Relevant bibliographies by topics / LLL algorithm

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'LLL algorithm'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "LLL algorithm"

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.

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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.

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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.

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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.

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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.

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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
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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.

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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,
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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.

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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.

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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
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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.

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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
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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.

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Dissertations / Theses on the topic "LLL algorithm"

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Pineda, Gerwin. "An application of the LLL algorithm to integer factorization." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531350449773791.

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Filip, Silviu-Ioan. "Robust tools for weighted Chebyshev approximation and applications to digital filter design." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN063/document.

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De nombreuses méthodes de traitement du signal reposent sur des résultats puissants d'approximation numérique. Un exemple significatif en est l'utilisation de l'approximation de type Chebyshev pour l'élaboration de filtres numériques.En pratique, le caractère fini des formats numériques utilisés en machine entraîne des difficultés supplémentaires pour la conception de filtres numériques (le traitement audio et le traitement d'images sont deux domaines qui utilisent beaucoup le filtrage). La majorité des outils actuels de conception de filtres ne sont pas optimisés et ne certifient pas non plus
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Zeitoun, Rina. "Méthodes algébriques pour l'analyse de sécurité des implantations d'algorithmes cryptographiques." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066310/document.

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Le 10ème problème de Hilbert, consistant à trouver les solutions entières d'équations polynomiales est un problème crucial en cryptanalyse. Si ce dernier a été prouvé indécidable, Coppersmith publia en 1996 une méthode basée sur la réduction de réseaux permettant de trouver efficacement l'ensemble des petites solutions de certaines équations polynomiales. De nombreuses applications de cette méthode ont vu le jour dans le domaine de la cryptanalyse à clé publique, notamment lorsque le cryptosystème est exécuté sur un système embarqué et qu'une partie de la clé secrète est dévoilée par la réalis
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Zeitoun, Rina. "Méthodes algébriques pour l'analyse de sécurité des implantations d'algorithmes cryptographiques." Electronic Thesis or Diss., Paris 6, 2015. http://www.theses.fr/2015PA066310.

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Le 10ème problème de Hilbert, consistant à trouver les solutions entières d'équations polynomiales est un problème crucial en cryptanalyse. Si ce dernier a été prouvé indécidable, Coppersmith publia en 1996 une méthode basée sur la réduction de réseaux permettant de trouver efficacement l'ensemble des petites solutions de certaines équations polynomiales. De nombreuses applications de cette méthode ont vu le jour dans le domaine de la cryptanalyse à clé publique, notamment lorsque le cryptosystème est exécuté sur un système embarqué et qu'une partie de la clé secrète est dévoilée par la réalis
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Zhou, Tianyang 1980. "Modified LLL algorithms." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99356.

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Lattice basis reduction arises from many applications, such as cryptography, communications, GPS and so on. This thesis is concerned with the widely used LLL reduction. We cast it as a QRZ matrix factorization for real bases. Based on the matrix factorization, we first give the real version of the LLL algorithm (the original LLL algorithm is for integer bases). Then we propose three modified algorithms to improve the computational efficiency, while the reduced matrices satisfy the LLL-reduced criteria. The first modified algorithm, to be referred to as MLLLPIVOT, uses a block pivoting strategy
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Vera, Antonio. "Analyses de l'algorithme de Gauss : applications à l'analyse de l'algorithme LLL." Phd thesis, Université de Caen, 2009. http://tel.archives-ouvertes.fr/tel-01073359.

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Cette thèse est dédiée à l'analyse probabiliste d'algorithmes de réduction des réseaux euclidiens. Un réseau euclidien est l'ensemble de combinaisons linéaires à coefficients entiers d'une base (b_1,..., b_n ) \subset R^n. La réduction d'un réseau consiste a en trouver une base formée de vecteurs assez courts et assez orthogonaux, à partir d'une base donnée en entrée. Le célèbre algorithme LLL résout ce problème de manière efficace en dimension arbitraire. Il est très utilisé, mais mal compris. Nous nous concentrons sur son analyse dans le cas n = 2, où LLL devient l'algorithme de Gauss, car c
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Xiao, Yancheng. "Two floating point LLL reduction algorithms." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=114503.

