialized iterative decoding with early termination(MIID-ET)is proposed,which improves the error-correcting performance and computation efficiency by using a reliability-based initialization method and a threshold-based decoding termination rule.Finally,numerical simulations are conducted on example codes of rates 7/8 and 1/2 to evaluate the performance of different LDPC decoding algorithms,where the proposed MIID-ET outperforms the BIID with a coding gain of 0.38 dB and variable node calculation saving of 37%.With this advantage,the proposed MIID-ET can notably reduce LDPC decoder’s hardware implementation complexity under the same bit error rate performance,which successfully doubles the total throughput to 10 Gbps on a single-chip FPGA. 展开更多
关键词 computation-efficient decoding highspeed decoders LDPC codes LLR initialization space laser communications
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Research on deep learning decoding method for polar codes in ACO-OFDM spatial optical communication system
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作者 LIU Kangrui LI Ming +2 位作者 CHEN Sizhe QU Jiashun ZHOU Ming’ou 《Optoelectronics Letters》 2025年第7期427-433,共7页
Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbule... Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbulence intensities,the deep learning technique is proposed to the polarization code decoding in ACO-OFDM space optical communication system.Moreover,this system realizes the polarization code decoding and signal demodulation without frequency conduction with superior performance and robustness compared with the performance of traditional decoder.Simulations under different turbulence intensities as well as different mapping orders show that the convolutional neural network(CNN)decoder trained under weak-medium-strong turbulence atmospheric channels achieves a performance improvement of about 10^(2)compared to the conventional decoder at 4-quadrature amplitude modulation(4QAM),and the BERs for both 16QAM and 64QAM are in between those of the conventional decoder. 展开更多
关键词 frequency conduction polar codes deep learning signal demodulation deep learning technique decoding ACO OFDM polarization code decoding
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Low Complexity Successive Cancellation List Decoding of U-UV Codes
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作者 Chen Wenhao Chen Li +1 位作者 Lin Jingyu Zhang Huazi 《China Communications》 2025年第1期41-60,共20页
Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-med... Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-medium length regime.However,this list decoding complexity becomes formidable as the decoding output list size increases.This is primarily incurred by the OSD.Addressing this challenge,this paper proposes the low complexity SCL decoding through reducing the complexity of component code decoding,and pruning the redundant SCL decoding paths.For the former,an efficient skipping rule is introduced for the OSD so that the higher order decoding can be skipped when they are not possible to provide a more likely codeword candidate.It is further extended to the OSD variant,the box-andmatch algorithm(BMA),in facilitating the component code decoding.Moreover,through estimating the correlation distance lower bounds(CDLBs)of the component code decoding outputs,a path pruning(PP)-SCL decoding is proposed to further facilitate the decoding of U-UV codes.In particular,its integration with the improved OSD and BMA is discussed.Simulation results show that significant complexity reduction can be achieved.Consequently,the U-UV codes can outperform the cyclic redundancy check(CRC)-polar codes with a similar decoding complexity. 展开更多
关键词 ordered statistics decoding successive cancellation list decoding U-UV codes
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Large Language Models With Contrastive Decoding Algorithm for Hallucination Mitigation in Low-Resource Languages
