Log in

Relevant bibliographies by topics / LLL algorithm / Journal articles

To see the other types of publications on this topic, follow the link: LLL algorithm.

Journal articles on the topic 'LLL algorithm'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'LLL algorithm.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Luk, Franklin T., and Sanzheng Qiao. "A pivoted LLL algorithm." Linear Algebra and its Applications 434, no. 11 (2011): 2296–307. http://dx.doi.org/10.1016/j.laa.2010.04.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Vetter, H., V. Ponnampalam, M. Sandell, and P. A. Hoeher. "Fixed Complexity LLL Algorithm." IEEE Transactions on Signal Processing 57, no. 4 (2009): 1634–37. http://dx.doi.org/10.1109/tsp.2008.2011827.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Luk, Franklin T., and Daniel M. Tracy. "An improved LLL algorithm." Linear Algebra and its Applications 428, no. 2-3 (2008): 441–52. http://dx.doi.org/10.1016/j.laa.2007.02.029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Thiemann, René, Ralph Bottesch, Jose Divasón, Max W. Haslbeck, Sebastiaan J. C. Joosten, and Akihisa Yamada. "Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL." Journal of Automated Reasoning 64, no. 5 (2020): 827–56. http://dx.doi.org/10.1007/s10817-020-09552-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Cao, Ronghui, Julong Wang, Liming Zheng, et al. "Optimizing Lattice Basis Reduction Algorithm on ARM V8 Processors." Applied Sciences 15, no. 4 (2025): 2021. https://doi.org/10.3390/app15042021.

Full text

Abstract:

The LLL (Lenstra–Lenstra–Lovász) algorithm is an important method for lattice basis reduction and has broad applications in computer algebra, cryptography, number theory, and combinatorial optimization. However, current LLL algorithms face challenges such as inadequate adaptation to domestic supercomputers and low efficiency. To enhance the efficiency of the LLL algorithm in practical applications, this research focuses on parallel optimization of the LLL_FP (LLL double-precision floating-point type) algorithm from the NTL library on the domestic Tianhe supercomputer using the Phytium ARM V8 p

APA, Harvard, Vancouver, ISO, and other styles

6

Salleh, N., and H. Kamarulhaili. "On the Properties of Reduced Basis Related to Lattice-Reduced Algorithm." Malaysian Journal of Mathematical Sciences 18, no. 2 (2024): 287–300. http://dx.doi.org/10.47836/mjms.18.2.05.

Full text

Abstract:

The concept of the Shortest Vector Problem (SVP) has surprisingly been used widely in many applications of lattice-based cryptography, notably in public-key cryptanalysis. One of the applications is to develop a well-known algorithm of lattice reduction, namely the LLL (Lenstra-Lenstra-Lovasz) algorithm. The LLL algorithm is known to be able to reduce the basis of a lattice to a minimum set of vectors, which is called the LLL-reduced basis. In this paper, we investigate the properties of the LLL-reduced basis for some different factor δ values. By changing and adjusting the value of factor δ,

APA, Harvard, Vancouver, ISO, and other styles

7

Nguyen, Phong Q., and Damien Stehlé. "An LLL Algorithm with Quadratic Complexity." SIAM Journal on Computing 39, no. 3 (2009): 874–903. http://dx.doi.org/10.1137/070705702.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Song, Kyunghwan, and Yun Am Seo. "A Study on the Average Number of LLL-based Using Statistical Learning." International Journal on Advanced Science, Engineering and Information Technology 14, no. 3 (2024): 906–11. http://dx.doi.org/10.18517/ijaseit.14.3.19890.

Full text

Abstract:

Lattice-based Cryptography is known as one of the key technologies in modern cryptography. This encryption scheme has the basis vectors from the lattice as the public key and a short-length vector in the lattice consisting of an integer combination of the basis vectors as the secret key. To break this encryption, we need to solve the Shortest Vector Problem (SVP), known as NP-hard. Therefore, instead of finding the shortest vector, LLL algorithm is often used to find a vector of sufficiently short length to break the encryption. The LLL algorithm is a well-known method for breaking this encryp

APA, Harvard, Vancouver, ISO, and other styles

9

Zhang, Qi Bo, Su Zhang, Yu Zhang, and Wen Sheng Wang. "Optical Correlation Recognition Research of Low Light Level Target Based on Lifting Wavelet Transform." Key Engineering Materials 552 (May 2013): 529–35. http://dx.doi.org/10.4028/www.scientific.net/kem.552.529.