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The Lenstra, Lenstra and Lov\'sz (LLL) reduction is the most popular lattice reduction and is a powerful tool for solving many complex problems in mathematics and computer science. The blocking technique casts matrix algorithms in terms of matrix-matrix operations to permit efficient reuse of data in the algorithms. In this thesis, we use the blocking technique to develop two floating point block LLL reduction algorithms, the left-to-right block LLL (LRBLLL) reduction algorithm and the alternating partition block LLL (APBLLL) reduction algorithm, and give the complexity analysis of these two a
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Guedj, Michaël. "BSP algorithms for LTL & CTL model checking of security protocols." Thesis, Paris Est, 2012. http://www.theses.fr/2012PEST1081.

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Dans un monde fortement dépendant de la communication de données distribuées, la conception d’infrastructures sécurisées est une tâche cruciale. Les systèmes et réseaux distribués prennent de plus en plus d’importance, car la plupart des services et des possibilités qui caractérisent la société moderne sont basés sur ces technologies.La communication entre les agents sur les réseaux a donc suscité un grand intérêt pour la recherche. Afin de fournir des moyens de communication efficaces et fiables, de plus en plus de protocoles de communication sont inventés, et pour la plupart d’entre eux, la
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Basiri, Abdolali. "Bases de Gröbner et LLL : arithmétique rapide des courbes C ab." Paris 6, 2003. http://www.theses.fr/2003PA066358.

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Baltrušaitis, Vytautas. "LLE algoritmo taikymas daugiamačiams duomenims vizualizuoti." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20090630_095032-57163.

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Šiame darbe buvo tiriama LLE algoritmo darbo kokybės priklausomybė nuo vienintelio tam įtakos turinčio parametro, tai taško kaimynų naudojamų skaičiavimams skaičiaus k. Taip pat buvo tiriamas keturių topologijos išlaikymo įverčių: Spirmano koeficiento, liekamosios dispersijos, DS paklaidos ir Prokrusto analizės tinkamumas LLE algoritmo darbo rezultatų kokybės įvertinimui, ir galimybė panaudojant juos parinkti geriausias taško kaimynų naudojamų skaičiavimuose skaičiaus k reikšmes, ar reikšmių intervalus. Tyrimai atlikti naudojant MATLAB 7.1programinę terpę.<br>The paper Application of LLE algor
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Books on the topic "LLL algorithm"

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Nguyen, Phong Q., and Brigitte Vallée, eds. The LLL Algorithm. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-02295-1.

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Brigitte, Vallée, and SpringerLink (Online service), eds. The LLL Algorithm: Survey and Applications. Springer-Verlag Berlin Heidelberg, 2010.

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Nguyen, Phong Q., and Brigitte Vall E. The LLL Algorithm. Springer, 2010.

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Nguyen, Phong Q., and Brigitte Vallée. The LLL Algorithm: Survey and Applications. Springer, 2012.

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Bremner, Murray R. Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications. Taylor & Francis Group, 2011.

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Bremner, Murray R. Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications. Taylor & Francis Group, 2011.

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Bremner, Murray R. Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications. Taylor & Francis Group, 2011.

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Lattice basis reduction: An introduction to the LLL algorithm and its applications. Taylor & Francis, 2012.

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Mahl, Matthias. Konstruktion Guter Abc-Tripel Mit Dem Lll-Algorithmus. GRIN Verlag GmbH, 2010.

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Book chapters on the topic "LLL algorithm"

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Smeets, Ionica, Arjen Lenstra, Hendrik Lenstra, László Lovász, and Peter van Emde Boas. "The History of the LLL-Algorithm." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_1.