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作者 Zan Hongying Arifa Javed +2 位作者 Muhammad Abdullah Javed Rashid Muhammad Faheem 《CAAI Transactions on Intelligence Technology》 2025年第4期1104-1117,共14页
Neural machine translation(NMT)has advanced with deep learning and large-scale multilingual models,yet translating lowresource languages often lacks sufficient training data and leads to hallucinations.This often resu... Neural machine translation(NMT)has advanced with deep learning and large-scale multilingual models,yet translating lowresource languages often lacks sufficient training data and leads to hallucinations.This often results in translated content that diverges significantly from the source text.This research proposes a refined Contrastive Decoding(CD)algorithm that dynamically adjusts weights of log probabilities from strong expert and weak amateur models to mitigate hallucinations in lowresource NMT and improve translation quality.Advanced large language NMT models,including ChatGLM and LLaMA,are fine-tuned and implemented for their superior contextual understanding and cross-lingual capabilities.The refined CD algorithm evaluates multiple candidate translations using BLEU score,semantic similarity,and Named Entity Recognition accuracy.Extensive experimental results show substantial improvements in translation quality and a significant reduction in hallucination rates.Fine-tuned models achieve higher evaluation metrics compared to baseline models and state-of-the-art models.An ablation study confirms the contributions of each methodological component and highlights the effectiveness of the refined CD algorithm and advanced models in mitigating hallucinations.Notably,the refined methodology increased the BLEU score by approximately 30%compared to baseline models. 展开更多
关键词 ChatGLM contrastive decoding HALLUCINATION LLAMA LLM low resource NMT
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Modulation of tRNA^(Cln)decoding efficacy by metal ion binding and glutamine supply
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作者 Yuxuan Shen Tianchang Wang +3 位作者 Hua Qiao Qing Liang Jingru Lv Qing Xia 《Journal of Chinese Pharmaceutical Sciences》 2025年第1期28-40,共13页
Transfer RNAs(tRNAs)adopt a stable L-shaped tertiary structure crucial for their involvement in protein translation.Among various divalent metal ions,magnesium ions play a pivotal role in preserving the tertiary struc... Transfer RNAs(tRNAs)adopt a stable L-shaped tertiary structure crucial for their involvement in protein translation.Among various divalent metal ions,magnesium ions play a pivotal role in preserving the tertiary structure of tRNA.However,the precise location of the Mg^(2+)binding pocket in human tRNA remains elusive.In this investigation,we identified the Mg^(2+)binding site within human tRNAGln using suppressor tRNA^(Gln).This variant of tRNA recognizes premature stop codons(specificlly UAG)and facilitates the expression of fll-length proteis.By mutating sites 8 and C72 in supprssr tRNAcl,we assessed the decoding efficiency of the resulting mutant suppressor tRNAs,which serves as a measure of tRNA's ability to decode genetic information.Our analysis revealed that the U8C mutant suppressor tRNA exhibited a significantly lower Mg^(2+)content compared to the C72U mutant.Furthermore,we observed a notable reduction in decoding efficiency in the U8-mutated suppressor tRNA,as evidenced by GFP fluorescence and Western blotting analysis.Conversely,mutations at the C72 site had a comparatively minor impact on decoding efficiency.These findings underscored the tight binding of Mg^(2+)to the U8 site of human tRNAGln,crucial for maintaining the stability of tRNA tertiary structure and translation efficacy.Additionally,our investigation delved into the influence of glutamine availability on tRNA decoding efficiency at the cellular level.The results indicated that both the concentration of amino acids and the codon context of TAG could modulate tRNA decoding efficiency.This study provided valuable insights into the structure and function of tRNA,laying the groundwork for further exploration in this field. 展开更多
