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» Worst Cases and Lattice Reduction
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FOCS
2004
IEEE
13 years 8 months ago
Worst-Case to Average-Case Reductions Based on Gaussian Measures
We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost line...
Daniele Micciancio, Oded Regev
ARITH
2003
IEEE
13 years 10 months ago
Worst Cases and Lattice Reduction
Damien Stehlé, Vincent Lefèvre, Paul...
ECCC
2008
98views more  ECCC 2008»
13 years 4 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
APPROX
2010
Springer
132views Algorithms» more  APPROX 2010»
13 years 6 months ago
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
We prove that relative to an oracle, there is no worst-case to average-case reduction for NP. We also handle classes that are somewhat larger than NP, as well as worst-case to err...
Thomas Watson
ASIACRYPT
2008
Springer
13 years 6 months ago
Concurrently Secure Identification Schemes Based on the Worst-Case Hardness of Lattice Problems
In this paper, we show that two variants of Stern's identification scheme [IEEE Transaction on Information Theory '96] are provably secure against concurrent attack unde...
Akinori Kawachi, Keisuke Tanaka, Keita Xagawa