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» Worst Cases and Lattice Reduction
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ICASSP
2008
IEEE
13 years 11 months ago
Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems
Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and t...
Joakim Jalden, Dominik Seethaler, Gerald Matz
APPROX
2007
Springer
104views Algorithms» more  APPROX 2007»
13 years 11 months ago
Worst-Case to Average-Case Reductions Revisited
Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomial-time samplable distribution (e.g., the uniform distribution) and...
Dan Gutfreund, Amnon Ta-Shma
FOCS
2003
IEEE
13 years 10 months ago
On Worst-Case to Average-Case Reductions for NP Problems
We show that if an NP-complete problem has a non-adaptive self-corrector with respect to a samplable distribution then coNP is contained in NP/poly and the polynomial hierarchy co...
Andrej Bogdanov, Luca Trevisan
EUROCRYPT
2011
Springer
12 years 8 months ago
Making NTRU as Secure as Worst-Case Problems over Ideal Lattices
Abstract. NTRUEncrypt, proposed in 1996 by Hostein, Pipher and Silverman, is the fastest known lattice-based encryption scheme. Its moderate key-sizes, excellent asymptotic perfor...
Damien Stehlé, Ron Steinfeld
STOC
2007
ACM
83views Algorithms» more  STOC 2007»
14 years 5 months 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