关键词 Metal ions tRNA tertiary structure Glutamine supply decoding efficacy
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Decoding of Surface Meteorological Observation Data Files and Application Research on Climatic Data
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作者 Hui LIANG Xianqiang SU Qingyun ZHU 《Meteorological and Environmental Research》 2025年第2期16-21,25,共7页
In this paper,Wuzhou City of Guangxi was taken as the research object.Through the design of a climatic data warehousing system,the decoding methods of surface meteorological data and their application in the managemen... In this paper,Wuzhou City of Guangxi was taken as the research object.Through the design of a climatic data warehousing system,the decoding methods of surface meteorological data and their application in the management of climatic data were explored.Based on the parsing technology of the monthly report of surface meteorological records(A-file),the design of Wuzhou climatic data warehousing system was realized,completing the precise extraction and database construction of observational elements such as regional temperature,wind direction,and weather phenomena.Based on this system,the meteorological data in 2024 were analyzed,and the probabilistic characteristics of dominant wind direction in Wuzhou(northeast wind accounting for the largest proportion),the spatiotemporal distribution patterns of extreme temperatures(annual extreme high temperature of 37.1℃in August and extreme low temperature of 1.9℃in January),and the general climatic overview of Wuzhou City(annual precipitation 3.2%higher than the standard value)were revealed.The research shows that climate change has a significant impact on agricultural production and economic development in Wuzhou City,and the construction of a reasonable climatic data database is of great significance for enhancing professional meteorological service capabilities in the context of climate change.This study not only provides a scientific basis for the economic development of Wuzhou region,but also offers reference ideas for other regions to cope with regional climate adaptation planning. 展开更多
关键词 Surface meteorological observation A-file decoding Climatic database Climate change
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An Efficient Temporal Decoding Module for Action Recognition
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作者 HUANG Qiubo MEI Jianmin +3 位作者 ZHAO Wupeng LU Yiru WANG Mei CHEN Dehua 《Journal of Donghua University(English Edition)》 2025年第2期187-196,共10页
Action recognition,a fundamental task in the field of video understanding,has been extensively researched and applied.In contrast to an image,a video introduces an extra temporal dimension.However,many existing action... Action recognition,a fundamental task in the field of video understanding,has been extensively researched and applied.In contrast to an image,a video introduces an extra temporal dimension.However,many existing action recognition networks either perform simple temporal fusion through averaging or rely on pre-trained models from image recognition,resulting in limited temporal information extraction capabilities.This work proposes a highly efficient temporal decoding module that can be seamlessly integrated into any action recognition backbone network to enhance the focus on temporal relationships between video frames.Firstly,the decoder initializes a set of learnable queries,termed video-level action category prediction queries.Then,they are combined with the video frame features extracted by the backbone network after self-attention learning to extract video context information.Finally,these prediction queries with rich temporal features are used for category prediction.Experimental results on HMDB51,MSRDailyAct3D,Diving48 and Breakfast datasets show that using TokShift-Transformer and VideoMAE as encoders