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WorstCase to AverageCase Reductions Revisited
"... 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 this dis ..."
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Cited by 5 (1 self)
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to this distribution, given that NP is worstcase hard (i.e. NP ̸ = P, or NP ̸ ⊆ BPP). Currently, no such result is known even if we relax the language to be in nondeterministic subexponential time. There has been a long line of research trying to explain our failure in proving such worstcase/averagecase
AverageCase Intractability vs. WorstCase Intractability
 IN THE 23RD INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
, 1998
"... We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable in the a ..."
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Cited by 3 (1 self)
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We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable
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 ..."
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Cited by 131 (23 self)
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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 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. ..."
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Cited by 6 (1 self)
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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
WorstCase Running Times for AverageCase Algorithms
"... Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space, then t ..."
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Cited by 3 (0 self)
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Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space
Pseudorandomness and averagecase complexity via uniform reductions
 IN PROCEEDINGS OF THE 17TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 2002
"... Impagliazzo and Wigderson (36th FOCS, 1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP � = BPP). Unlike results in the nonuniform setting, their result does not provide a continuous tradeoff between worstcase hardness and pseudor ..."
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Cited by 51 (7 self)
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and pseudorandomness, nor does it explicitly establish an averagecase hardness result. In this paper: ◦ We obtain an optimal worstcase to averagecase connection for EXP: if EXP � ⊆ BPTIME(t(n)), then EXP has problems that cannot be solved on a fraction 1/2 + 1/t ′ (n) of the inputs by BPTIME(t ′ (n)) algorithms
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 ..."
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Cited by 55 (10 self)
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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
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 ..."
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Cited by 3 (1 self)
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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
Results 1  10
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726,286