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Lenstra–Lenstra–Lovász lattice basis reduction algorithm

Known as: LLL basis reduction method, Lenstra–Lenstra–Lovasz lattice basis reduction algorithm, Lenstra-Lenstra-Lovasz algorithm 
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra… Expand
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Related topics

Related topics

20 relations
AlgorithmArjen LenstraBasis (linear algebra)Coppersmith method
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Broader (1)

Computational number theory

Papers overview

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2016
2016
An Introduction to Lenstra-Lenstra-Lovasz Lattice Basis Reduction Algorithm
Lenstra-Lenstra-Lovasz (LLL) Algorithm is an approximation algorithm of the shortest vector problem, which runs in polynomial… Expand
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Highly Cited
2010
Highly Cited
2010
Fully Homomorphic Encryption over the Integers
We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to… Expand
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Highly Cited
2009
Highly Cited
2009
Complex Lattice Reduction Algorithm for Low-Complexity Full-Diversity MIMO Detection
Recently, lattice-reduction-aided detectors have been proposed for multiinput multioutput (MIMO) systems to achieve performance… Expand
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Highly Cited
2007
Highly Cited
2007
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction
A new viewpoint for adopting the lattice reduction in communication over multiple-input multiple-output (MIMO) broadcast channels… Expand
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Highly Cited
2005
Highly Cited
2005
Learning Language in Logic - Genic Interaction Extraction Challenge
We describe here the context of the LLL challenge of Genic Interaction extraction, the background of its organization and the… Expand
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Highly Cited
2003
Highly Cited
2003
Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction
We consider the lattice-reduction-aided detection scheme for 2/spl times/2 channels recently proposed by H. Yao and G.W. Wornell… Expand
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Highly Cited
1999
Highly Cited
1999
Fundamental problems of algorithmic algebra
O INTRODUCTION 1. Fundamental Problem of Algebra 2. Fundamental Problem of Classical Algebraic Geometry 3. Fundamental Problem of… Expand
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1998
1998
Complexity Analysis of a Parallel Lattice Basis Reduction Algorithm
Lattice basis reduction is an important problem in geometry of numbers with applications in combinatorial optimization, computer… Expand
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Highly Cited
1991
Highly Cited
1991
Basis Reduction Algorithms and Subset Sum Problems
This thesis investigates a new approach to lattice basis reduction suggested by M. Seysen. Seysen''s algorithm attempts to… Expand
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Highly Cited
1988
Highly Cited
1988
A More Efficient Algorithm for Lattice Basis Reduction
Abstract The famous lattice basis reduction algorithm of Lovasz transforms a given integer lattice basis b 1 , …, b n ϵ Z n into… Expand
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