Results 1  10
of
948,650
On WorstCase to AverageCase Reductions for NP Problems
"... 1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where ..."
Abstract
 Add to MetaCart
1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where
WorstCase to AverageCase Reductions Revisited
"... Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomialtime samplable distribution (e.g., the uniform distribution) and a language in NTIME(f(n)) for some polynomial function f, such that the language is hard on the average with respect to ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
connections. While we can not do that unconditionally, we are able to show that under a mild derandomization assumption, the worstcase hardness of NP implies the averagecase hardness of NTIME(f(n)) (under the uniform distribution) where f is computable in quasipolynomial time. 1
Worstcase to averagecase reductions based on Gaussian measures
 SIAM J. on Computing
, 2004
"... 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 linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest indepe ..."
Abstract

Cited by 128 (23 self)
 Add to MetaCart
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 linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest
Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
Abstract

Cited by 851 (17 self)
 Add to MetaCart
In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a
Relativized Worlds Without WorstCase to AverageCase Reductions for NP
, 2010
"... We prove that relative to an oracle, there is no worstcase to averagecase reduction for NP. We also handle classes that are somewhat larger than NP, as well as worstcase to errorlessaveragecase reductions. In fact, we prove that relative to an oracle, there is no worstcase. We also handle reduc ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We prove that relative to an oracle, there is no worstcase to averagecase reduction for NP. We also handle classes that are somewhat larger than NP, as well as worstcase to errorlessaveragecase reductions. In fact, we prove that relative to an oracle, there is no worstcase. We also handle
A WorstCase to AverageCase Connection for CVP
"... We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least with ..."
Abstract
 Add to MetaCart
We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least
On WorstCase to AverageCase Reductions for NP Problems
 IN PROCEEDINGS OF THE 44TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2003
"... We show that if an NPcomplete problem has a nonadaptive selfcorrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NPcompl ..."
Abstract

Cited by 61 (6 self)
 Add to MetaCart
We show that if an NPcomplete problem has a nonadaptive selfcorrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NP
WorstCase to AverageCase Reductions for Module Lattices
"... Abstract. Most latticebased cryptographic schemes are built upon the assumed hardness of the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. Their efficiencies can be drastically improved by switching the hardness assumptions to the more compact RingSIS and RingLWE problems. ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
lattices (which themselves generalize arbitrary and ideal lattices). As these new problems enlarge the toolbox of the latticebased cryptographer, they could prove useful for designing new schemes. Importantly, the worstcase to averagecase reductions for the module problems are (qualitatively) sharp
An Improved WorstCase to AverageCase Connection for Lattice Problems (extended abstract)
 In FOCS
, 1997
"... We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State Unive ..."
Abstract

Cited by 57 (10 self)
 Add to MetaCart
We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State
Results 1  10
of
948,650