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May, Alexander. "Using LLL-Reduction for Solving RSA and Factorization Problems." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_10.

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Hoffstein, Jeff, Nick Howgrave-Graham, Jill Pipher, and William Whyte. "Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_11.

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Gentry, Craig. "The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_12.

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Micciancio, Daniele. "Cryptographic Functions from Worst-Case Complexity Assumptions." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_13.

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Khot, Subhash. "Inapproximability Results for Computational Problems on Lattices." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_14.

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Regev, Oded. "On the Complexity of Lattice Problems with Polynomial Approximation Factors." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_15.

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Nguyen, Phong Q. "Hermite’s Constant and Lattice Algorithms." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_2.

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Vallée, Brigitte, and Antonio Vera. "Probabilistic Analyses of Lattice Reduction Algorithms." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_3.

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Schnorr, Claus Peter. "Progress on LLL and Lattice Reduction." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_4.

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Conference papers on the topic "LLL algorithm"

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Tan, Zhijie, Yuzhi Li, Xiang Yuan, Shengwei Meng, Weiping Li, and Tong Mo. "LLM-MHR: A LLM-Augmented Multimodal Hashtag Recommendation Algorithm." In 2024 IEEE International Conference on Web Services (ICWS). IEEE, 2024. http://dx.doi.org/10.1109/icws62655.2024.00100.

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Nie, Runze, Hao Wu, Lan Ma, Zhenyu Liu, Zhigang Wang, and Ping Zhang. "Towards a Conversational Invoice Issuance LLM-Based Agent." In 2024 7th International Conference on Algorithms, Computing and Artificial Intelligence (ACAI). IEEE, 2024. https://doi.org/10.1109/acai63924.2024.10899737.

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Qin, Dayu, Yan Yi, and Ercan E. Kuruoglu. "Graph LLM-Based Portfolio Management Algorithm." In 2025 IEEE Conference on Artificial Intelligence (CAI). IEEE, 2025. https://doi.org/10.1109/cai64502.2025.00032.

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Fan, Sunjia, Yichao Yang, Weiqi Huang, Ke Ma, Yucen Liu, and Yuxin Zheng. "Defense methods against multi-language and multi-intent LLM attacks." In International Conference on Algorithms, High Performance Computing and Artificial Intelligence, edited by Pavel Loskot and Liang Hu. SPIE, 2024. http://dx.doi.org/10.1117/12.3051624.

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Zhong, Huageng, Xiao Wei, and Huiran Zhang. "Leveraging LLM for Enhancing Document-Level Relation Extraction with Correction and Completion." In 2025 8th International Conference on Advanced Algorithms and Control Engineering (ICAACE). IEEE, 2025. https://doi.org/10.1109/icaace65325.2025.11019681.

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Huang, Tianyi, Jingyuan Yi, Peiyang Yu, and Xiaochuan Xu. "Unmasking Digital Falsehoods: A Comparative Analysis of LLM-Based Misinformation Detection Strategies." In 2025 8th International Conference on Advanced Algorithms and Control Engineering (ICAACE). IEEE, 2025. https://doi.org/10.1109/icaace65325.2025.11020217.

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Cen, Shipeng, and Ying Tan. "LLM-Driven Customizable Fireworks Algorithm for Diverse Optimization Tasks." In 2025 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2025. https://doi.org/10.1109/cec65147.2025.11043019.

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Duan, Zhihua, and Jialin Wang. "Enhancing Multi-Agent Consensus Through Third-Party LLM Integration: Analyzing Uncertainty and Mitigating Hallucinations in Large Language Models." In 2025 8th International Conference on Advanced Algorithms and Control Engineering (ICAACE). IEEE, 2025. https://doi.org/10.1109/icaace65325.2025.11019272.

