Results 241 to 250 of about 6,745,331 (273)
The Hardness of the Closest Vector Problem With Preprocessing
IEEE Transactions on Information Theory, 2001 We give a new simple proof of the NP-hardness of the closest vector problem. In addition to being much simpler than all previously known proofs, the new proof yields new interesting results about the complexity of the closest vector problem with ...
D Micciancio
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On the Closest Vector Problem With a Distance Guarantee [PDF]
2014 IEEE 29th Conference on Computational Complexity (CCC), 2014 We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n/√log n), improving on the previous best of O(n1.5) due to Lagarias ...
Daniel Dadush +2 more
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On the Maximum Distance Sublattice Problem and Closest Vector Problem [PDF]
2024 26th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)In this paper, we introduce the Maximum Distance Sublattice Problem (MDSP). We observed that the problem of solving an instance of the Closest Vector Problem (CVP) in a lattice $\mathcal{L}$ is the same as solving an instance of MDSP in the dual lattice ...
Mehta, Shashank K +2 more
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Solving the Closest Vector Problem in 2^n Time -- The Discrete Gaussian Strikes Again! [PDF]
2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015 We give a 2n+o(n)-time and space randomized algorithm for solving the exact Closest Vector Problem (CVP) on n-dimensional Euclidean lattices. This improves on the previous fastest algorithm, the deterministic O (4n)-time and O(2n)-space algorithm of ...
Daniel Dadush, Noah Stephens-Davidowitz
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Hardness of Approximating the Closest Vector Problem With Pre-Processing
computational complexity, 2005 We show that, unless NP⊆DTIME(2 poly log(n)), the closest vector problem with pre-processing, for ℓp norm for any p ≥ 1, is hard to approximate within a factor of (log n) 1/p−ɛ for any ɛ> 0.
Mikhail Alekhnovich +3 more
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Dual Lattice Attacks for Closest Vector Problems (With Preprocessing)
Lecture Notes in Computer Science, 2021 The dual attack has long been considered a relevant attack on lattice-based cryptographic schemes relying on the hardness of learning with errors (LWE) and its structured variants. As solving LWE corresponds to finding a nearest point on a lattice, one may naturally wonder how efficient this dual approach is for solving more general closest vector ...
Thijs Laarhoven, Michael Walter
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The Closest Vector Problem on Some Lattices
Lecture Notes in Computer Science, 2004The closest vector problem for general lattices is NP-hard. However, we can efficiently find the closest lattice points for some special lattices, such as root lattices (A n , D n and some E n ). In this paper, we discuss the closest vector problem on more general lattices than root lattices.
Haibin Kan
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A Polynomial Time Algorithm for Solving the Closest Vector Problem in Zonotopal Lattices [PDF]
SIAM Journal on Discrete Mathematics, 2021 12 pages, v3: Comments of referees incorporated, to appear in SIAM Journal on Discrete Mathematics (SIDMA)
Thomas McCormick +2 more
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Algorithms for the Shortest and Closest Lattice Vector Problems [PDF]
Lecture Notes in Computer Science, 2011 We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in the Euclidean norm. We recall the three main families of algorithms for these problems, namely the algorithm by Micciancio and Voulgaris based on the Voronoi cell [STOC'10], the Monte-Carlo algorithms derived from the Ajtai, Kumar and Sivakumar algorithm ...
Damien Stehlé
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