Full text

Abstract:

Optical correlation technology is an important application in target recognition field, which can apply Joint Transform Correlator (JTC) to achieve target recognition. For the Low Light Level (LLL) target with low contrast and background noise interference, using optical correlation method may reduce the recognition ratio. In order to solve the problem, an effective algorithm-adaptive directional lifting based on wavelet transform (ADL) is used to process LLL target image. LLL image enhancement and target edge extraction are applied in this algorithm. Experimental results show that this algori

APA, Harvard, Vancouver, ISO, and other styles

10

Pohst, M. "A modification of the LLL reduction algorithm." Journal of Symbolic Computation 4, no. 1 (1987): 123–27. http://dx.doi.org/10.1016/s0747-7171(87)80061-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Niu, Zhongfeng, Siwei Sun, and Lei Hu. "On the additive differential probability of ARX construction." Journal of Surveillance, Security and Safety 4, no. 3 (2023): 94–111. http://dx.doi.org/10.20517/jsss.2023.09.

Full text

Abstract:

Aim The additive differential cryptanalysis is a significant technique used in the analysis of ARX ciphers. In this paper, we will focus on accurately and efficiently calculating the additive differential probability of $$ x \lll d \oplus y \lll e $$ . Methods Inspired by the work of Niu et al . at Crypto 2022, we use a delicate partition of $$ \mathbf{F}_2^m \times \mathbf{F}_2^m $$ into subsets. Result We derive an algorithm that can calculate it with linear time complexity. Compared with our algorithm, the one proposed by Velichkov et al . is only suitable when $$ e=0 $$ . Conclusion For th

APA, Harvard, Vancouver, ISO, and other styles

12

Omar, Sapti Guma'a, Mohammed Hussein Qasim, and Tariq Mustafa Al-Ta'i Ziyad. "Dynamic keys generation for internet of things." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 18, no. 2 (2020): 1066–73. https://doi.org/10.11591/ijeecs.v18.i2.pp1066-1073.

Full text

Abstract:

In several aspects, interest in IoT has become considerable by researchers and academics in recent years. Data security becomes one of the important challenges facing development of IoT environment. Many algorithms were proposed to secure the IoT applications. The traditional public key cryptographic are inappropriate because it requires high computational. Therefore, lattice-based public-key cryptosystem (LB-PKC) is a favorable technique for IoT security. NTRU is one of a LB-PKC that based on truncated polynomial ring, it has good features, which make it to be an effective alternative to the

APA, Harvard, Vancouver, ISO, and other styles

13

Deng, Zhongliang, Di Zhu, and Lu Yin. "N-Dimensional LLL Reduction Algorithm with Pivoted Reflection." Sensors 18, no. 1 (2018): 283. http://dx.doi.org/10.3390/s18010283.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Guma'a, Omar Sapti, Qasim Mohammed Hussein, and Ziyad Tariq Mustafa Al-Ta'i. "Dynamic keys generation for internet of things." Indonesian Journal of Electrical Engineering and Computer Science 18, no. 2 (2020): 1066. http://dx.doi.org/10.11591/ijeecs.v18.i2.pp1066-1073.

Full text

Abstract:

<span>In several aspects, interest in IoT has become considerable by researchers and academics in recent years. Data security becomes one of the important challenges facing development of IoT environment. Many algorithms were proposed to secure the IoT applications. The traditional public key cryptographic are inappropriate because it requires high computational. Therefore, lattice-based public-key cryptosystem (LB-PKC) is a favorable technique for IoT security. NTRU is one of a LB-PKC that based on truncated polynomial ring, it has good features, which make it to be an effective alterna

APA, Harvard, Vancouver, ISO, and other styles

15

Li, Xinzhong, Yongliang Xiong, Weiwei Chen, Shaoguang Xu, and Rui Zhang. "Improved GNSS Ambiguity Fast Estimation Reduction Algorithm." Sensors 23, no. 20 (2023): 8568. http://dx.doi.org/10.3390/s23208568.

