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FOCS
2004
IEEE
15 years 6 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
146
Voted
STOC
2005
ACM
198views Algorithms» more  STOC 2005»
16 years 2 months ago
On lattices, learning with errors, random linear codes, and cryptography
Our main result is a reduction from worst-case lattice problems such as GAPSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learnin...
Oded Regev
128
Voted
GLOBECOM
2007
IEEE
15 years 9 months ago
Reduced Complexity Sphere Decoding for Square QAM via a New Lattice Representation
— Sphere decoding (SD) is a low complexity maximum likelihood (ML) detection algorithm, which has been adapted for different linear channels in digital communications. The comple...
Luay Azzam, Ender Ayanoglu
FOCS
1998
IEEE
15 years 6 months ago
The Shortest Vector in a Lattice is Hard to Approximate to Within Some Constant
We show that approximating the shortest vector problem (in any p norm) to within any constant factor less than p 2 is hard for NP under reverse unfaithful random reductions with i...
Daniele Micciancio
LATINCRYPT
2010
15 years 29 days ago
A Lattice-Based Threshold Ring Signature Scheme
In this article, we propose a new lattice-based threshold ring signature scheme, modifying Aguilar’s code-based solution to use the short integer solution (SIS) problem as securi...
Pierre-Louis Cayrel, Richard Lindner, Markus R&uum...