CORR
2010
Springer
13 years 3 months ago
2010
Springer
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...
TOC
2008
13 years 4 months ago
2008
Abstract: Schnorr's algorithm for finding an approximation for the shortest nonzero vector in an n-dimensional lattice depends on a parameter k. He proved that for a fixed k ...
ECCC
2008
13 years 4 months ago
2008
We construct public-key cryptosystems that are secure assuming the worst-case hardness of approximating the minimum distance on n-dimensional lattices to within small poly(n) fact...
CRYPTO
2008
Springer
13 years 6 months ago
2008
Springer
We construct noninteractive statistical zero-knowledge (NISZK) proof systems for a variety of standard approximation problems on lattices, such as the shortest independent vectors...
FOCS
2004
IEEE
13 years 8 months ago
2004
IEEE
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 ...
FOCS
1998
IEEE
13 years 8 months ago
1998
IEEE
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...
CALC
2001
Springer
13 years 9 months ago
2001
Springer
In this paper we investigate how the complexity of the shortest vector problem in a lattice Λ depends on the cycle structure of the additive group Zn /Λ. We give a proof that the...
FOCS
2002
IEEE
13 years 9 months ago
2002
IEEE
We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the Unique Shortest Vector Problem (SVP) under ...
STOC
2003
ACM
13 years 9 months ago
2003
ACM
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian d...
STACS
2004
Springer
13 years 10 months ago
2004
Springer
Abstract We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Zn /Λ has n − 1 cycles of equal length with arbitrary precision. We al...