Full text

Abstract:

The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to improve the efficiency of the lattice basis reduction algorithm. The Householder QR decomposition with minimal column pivoting is utilized to pre-sort the basis vectors and reduce the number of basis vector exchanges during the reduction process by partial size reduction and relaxing the basis vector exchange c

APA, Harvard, Vancouver, ISO, and other styles

16

Huazhang, L., and L. Jianping. "A NOVEL INDEPENDENT PROCESSING LLL ALGORITHM FOR MIMO DETECTION." Telecommunications and Radio Engineering 75, no. 7 (2016): 607–20. http://dx.doi.org/10.1615/telecomradeng.v75.i7.40.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Kodek, Dušan M. "LLL Algorithm and the Optimal Finite Wordlength FIR Design." IEEE Transactions on Signal Processing 60, no. 3 (2012): 1493–98. http://dx.doi.org/10.1109/tsp.2011.2177974.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Cho, Gook Hwa, Hyang-Sook Lee, Seongan Lim, and Yoonjeong Kim. "Storage efficient algorithm for Hermite Normal Form using LLL." Linear Algebra and its Applications 613 (March 2021): 183–200. http://dx.doi.org/10.1016/j.laa.2020.12.022.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Liu, Menglong, Liang Jin, Xiaomei Zhang, and Yilin Fang. "Dynamic Multi-objective Optimization for Coagulating Process of Carbon Fiber Precursor Based on Lifelong Learning." Journal of Physics: Conference Series 2562, no. 1 (2023): 012070. http://dx.doi.org/10.1088/1742-6596/2562/1/012070.

Full text

Abstract:

Abstract Process parameter optimization is an essential link in the coagulating process of carbon fiber. In this paper, considering the dynamic factors of the coagulating bath environment, a dynamic multi-objective optimization problem (DMOP) model for the coagulating process is constructed with process parameters as decision variables and performance indicators as optimization objectives. We combine lifelong learning (LLL) and multi-objective optimization to solve this model and propose a lifelong learning-based dynamic multi-objective evolutionary algorithm (LLL-DMOEA). In LLL-DMOEA, the lif

APA, Harvard, Vancouver, ISO, and other styles

20

OUNI, Nizar, and Ridha BOUALLEGUE. "Modified LLL Algorithm with Shifted Start Column for Complexity Reduction." International Journal of Wireless & Mobile Networks 8, no. 3 (2016): 83–93. http://dx.doi.org/10.5121/ijwmn.2016.8306.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Goldberger, Assaf, and Yossi Strassler. "A practical algorithm for completing half-Hadamard matrices using LLL." Journal of Algebraic Combinatorics 55, no. 1 (2021): 217–44. http://dx.doi.org/10.1007/s10801-021-01077-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

OUNI, Nizar, and Ridha BOUALLEGUE. "Performance and Complexity Analysis of a Reduced Iterations LLL Algorithm." International journal of Computer Networks & Communications 8, no. 3 (2016): 123–35. http://dx.doi.org/10.5121/ijcnc.2016.8309.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Akhavi, Ali. "The optimal LLL algorithm is still polynomial in fixed dimension." Theoretical Computer Science 297, no. 1-3 (2003): 3–23. http://dx.doi.org/10.1016/s0304-3975(02)00616-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Chen, Chien-Yuan, Cheng-Yuan Ku, and David C. Yen. "Cryptanalysis of large RSA exponent by using the LLL algorithm." Applied Mathematics and Computation 169, no. 1 (2005): 516–25. http://dx.doi.org/10.1016/j.amc.2004.10.082.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Li, Kezhao, Chendong Tian, Yingxiang Jiao, and Zhe Yue. "Improved HLLL Lattice Basis Reduction Algorithm to Solve GNSS Integer Ambiguity." International Journal of Aerospace Engineering 2023 (February 15, 2023): 1–8. http://dx.doi.org/10.1155/2023/5978373.