results in a significant improvement in Top-1 accuracy compared to the original models(TokShift-Transformer and VideoMAE),after introducing the proposed temporal decoder.The introduction of the temporal decoder results in an average performance increase exceeding 11%for TokShift-Transformer and nearly 5%for VideoMAE across the four datasets.Furthermore,the work explores the combination of the decoder with various action recognition networks,including Timesformer,as encoders.This results in an average accuracy improvement of more than 3.5%on the HMDB51 dataset.The code is available at https://github.com/huangturbo/TempDecoder. 展开更多
关键词 action recognition video understanding temporal relationship temporal decoder TRANSFORMER
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An Optimization of Weak Key Attacks Based on the BGF Decoding Algorithm
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作者 Bing Liu Ting Nie +1 位作者 Yansong Liu Weibo Hu 《Computers, Materials & Continua》 2025年第9期4583-4599,共17页
Among the four candidate algorithms in the fourth round of NIST standardization,the BIKE(Bit Flipping Key Encapsulation)scheme has a small key size and high efficiency,showing good prospects for application.However,th... Among the four candidate algorithms in the fourth round of NIST standardization,the BIKE(Bit Flipping Key Encapsulation)scheme has a small key size and high efficiency,showing good prospects for application.However,the BIKE scheme based on QC-MDPC(Quasi Cyclic Medium Density Parity Check)codes still faces challenges such as the GJS attack and weak key attacks targeting the decoding failure rate(DFR).This paper analyzes the BGF decoding algorithm of the BIKE scheme,revealing two deep factors that lead to DFR,and proposes a weak key optimization attack method for the BGF decoding algorithm based on these two factors.The proposed method constructs a new weak key set,and experiment results eventually indicate that,considering BIKE’s parameter set targeting 128-bit security,the average decryption failure rate is lowerly bounded by.This result not only highlights a significant vulnerability in the BIKE scheme but also provides valuable insights for future improvements in its design.By addressing these weaknesses,the robustness of QC-MDPC code-based cryptographic systems can be enhanced,paving the way for more secure post-quantum cryptographic solutions. 展开更多
关键词 BIKE BGF decoding algorithm weak key attack GJS attack
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Improved Polytope Generation for CRC-Aided Adaptive Linear Programming Polar Decoding
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作者 Xie Mutong Du Zhongze +2 位作者 Zou Guoxue Tian Lin Yuan Jinhong 《China Communications》 2025年第12期124-136,共13页
Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long bee... Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions. 展开更多
关键词 codeword polytope cyclic redundancy check 5G NR linear programming decoding polar code
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Multi-protocol quantum key distribution decoding chip
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作者 Chun-Xue Zhang Jian-Guang Li +3 位作者 Yue Wang Wei Chen Jia-Shun Zhang Jun-Ming An 《Chinese Physics B》 2025年第5期34-41,共8页
Quantum key distribution(QKD)is a method for secure communication that utilizes quantum mechanics principles to distribute cryptographic keys between parties.Integrated photonics offer benefits such as compactness,sca... Quantum key distribution(QKD)is a method for secure communication that utilizes quantum mechanics principles to distribute cryptographic keys between parties.Integrated photonics offer benefits such as compactness,scalability,energy efficiency and the potential for extensive integration.We have achieved BB84 phase encoding and decoding,time-bin phase QKD,and the coherent one-way(COW)protocol on a planar lightwave circuit(PLC)platform.At the optimal temperature,our chip successfully prepared quantum states,performed decoding and calculated the secure key rate of the time-bin phasedecoding QKD to be 80.46 kbps over a 20 km transmission with a quantum bit error rate(QBER)of 4.23%.The secure key rate of the COW protocol was 18.18 kbps,with a phase error rate of 3.627%and a time error rate of 0.377%.The uniqueness of this technology lies in its combination of high integration and protocol flexibility,providing an innovative solution for the development of future quantum communication networks. 展开更多
