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» Quantum Computation and Lattice Problems
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FOCS
2004
IEEE
15 years 3 months ago
Hardness of Approximating the Shortest Vector Problem in Lattices
Let p > 1 be any fixed real. We show that assuming NP RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in p norm within a constant ...
Subhash Khot
89
Voted
STOC
2007
ACM
83views Algorithms» more  STOC 2007»
16 years 15 hour ago
Lattices that admit logarithmic worst-case to average-case connection factors
We demonstrate an average-case problem that is as hard as finding (n)-approximate shortest vectors in certain n-dimensional lattices in the worst case, where (n) = O( log n). The...
Chris Peikert, Alon Rosen
ECCV
2006
Springer
16 years 1 months ago
Discovering Texture Regularity as a Higher-Order Correspondence Problem
Abstract. Understanding texture regularity in real images is a challenging computer vision task. We propose a higher-order feature matching algorithm to discover the lattices of ne...
James Hays, Marius Leordeanu, Alexei A. Efros, Yan...
CORR
2010
Springer
178views Education» more  CORR 2010»
14 years 10 months ago
Enumerative Algorithms for the Shortest and Closest Lattice Vector Problems in Any Norm via M-Ellipsoid Coverings
We give an algorithm for solving the exact Shortest Vector Problem in n-dimensional lattices, in any norm, in deterministic 2O(n) time (and space), given poly(n)-sized advice that...
Daniel Dadush, Chris Peikert, Santosh Vempala
CRYPTO
1997
Springer
207views Cryptology» more  CRYPTO 1997»
15 years 3 months ago
Public-Key Cryptosystems from Lattice Reduction Problems
We present a new proposal for a trapdoor one-way function, from which we derive public-key encryption and digital signatures. The security of the new construction is based on the ...
Oded Goldreich, Shafi Goldwasser, Shai Halevi