Full text

Abstract:

Recently, lattice theory has been widely used for integer ambiguity resolution in the Global Navigation Satellite System (GNSS). When using lattice theory to deal with integer ambiguity, we need to reduce the correlation between lattice bases to ensure the efficiency of the solution. Lattice reduction is divided into scale reduction and basis vector exchange. The scale reduction has no direct impact on the subsequent search efficiency, while the basis vector exchange directly impacts the search efficiency. Hence, Lenstra-Lenstra-Lovász (LLL) is applied in the ambiguity resolution to improve th

APA, Harvard, Vancouver, ISO, and other styles

26

Zhang, Lu, Baodong Qin, Wen Gao, and Yiyuan Luo. "An Improved Coppersmith Algorithm Based on Block Preprocessing." Mathematics 12, no. 2 (2024): 173. http://dx.doi.org/10.3390/math12020173.

Full text

Abstract:

Since Coppersmith proposed the use of the LLL algorithm to solve univariate modular polynomial equations at EUROCRYPT’96, it has sparked a fervent research interest in lattice analysis among cryptographers. Despite its polynomial-time nature, the LLL algorithm exhibits a high-order polynomial upper bound in terms of theoretical complexity, particularly with longer computation times when applied to high-dimensional lattices. In addressing this issue, we propose an improved algorithm based on block preprocessing, building on the original Coppersmith algorithm and thus providing proof of correctn

APA, Harvard, Vancouver, ISO, and other styles

27

Huazhang, L. "A NOVEL GENERALIZED LLL ALGORITHM IN LATTICE REDUCTION FOR MIMO SYSTEM." Telecommunications and Radio Engineering 76, no. 6 (2017): 491–509. http://dx.doi.org/10.1615/telecomradeng.v76.i6.40.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Chunxiao, D., and Y. Fei. "PERFORMANCE SIMULATION ON LOW- COMPLEXITY LLL-BASED ALGORITHM FOR MIMO SYSTEM." Telecommunications and Radio Engineering 77, no. 14 (2018): 1249–64. http://dx.doi.org/10.1615/telecomradeng.v77.i14.30.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Napias, Huguette. "A generalization of the LLL-algorithm over euclidean rings or orders." Journal de Théorie des Nombres de Bordeaux 8, no. 2 (1996): 387–96. http://dx.doi.org/10.5802/jtnb.176.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Roger, Sandra, Alberto Gonzalez, Vicenc Almenar, and Antonio Vidal. "Extended LLL algorithm for efficient signal precoding in multiuser communication systems." IEEE Communications Letters 14, no. 3 (2010): 220–22. http://dx.doi.org/10.1109/lcomm.2010.03.092235.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

PARK, YUNJU, and JAEHYUN PARK. "ANALYSIS OF THE UPPER BOUND ON THE COMPLEXITY OF LLL ALGORITHM." Journal of the Korea Society for Industrial and Applied Mathematics 20, no. 2 (2016): 107–21. http://dx.doi.org/10.12941/jksiam.2016.20.107.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Ling, Cong, Wai Ho Mow, and Nick Howgrave-Graham. "Reduced and Fixed-Complexity Variants of the LLL Algorithm for Communications." IEEE Transactions on Communications 61, no. 3 (2013): 1040–50. http://dx.doi.org/10.1109/tcomm.2012.010313.120072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Van Der Kallen, Wilberd. "Complexity of the Havas, Majewski, Matthews LLL Hermite Normal Form Algorithm." Journal of Symbolic Computation 30, no. 3 (2000): 329–37. http://dx.doi.org/10.1006/jsco.2000.0374.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Xiao, Zuo Jiang, Xiao Xue Guo, Hai Bin Zhu, Zhi Gang Xu, and Zhi Yong An. "Temperature Control Features and Simulation Research on High and Low Gimbals." Advanced Materials Research 989-994 (July 2014): 3195–98. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.3195.