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Siddheshwar, Anagha, Anirudh G. Joshi, Agnel Elizabeth, Arnab Karmakar, and Badri Prasad V. R. "Survival of the Smallest: Genetic Algorithms for LLM Compression." In 2025 15th International Conference on Electrical Engineering (ICEENG). IEEE, 2025. https://doi.org/10.1109/iceeng64546.2025.11031301.

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Feng, Chunyu, Juanjuan Yu, Lei Shao, Ji Li, Chao Li, and Hongli Liu. "Fan Bearing Fault Diagnosis Algorithm Based on Improved VMD and LLe." In 2024 IEEE International Conference on Mechatronics and Automation (ICMA). IEEE, 2024. http://dx.doi.org/10.1109/icma61710.2024.10633020.

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Reports on the topic "LLL algorithm"

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Vemuri, V. R. Genetic algorithms at UC Davis/LLNL. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10122640.

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Stone, D. K. Comprehensive Angular Response Study of LLNL Panasonic Dosimeter Configurations and Artificial Intelligence Algorithm. Office of Scientific and Technical Information (OSTI), 2017. http://dx.doi.org/10.2172/1373656.

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Cowell and Roesch. PR-283-14204-R01 SoLoNOx Low Load Controls to Reduce Emissions for Less Restrictive Load Following. Pipeline Research Council International, Inc. (PRCI), 2016. http://dx.doi.org/10.55274/r0011016.

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A Mobile Emissions Lab (MEL) and two site visits for extensive low load emissions mapping were used to document the emissions performance of the test unit over a 10 month period from June 2015 to April 2016. Data was collected over a wide ambient temperature range from 35 to 108?F. The field trial has demonstrated that the new algorithm results in a significant reduction in NOx, CO and UHC emissions from idle to 50% load. Reductions in CO and UHC emission of 50 to 99% were demonstrated from idle to 50% load. NOx emissions reductions were slightly less ranging from 20 to 75% from idle to 50% lo
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Stone, Daniel K. Comprehensive Angular Response Study of LLNL Panasonic Dosimeter Configurations and Artificial Intelligence Algorithm (Rev. 1). Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1529829.

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Akbari, H., L. Rainer, K. Heinemeier, J. Huang, and E. Franconi. Measured commercial load shapes and energy-use intensities and validation of the LBL end-use disaggregation algorithm. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/6402888.

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Akbari, H., L. Rainer, K. Heinemeier, J. Huang, and E. Franconi. Measured commercial load shapes and energy-use intensities and validation of the LBL end-use disaggregation algorithm. Final report. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10163882.

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Dufur and Chapman. PR-325-07205-R01 Development of a Turbocharger Monitoring System. Pipeline Research Council International, Inc. (PRCI), 2008. http://dx.doi.org/10.55274/r0010771.

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Turbocharger performance, especially on SIP-call engines, remains essentially unmeasured even though tracking information over time would provide critical information to help field engineers lower their engine emissions as well as the cost of operations. In 2006, with the assistance of funding from the Pipeline Research Council International Inc., ScavengeTech LLC developed and field tested a turbocharger monitoring system that consisted of a set of analog sensors to measure key turbocharger performance parameters and hardware to interface the sensor outputs to a computer. The collected data w
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Guedes, Jéssica, Diego Torres, Paulino Sánchez-Escribano, and José Boyano. Incertidumbre en el mercado de bonos: una propuesta para identificar sus narrativas con GDELT. Banco de España, 2025. https://doi.org/10.53479/39440.

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Este estudio analiza la relación entre las narrativas de las noticias financieras y la volatilidad del mercado de bonos del Gobierno de Estados Unidos, medida por el índice MOVE. Para ello, se analiza un conjunto de datos poco explorado —la base de datos global de eventos, lenguaje y tono (GDELT, por sus siglas en inglés)—, en el que los artículos de noticias publicados en Internet tienen asignados metadatos, como temáticas y sentimiento. A partir de este conjunto de datos, se propone la utilización de grandes modelos de lenguaje (LLM, por sus siglas en inglés) para realizar una preselección d
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