关键词 quantum key distribution(QKD) secure key rate decoding chip quantum bit error rate
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DDFNet:real-time salient object detection with dual-branch decoding fusion for steel plate surface defects
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作者 Tao Wang Wang-zhe Du +5 位作者 Xu-wei Li Hua-xin Liu Yuan-ming Liu Xiao-miao Niu Ya-xing Liu Tao Wang 《Journal of Iron and Steel Research International》 2025年第8期2421-2433,共13页
A novel dual-branch decoding fusion convolutional neural network model(DDFNet)specifically designed for real-time salient object detection(SOD)on steel surfaces is proposed.DDFNet is based on a standard encoder–decod... A novel dual-branch decoding fusion convolutional neural network model(DDFNet)specifically designed for real-time salient object detection(SOD)on steel surfaces is proposed.DDFNet is based on a standard encoder–decoder architecture.DDFNet integrates three key innovations:first,we introduce a novel,lightweight multi-scale progressive aggregation residual network that effectively suppresses background interference and refines defect details,enabling efficient salient feature extraction.Then,we propose an innovative dual-branch decoding fusion structure,comprising the refined defect representation branch and the enhanced defect representation branch,which enhance accuracy in defect region identification and feature representation.Additionally,to further improve the detection of small and complex defects,we incorporate a multi-scale attention fusion module.Experimental results on the public ESDIs-SOD dataset show that DDFNet,with only 3.69 million parameters,achieves detection performance comparable to current state-of-the-art models,demonstrating its potential for real-time industrial applications.Furthermore,our DDFNet-L variant consistently outperforms leading methods in detection performance.The code is available at https://github.com/13140W/DDFNet. 展开更多
关键词 Steel plate surface defect Real-time detection Salient object detection Dual-branch decoder Multi-scale attention fusion Multi-scale residual fusion
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Decoding the Commercial“Rubik’s Cube”In the New Consumption Era
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作者 Ada Wang Zhang Ximeng 《China's Foreign Trade》 2025年第2期49-52,共4页
The 51st China Beijing International Gifts,Premium and Houseware Exhibition(hereinafter referred to as the Gifts Exhibition) officially opened the kaleidoscope of creative gifts at China International Exhibition Cente... The 51st China Beijing International Gifts,Premium and Houseware Exhibition(hereinafter referred to as the Gifts Exhibition) officially opened the kaleidoscope of creative gifts at China International Exhibition Center (Chaoyang Pavilion) on March 20th.More than 900 exhibitors built an aesthetic corridor of quality life with 200,000 gifts. 展开更多
关键词 Chaoyang Pavilion premium houseware exhibition new consumption era kaleidoscope creative gifts commercial decoding creative gifts China International Exhibition Center Rubiks cube
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Decoding Quantum Search Advantage:The Critical Role of State Properties in Random Walks
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作者 Si-Qi Zhou Jin-Min Liang +3 位作者 Zi-Heng Ding Zhi-Hua Chen Shao-Ming Fei Zhi-Hao Ma 《Chinese Physics Letters》 2025年第9期88-101,共14页
Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we de... Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning. 展开更多