Full text

Abstract:

In view of characteristics owned by high and low gimbals, for instance pure lag, large inertia, strongly nonlinear and so on, which was employed in low light level (LLL) weapon sight reliability detection system. The basic working principle and mathematical model of Dahlin and Smith predictive control algorithm were mainly researched. And ideal control curves were obtained by software emulation. The simulated results showed that the two algorithms each have their advantages, shortcomings and the proper situations, but as to improve the control efficiency of system, the Dahlin is superior.

APA, Harvard, Vancouver, ISO, and other styles

35

Muisyo, Irene Ndunge, Christopher Maina Muriithi, and Stanley Irungu Kamau. "STATCOM Controller Tuning to Enhance LVRT Capability of Grid-Connected Wind Power Generating Plants." Journal of Electrical and Computer Engineering 2022 (June 25, 2022): 1–26. http://dx.doi.org/10.1155/2022/2873053.

Full text

Abstract:

This paper investigates the utilization of a STATCOM to enhance the LVRT capability of wind power plants (WPPs) during grid faults. The STATCOM under investigation is tuned using the Water Cycle Algorithm (WCA), Particle Swarm Optimization (PSO), and a hybrid algorithm of both WCA and PSO. Simulations are conducted in MATLAB programming software, using the SimScape power system toolbox, where two test systems are investigated: a 9 MW WPP and the IEEE 39 bus test system. Performance analysis is done by investigating the ability of the WPPs to ride through grid voltage sags, with the incorporati

APA, Harvard, Vancouver, ISO, and other styles

36

Liao, Chun-Fu, Li-Wei Chai, and Yuan-Hao Huang. "Loop-Reduction LLL Algorithm and Architecture for Lattice-Reduction-Aided MIMO Detection." Journal of Electrical and Computer Engineering 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/876380.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Lv, Huazhang, and Jianping Li. "A novel hybrid fix-LLL lattice reduction algorithm for MIMO detection system." IEEJ Transactions on Electrical and Electronic Engineering 12, no. 3 (2016): 372–78. http://dx.doi.org/10.1002/tee.22387.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Lapidus, Michel L., Machiel van Frankenhuijsen, and Edward K. Voskanian. "Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm." Mathematics 9, no. 6 (2021): 591. http://dx.doi.org/10.3390/math9060591.

Full text

Abstract:

The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self-similar fractal string. The implication of this procedure is that the set of complex dimensions of a nonlattice string has a quasiperiodic pattern. Using the LSA algorithm, together with the multiprecision polynomial solver MPSolve which is due to D. A. Bini, G. Fiorentino and L. Robol, we give a new and significantly more powerful presentation of t

APA, Harvard, Vancouver, ISO, and other styles

39

Buhler, Joe, and Neal Koblitz. "Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems." Bulletin of the Australian Mathematical Society 58, no. 1 (1998): 147–54. http://dx.doi.org/10.1017/s000497270003207x.

Full text

Abstract:

Using the LLL-algorithm for finding short vectors in lattices, we show how to compute a Jacobi sum for the prime field Fp in Q(e2πi/n) in time O(log3p), where n is small and fixed, p is large, and p = 1 (mod n). This result is useful in the construction of hyperelliptic cryptosystems.

APA, Harvard, Vancouver, ISO, and other styles

40

Li, Jianping. "A Novel Fix-Effective-LLL Algorithm Using Fast-Givens Rotations for MIMO System." Journal of Information and Computational Science 12, no. 12 (2015): 4603–13. http://dx.doi.org/10.12733/jics20106363.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Chen, Lirui, Zuocheng Xing, Yongzhong Li, and Shikai Qiu. "Efficient MIMO Preprocessor With Sorting-Relaxed QR Decomposition and Modified Greedy LLL Algorithm." IEEE Access 8 (2020): 54085–99. http://dx.doi.org/10.1109/access.2020.2980922.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Narayanan, Krishnan. "Review of The LLL Algorithm Edited by Phong Q. Nguyen and Brigitte Vallée." ACM SIGACT News 45, no. 4 (2014): 24–31. http://dx.doi.org/10.1145/2696081.2696086.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Daudé, Hervé, and Brigitte Vallée. "An upper bound on the average number of iterations of the LLL algorithm." Theoretical Computer Science 123, no. 1 (1994): 95–115. http://dx.doi.org/10.1016/0304-3975(94)90071-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Bambang Harjito and Muhammad Fadhli Putra Mulyana. "Comparison of Security Performance of NTRU and ECC Algorithms For RFID Authentication." E3S Web of Conferences 448 (2023): 02047. http://dx.doi.org/10.1051/e3sconf/202344802047.

