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Lenstra–Lenstra–Lovász lattice basis reduction algorithm
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#	Item
1	Lattice-Reduction-Aided Receivers for MIMO-OFDM in Spatial Multiplexing Systems Inaki Berenguer1 , Jaime Adeane1 , Ian J. Wassell1 , and Xiaodong Wang2 1 Laboratory for Communication Engineering Department of Engineering Add to Reading List Source URL: www.cl.cam.ac.uk Language: English - Date: 2007-06-29 06:52:44 Mathematics OSI protocols Computational number theory Lattice points Algebra Orthogonal frequency-division multiplexing MIMO Cyclic prefix Lenstra–Lenstra–Lovász lattice basis reduction algorithm Radio resource management Information theory IEEE 802
2	The nc-Unique Shortest Vector Problem is Hard Vadim Lyubashevsky∗ Abstract The unique Shortest Vector Problem (uSVP) gained prominence because it was the problem upon which the first provably-secure lattice-based crypt Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2008-12-01 09:32:36 Abstract algebra Lattice problem Lattice Learning with errors Vector space Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice-based cryptography Algebra Mathematics Cryptography
3	A Fast Phase-Based Enumeration Algorithm for SVP Challenge through y-Sparse Representations of Short Lattice Vectors ? ?? Dan Ding1 , Guizhen Zhu2 , Yang Yu1 , Zhongxiang Zheng1 1 Department of Computer Science and Tech Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2014-12-04 01:20:06 Lattice points Cryptography Computational number theory Linear algebra Quadratic forms Lattice problem Lattice reduction Lattice Lenstra–Lenstra–Lovász lattice basis reduction algorithm Algebra Mathematics Abstract algebra
4	Solving the Shortest Lattice Vector Problem in Time 22.465n Xavier Pujol1 and Damien Stehl´e2 1 Universit´e de Lyon, Laboratoire LIP, CNRS-ENSL-INRIA-UCBL, 46 All´ee d’Italie, 69364 Lyon Cedex 07, France 2 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-02-08 02:45:52 Cryptography Lattice points Linear algebra Computational number theory Lattice problem Lattice Lenstra–Lenstra–Lovász lattice basis reduction algorithm Vector space Algebra Mathematics Abstract algebra
5	Improved Nguyen-Vidick Heuristic Sieve Algorithm for Shortest Vector Problem ? Xiaoyun Wang1,2 , Mingjie Liu1 , Chengliang Tian2 and Jingguo Bi2 1 Institute for Advanced Study, Tsinghua University, Beijing, China Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2011-08-28 09:14:48 Cryptography Lattice points Computational number theory Linear algebra Lattice problem Lattice Normal distribution Lenstra–Lenstra–Lovász lattice basis reduction algorithm Vector space Mathematics Algebra Abstract algebra
6	Parallel Shortest Lattice Vector Enumeration on Graphics Cards? Jens Hermans ??1 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-02-26 11:26:24 Algebra Computational number theory Graphics hardware GPGPU Cryptography Lattice problem Lattice reduction Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice Mathematics Lattice points Applied mathematics
7	Abstract Fix an integer m > 2 and let K be a number field containing the mth roots of unity with ring of integers R. Suppose that a is an element of K with a = c/d for c, d ∈ R, and that b is an ideal of R relatively Add to Reading List Source URL: douglassquirrel.com Language: English - Date: 2013-08-17 18:16:01 Lattice points Algebraic number theory Analytic geometry Lattice Lenstra–Lenstra–Lovász lattice basis reduction algorithm Algebraic number field Field extension Vector space Ideal lattice cryptography Algebra Abstract algebra Mathematics
8	SOLILOQUY: A CAUTIONARY TALE Peter Campbell, Michael Groves and Dan Shepherd CESG, Cheltenham, UK 1. Introduction The Soliloquy primitive, first proposed by the third author in 2007, is Add to Reading List Source URL: docbox.etsi.org Language: English - Date: 2014-10-13 10:57:18 Theoretical computer science Cryptography Lattice points Quantum information science Analytic geometry Lattice Quantum algorithm Quantum computer Lenstra–Lenstra–Lovász lattice basis reduction algorithm Mathematics Applied mathematics Abstract algebra
9	Selected Applications of LLL in Number Theory Denis SIMON Abstract In this survey, I describe some applications of LLL in number theory. I show in particular how it can be used to solve many different linear problems, to Add to Reading List Source URL: www.math.unicaen.fr Language: English - Date: 2014-01-09 12:01:30 Polynomials Linear algebra Quadratic forms Elementary algebra Equations Factorization of polynomials Lenstra–Lenstra–Lovász lattice basis reduction algorithm Quadratic equation Algebraic number field Algebra Mathematics Abstract algebra
10	Lattice Reduction: a Toolbox for the Cryptanalyst Antoine Joux Jacques Stern Add to Reading List Source URL: www1.lip6.fr Language: English - Date: 2015-01-20 15:22:52 Linear algebra Computational number theory Cryptography Lattice reduction Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice problem Lattice Integer relation algorithm Vector space Mathematics Algebra Lattice points

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