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Lattice reduction
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#	Item
21	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
22	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
23	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
24	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
25	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
26	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
27	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
28	On Quantum Sieve Approaches to the Lattice Shortest Vector Problem Daniel Epelbaum December[removed] Add to Reading List Source URL: www.scottaaronson.com Language: English - Date: 2014-12-25 20:29:11 Quantum algorithms Cryptography Group theory Computational complexity theory Lattice problem Lattice Hidden subgroup problem Lenstra–Lenstra–Lovász lattice basis reduction algorithm Quantum computer Mathematics Theoretical computer science Algebra
29	The Insecurity of Esign in Practical Implementations Pierre-Alain Fouque1 , Nick Howgrave-Graham2 , Gwena¨elle Martinet3 , and Guillaume Poupard3 ´ Ecole Add to Reading List Source URL: www.iacr.org Language: English - Date: 2008-09-15 00:54:54 Computational number theory Lattice points Algebra Abstract algebra RSA Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice Mathematics Electronic commerce Public-key cryptography
30	Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures Phong Q. Nguyen?1 and Oded Regev??2 ´ CNRS & Ecole normale sup´erieure, DI, 45 rue d’Ulm, 75005 Paris, France. Add to Reading List Source URL: www.iacr.org Language: English - Date: 2008-09-15 01:06:09 Post-quantum cryptography Linear algebra NTRUSign GGH signature scheme GGH encryption scheme Lattice reduction Lattice Parallelepiped Vector space Cryptography Algebra Mathematics