Sciweavers

CORR
2010
Springer
178views Education» more  CORR 2010»
13 years 9 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
TOC
2008
94views more  TOC 2008»
13 years 10 months ago
Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector prob
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 ...
Miklós Ajtai
ECCC
2008
98views more  ECCC 2008»
13 years 11 months ago
Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem
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...
Chris Peikert
CRYPTO
2008
Springer
134views Cryptology» more  CRYPTO 2008»
14 years 20 days ago
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
We construct noninteractive statistical zero-knowledge (NISZK) proof systems for a variety of standard approximation problems on lattices, such as the shortest independent vectors...
Chris Peikert, Vinod Vaikuntanathan
FOCS
2004
IEEE
14 years 2 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
FOCS
1998
IEEE
14 years 3 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
CALC
2001
Springer
161views Cryptology» more  CALC 2001»
14 years 3 months ago
The Shortest Vector Problem in Lattices with Many Cycles
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...
Mårten Trolin
FOCS
2002
IEEE
14 years 3 months ago
Quantum Computation and Lattice Problems
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 ...
Oded Regev
STOC
2003
ACM
116views Algorithms» more  STOC 2003»
14 years 4 months ago
New lattice based cryptographic constructions
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...
Oded Regev
STACS
2004
Springer
14 years 4 months ago
Lattices with Many Cycles Are Dense
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...
Mårten Trolin