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254
Average Time Fast SVP and CVP Algorithms for Low Density Lattices and the Factorization of Integers
, 2010
"... Abstract. We propose and analyze novel algorithms for finding shortest and closest lattice vectors. The algorithm New Enum performs the stages of exhaustive enumeration of short / close lattice vectors in order of decreasing success rate. We analyze New Enum under GSA which in practice holds on the ..."
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Cited by 6 (1 self)
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Abstract. We propose and analyze novel algorithms for finding shortest and closest lattice vectors. The algorithm New Enum performs the stages of exhaustive enumeration of short / close lattice vectors in order of decreasing success rate. We analyze New Enum under GSA which in practice holds
Factoring Integers by CVP Algorithms
"... work in progress 14.08.2015 Abstract. We use pruned enumeration algorithms to find lattice vectors close to a specific target vector for the prime number lattice. These algorithms generate multiplicative prime number relations modulo N that factorize a given integer N. The algorithm New Enum perfor ..."
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work in progress 14.08.2015 Abstract. We use pruned enumeration algorithms to find lattice vectors close to a specific target vector for the prime number lattice. These algorithms generate multiplicative prime number relations modulo N that factorize a given integer N. The algorithm New Enum
Parallel Shortest Lattice Vector Enumeration on Graphics Cards
, 2010
"... In this paper we present an algorithm for parallel exhaustive search for short vectors in lattices. This algorithm can be applied to a wide range of parallel computing systems. To illustrate the algorithm, it was implemented on graphics cards using CUDA, a programming framework for NVIDIA graphics ..."
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Cited by 7 (3 self)
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In this paper we present an algorithm for parallel exhaustive search for short vectors in lattices. This algorithm can be applied to a wide range of parallel computing systems. To illustrate the algorithm, it was implemented on graphics cards using CUDA, a programming framework for NVIDIA
Approximating SVP∞ to within AlmostPolynomial Factors is NPhard
 ITUT RECOMMENDATION G.729
, 1996
"... This paper shows SVP∞ and CVP∞ to be NPhard to approximate to within any factor up to n 1= log log n . This improves on the best previous result [ABSS93] that showed quasiNP hardness for smaller factors, namely 2 log 1\Gamma" n for any constant " ? 0. We show a direct reduction ..."
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Cited by 21 (0 self)
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This paper shows SVP∞ and CVP∞ to be NPhard to approximate to within any factor up to n 1= log log n . This improves on the best previous result [ABSS93] that showed quasiNP hardness for smaller factors, namely 2 log 1\Gamma" n for any constant " ? 0. We show a direct reduction
A Fast PhaseBased Enumeration Algorithm for SVP Challenge through ySparse Representations of Short Lattice Vectors???
"... Abstract. In this paper, we propose a new phasebased enumeration algorithm based on two interesting and useful observations for ysparse representations of short lattice vectors in lattices from SVP challenge benchmarks[24]. Experimental results show that the phasebased algorithm greatly outperfor ..."
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Abstract. In this paper, we propose a new phasebased enumeration algorithm based on two interesting and useful observations for ysparse representations of short lattice vectors in lattices from SVP challenge benchmarks[24]. Experimental results show that the phasebased algorithm greatly
On the Limits of NonApproximability of Lattice Problems
, 1998
"... We show simple constantround interactive proof systems for problems capturing the approximability, to within a factor of p n, of optimization problems in integer lattices; specifically, the closest vector problem (CVP), and the shortest vector problem (SVP). These interactive proofs are for th ..."
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Cited by 102 (3 self)
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We show simple constantround interactive proof systems for problems capturing the approximability, to within a factor of p n, of optimization problems in integer lattices; specifically, the closest vector problem (CVP), and the shortest vector problem (SVP). These interactive proofs
Guest Column: Complexity of SVP  A reader's digest
, 2001
"... We present highlevel technical summaries of five recent results on the computational complexity of the shortest lattice vector problem. ..."
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We present highlevel technical summaries of five recent results on the computational complexity of the shortest lattice vector problem.
A Genetic Algorithm for Searching Shortest Lattice Vector of SVP Challenge???
"... Abstract. In this paper, we propose a genetic algorithm for solving the shortest vector problem (SVP) based on sparse integer representations of short vectors in lattices as chromesomes, which, we prove, can guarantee finding the shortest lattice vector under a Markov chain analysis. Moreover, we al ..."
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Cited by 2 (1 self)
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also suggest some improvements by introducing heuristic techniques: local search and heuristic pruning. The experimental results show that the genetic algorithm runs rather good on the SVP challenge benchmarks[32], and performs much faster than other practical algorithms: the Kannan
An Annotation Scheme for Free Word Order Languages
, 1997
"... We describe an annotation scheme and a tool developed for creating linguistically annotated corpora for nonconfigurational languages. Since the requirements for such a formalism differ from those posited for configurational languages, several features have been added, influencing the architecture o ..."
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Cited by 178 (8 self)
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We describe an annotation scheme and a tool developed for creating linguistically annotated corpora for nonconfigurational languages. Since the requirements for such a formalism differ from those posited for configurational languages, several features have been added, influencing the architecture of the scheme. The resulting scheme reflects a stratificational notion of language, and makes only minimal ,ssump tions about the interrelation of the particu lar representational strata.
Results 1  10
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254