Full text

Abstract:

The rapid development of the Internet of Things creates information security vulnerabilities due to the unavoidable process of exchanging data. One device that is vulnerable to data security is RFID. One way to increase its security is to embed a cryptosystem in it. The NTRU algorithm can be a solution because of its low computational power. However, ECC is widely used because its computational power requirements are lower than other traditional public key algorithms. This research proposes the implementation and performance analysis of the ECC and NTRU algorithms on RFID devices. Testing is c

APA, Harvard, Vancouver, ISO, and other styles

45

Futa, Yuichi, and Yasunari Shidama. "Isomorphism Theorem on Vector Spaces over a Ring." Formalized Mathematics 25, no. 3 (2017): 171–78. http://dx.doi.org/10.1515/forma-2017-0016.

Full text

Abstract:

Summary In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].

APA, Harvard, Vancouver, ISO, and other styles

46

Tran, Ha Thanh Nguyen. "Computing dimensions of spaces of Arakelov divisors of number fields." International Journal of Number Theory 13, no. 02 (2017): 487–512. http://dx.doi.org/10.1142/s1793042117500270.

Full text

Abstract:

The function [Formula: see text] for a number field is analogous to the dimension of the Riemann–Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for number fields with unit group of rank at most 2, even with large discriminant. This method is based on using LLL-reduced bases, the “jump algorithm” and Poisson summation formula.

APA, Harvard, Vancouver, ISO, and other styles

47

Arimoto, Koichi. "ON THE TERMINATION OF QUASI LLL LATTICE BASIS REDUCTION ALGORITHM OVER GAUSSIAN NUMBER FIELDS." Far East Journal of Mathematical Sciences (FJMS) 109, no. 1 (2018): 175–84. http://dx.doi.org/10.17654/ms109010175.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Ellis, Graham, and Irina Kholodna. "Three-Dimensional Presentations for the Groups of Order at Most 30." LMS Journal of Computation and Mathematics 2 (1999): 93–117. http://dx.doi.org/10.1112/s1461157000000085.

Full text

Abstract:

AbstractFor each group G of order up to 30 we compute a small 3-dimensional CW-space X with π1X≌ G and π2X = 0, and we quantify the ‘efficiency’ of X. Furthermore, we give a theoretical result for treating the case when G is a semi-direct product of two groups for which 3-presentations are known. We also describe the ZG-module structure on the second homotopy group π2X2 of the 2-skeleton of X. This module structure can in principle be used to determine the co-homology groups H2(G, A) and H3(G, A) with coefficients in a ZG-module A. Our computations, which involve the Todd–Coxeter procedure for

APA, Harvard, Vancouver, ISO, and other styles

49

Futa, Yuichi, Hiroyuki Okazaki, Kazuhisa Nakasho, and Yasunari Shidama. "Torsion Z-module and Torsion-free Z-module." Formalized Mathematics 22, no. 4 (2014): 277–89. http://dx.doi.org/10.2478/forma-2014-0028.

Full text

Abstract:

Summary In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lov´asz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11].

APA, Harvard, Vancouver, ISO, and other styles

50

Futa, Yuichi, and Yasunari Shidama. "Embedded Lattice and Properties of Gram Matrix." Formalized Mathematics 25, no. 1 (2017): 73–86. http://dx.doi.org/10.1515/forma-2017-0007.

Full text

Abstract:

Summary In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm [16] and cryptographic systems with lattice [17].

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!