关键词 derive exact analytical expressions quantum search establishing comprehensive theoretical framework understand quantum advantage quantum random walk ENTANGLEMENT success probability decode quantum search advantage COHERENCE
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一个快速的二进制多重精度gcd算法 被引量:3
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作者 罗永龙 黄刘生 周智 《中国科学技术大学学报》 CAS CSCD 北大核心 2002年第5期542-545,共4页
求两个整数的最大公因子 (gcd)的经典的Euclid算法时间复杂度为O(ln3 n) ,不适宜于多重精度运算 .论文证明了gcd的相关性质 ,提出了一个基于二进制的、适用于多重精度运算的改进算法 ,其时间复杂度为O(ln2 n)
关键词 二进制 多重精度gcd算法 Euclid算法 最大公因子 时间复杂度 公钥密码体制
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幂GCD矩阵及幂LCM矩阵的行列式的非整除性 被引量:2
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作者 谭千蓉 林宗兵 《武汉大学学报(理学版)》 CAS CSCD 北大核心 2010年第4期383-386,共4页
当S是任一因子链,且|S|≥2时,给出了幂GCD矩阵及幂LCM矩阵的行列式的计算公式,并且得到了一个关于其行列式的非整除性的结果.
关键词 整除 因子链 gcd矩阵 幂LCM矩阵
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基于整数近似GCD的全同态加密方案 被引量:2
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作者 于志敏 古春生 景征骏 《计算机应用研究》 CSCD 北大核心 2014年第7期2105-2108,共4页
设计了基于整数近似GCD问题新的全同态加密方案。跟随Gentry设计模式,构造somewhat同态加密方案,并归约其安全性到整数近似GCD;引入稀疏子集和难度假设来压缩解密电路,使其具有自举性;最后转换somewhat同态加密方案到全同态加密方案。... 设计了基于整数近似GCD问题新的全同态加密方案。跟随Gentry设计模式,构造somewhat同态加密方案,并归约其安全性到整数近似GCD;引入稀疏子集和难度假设来压缩解密电路,使其具有自举性;最后转换somewhat同态加密方案到全同态加密方案。与文献[1]方案相比,提出的somewhat同态加密方案更接近于文献[2]中公钥加密方案。 展开更多
关键词 近似整数最大公因数 公钥方案 全同态加密 稀疏子集和问题
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关于二进制GCD算法的注记 被引量:1
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作者 孙翠芳 《中国科学技术大学学报》 CAS CSCD 北大核心 2004年第1期126-127,共2页
Luo et al wrote in a recent paper [A Fast Algorithm for Computing gcd Based on Binary Multi Precision,this journal,2002,Vol.32,No.5,pp.542 545; MR 2003h:11161 ] that “the classical Euclid’s algorithm for computing t... Luo et al wrote in a recent paper [A Fast Algorithm for Computing gcd Based on Binary Multi Precision,this journal,2002,Vol.32,No.5,pp.542 545; MR 2003h:11161 ] that “the classical Euclid’s algorithm for computing the gcd of two integers takes time O(\%ln\% 3N)”, and “present” an improved algorithm (called “binary gcd” for short) based on binary multi precision with time complexity O(\%ln\% 2N). In this paper,we point out two well known facts: firstly,the binary gcd,without usefull implimentation improvements, is identical in mathematical theory to Stein’s Binary GCD algorithm published in 1967; secondly,both Euclid’s algorithm and Binary GCD have the same time complexity O(\%ln\% 2N). 展开更多
关键词 最大公因子(gcd) Euclid算法 二进制gcd算法
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GCD整环与自反模 被引量:3
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作者 王芳贵 《数学年刊(A辑)》 CSCD 北大核心 1994年第2期241-245,共5页
本文证明了凝聚整环是GCD整环当且仅当秩为1的自反模是自由模.同时还得到有限弱整体维数的凝聚整环是GCD整环当且仅当Pic(R)=1.特别地,有限整体维数的Noether整环是UFD当且仅当Pic(R)=1.
关键词 凝聚整环 自反模 gcd整环 自由模
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幂GCD矩阵与幂LCM矩阵的行列式的整除性
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作者 谭千蓉 李思霖 《华中师范大学学报(自然科学版)》 CAS CSCD 北大核心 2009年第4期541-544,共4页
设S={x_1,x_2,…,x_n}是由n个不同的正整数组成的集合,并设整数a≥1,如果n阶矩阵的第i行j列元素是S中元素x_i和x_j的最大公因子的a次幂(x_i,x_j)~a,则称该矩阵是定义在S上的a次幂GCD矩阵,用(S^a)表示.类似定义幂LCM矩阵[S^a].本文证明了... 设S={x_1,x_2,…,x_n}是由n个不同的正整数组成的集合,并设整数a≥1,如果n阶矩阵的第i行j列元素是S中元素x_i和x_j的最大公因子的a次幂(x_i,x_j)~a,则称该矩阵是定义在S上的a次幂GCD矩阵,用(S^a)表示.类似定义幂LCM矩阵[S^a].本文证明了:设S是由n个不同的正整数组成的一个最大公因子封闭集,且正整数a|b.如果n≤3,那么det(S^a)|det[S^b];如果,那么det(S^a)|det[S^b]. 展开更多
关键词 整除 因子链 最大型因子 gcd矩阵 幂LCM矩阵
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基于GCD算法的GF(2^m)上高速带模除法
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作者 丁勇 桂丰 《通信学报》 EI CSCD 北大核心 2008年第10期199-204,共6页
对常规GCD算法进行了深入分析,改进了算法的判断标准和体系结构,使得每轮迭代中的比较次数由4次降低为3次,与此同时,迭代次数不再固定为2m,改变成上限为分母的长度与m之和,从根本上加快了GCD算法的效率。在此基础上,根据A.Zadeh的思想,... 对常规GCD算法进行了深入分析,改进了算法的判断标准和体系结构,使得每轮迭代中的比较次数由4次降低为3次,与此同时,迭代次数不再固定为2m,改变成上限为分母的长度与m之和,从根本上加快了GCD算法的效率。在此基础上,根据A.Zadeh的思想,将新算法分别扩展到基4、基8,比较次数分别降低为50%和34%,从而大大缩短了计算时间。通过MATLAB实验验证了算法改进取得了很好的效果。 展开更多
关键词 gcd算法 有限域 基数8
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