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Results 1 - 10
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9,161
Flags and lattice basis reduction
- IN PROCEEDINGS OF THE THIRD EUROPEAN CONGRESS OF MATHEMATICS
, 2001
"... In this lecture we give a self-contained introduction to the theory of lattices in Euclidean vector spaces. We reinterpret a large class of lattice basis reduction algorithms by using the concept of a “flag”. In our reformu-lation, lattice basis reduction algorithms are more appropriately called “f ..."
Abstract
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Cited by 11 (0 self)
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In this lecture we give a self-contained introduction to the theory of lattices in Euclidean vector spaces. We reinterpret a large class of lattice basis reduction algorithms by using the concept of a “flag”. In our reformu-lation, lattice basis reduction algorithms are more appropriately called
Lattice Basis Reduction with Dynamic Approximation
"... Abstract. In this paper we present a heuristic based on dynamic approximations for improving the well-known Schnorr-Euchner lattice basis reduction algorithm. In particular, the new heuristic is more efficient in reducing large problem instances and extends the applicability of the Schnorr-Euchner a ..."
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Abstract. In this paper we present a heuristic based on dynamic approximations for improving the well-known Schnorr-Euchner lattice basis reduction algorithm. In particular, the new heuristic is more efficient in reducing large problem instances and extends the applicability of the Schnorr
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems.
- Math. Programming
, 1993
"... We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3-algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3- algorithm with "deep insertions" and a practical algorithm for block Korkin--Z ..."
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Cited by 327 (6 self)
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We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3-algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3- algorithm with "deep insertions" and a practical algorithm for block Korkin
Lattice Basis Reduction in Function Fields
- In ANTS-3 : Algorithmic
, 1998
"... We present an algorithm for lattice basis reduction in function fields. In contrast to integer lattices, there is a simple algorithm which provably computes a reduced basis in polynomial time. Moreover, this algorithm works only with the coefficients of the polynomials involved, so there is no polyn ..."
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Cited by 6 (1 self)
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We present an algorithm for lattice basis reduction in function fields. In contrast to integer lattices, there is a simple algorithm which provably computes a reduced basis in polynomial time. Moreover, this algorithm works only with the coefficients of the polynomials involved, so
A Jacobi Method for Lattice Basis Reduction
"... Abstract—Lattice reduction aided decoding has been successfully used in wireless communications. In this paper, we propose a Jacobi method for lattice basis reduction. Jacobi method is attractive, because it is inherently parallel. Thus high performance can be achieved by exploiting multiprocessor a ..."
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Cited by 6 (6 self)
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Abstract—Lattice reduction aided decoding has been successfully used in wireless communications. In this paper, we propose a Jacobi method for lattice basis reduction. Jacobi method is attractive, because it is inherently parallel. Thus high performance can be achieved by exploiting multiprocessor
A Lattice Basis Reduction Algorithm ∗
"... In this paper, we give a definition of an optimally reduced basis for a lattice in the sense that an optimally reduced basis is a shortest basis for the lattice. Then we present an algorithm for computing an approximation of an optimally reduced basis for a lattice using a novel unimodular transform ..."
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Cited by 9 (9 self)
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In this paper, we give a definition of an optimally reduced basis for a lattice in the sense that an optimally reduced basis is a shortest basis for the lattice. Then we present an algorithm for computing an approximation of an optimally reduced basis for a lattice using a novel unimodular
Practical, Predictable Lattice Basis Reduction
"... Lattice reduction algorithms are notoriously hard to predict, both in terms of running time and output quality, which poses a major problem for cryptanalysis. While easy to analyze algorithms with good worst-case behavior exist, previous experimental evidence suggests that they are outperformed in p ..."
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Lattice reduction algorithms are notoriously hard to predict, both in terms of running time and output quality, which poses a major problem for cryptanalysis. While easy to analyze algorithms with good worst-case behavior exist, previous experimental evidence suggests that they are outperformed
Blockwise Lattice Basis Reduction Revisited.
"... oflatticebaseswithKoy'sprimal-dualreductionforblocksize2k.Koy's Abstract. WecompareSchnorr'salgorithmforsemiblock2k-reduction algorithmguaranteeswithinthesametimeboundunderknownproofs betterapproximationsoftheshortestlatticevector.Underreasonable heuristics proveninworst-case.Wecombin ..."
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oflatticebaseswithKoy'sprimal-dualreductionforblocksize2k.Koy's Abstract. WecompareSchnorr'salgorithmforsemiblock2k-reduction algorithmguaranteeswithinthesametimeboundunderknownproofs betterapproximationsoftheshortestlatticevector.Underreasonable heuristics proveninworst
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9,161
