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Pseudorandom generators without the XOR Lemma (Extended Abstract)
, 1998
"... Impagliazzo and Wigderson [IW97] have recently shown that if there exists a decision problem solvable in time 2 O(n) and having circuit complexity 2 n) (for all but finitely many n) then P = BPP. This result is a culmination of a series of works showing connections between the existence of har ..."
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Cited by 137 (23 self)
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phase (encoding with multivariate polynomial) is necessary, since it already gives the required averagecase hardness. We prove this result by (i) establishing a connection between the hardnessamplification problem and a listdecoding...
Proofs of retrievability via hardness amplification
 In TCC
, 2009
"... Proofs of Retrievability (PoR), introduced by Juels and Kaliski [JK07], allow the client to store a file F on an untrusted server, and later run an efficient audit protocol in which the server proves that it (still) possesses the client’s data. Constructions of PoR schemes attempt to minimize the cl ..."
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Cited by 85 (4 self)
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of Shacham and Waters [SW08]. • Build the first boundeduse scheme with informationtheoretic security. The main insight of our work comes from a simple connection between PoR schemes and the notion of hardness amplification, extensively studied in complexity theory. In particular, our improvements come from
On uniform amplification of hardness in NP
 IN PROCEEDINGS OF THE THIRTYSEVENTH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2005
"... We continue the study of amplification of averagecase complexity within NP, and we focus on the uniform case. We prove that if every problem in NP admits an efficient uniform algorithm that (averaged over random inputs and over the internal coin tosses of the algorithm) succeeds with probability at ..."
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Cited by 24 (3 self)
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We continue the study of amplification of averagecase complexity within NP, and we focus on the uniform case. We prove that if every problem in NP admits an efficient uniform algorithm that (averaged over random inputs and over the internal coin tosses of the algorithm) succeeds with probability
Hardness Amplification for Errorless Heuristics
, 2007
"... An errorless heuristic is an algorithm that on all inputs returns either the correct answer or the special symbol ⊥, which means “I don’t know. ” A central question in averagecase complexity is whether every distributional decision problem in NP has an errorless heuristic scheme: This is an algorit ..."
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Cited by 3 (0 self)
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: This is an algorithm that, for every δ> 0, runs in time polynomial in the instance size and 1/δ and answers ⊥ only on a δ fraction of instances. We study the question from the standpoint of hardness amplification and show that • If every problem in (NP, U) has errorless heuristic circuits that output the correct
Input Locality and Hardness Amplification
"... We establish new hardness amplification results for oneway functions in which each input bit influences only a small number of output bits (a.k.a. inputlocal functions). Our transformations differ from previous ones in that they approximately preserve input locality and at the same time retain the ..."
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Cited by 4 (1 self)
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We establish new hardness amplification results for oneway functions in which each input bit influences only a small number of output bits (a.k.a. inputlocal functions). Our transformations differ from previous ones in that they approximately preserve input locality and at the same time retain
Security Preserving Amplification of Hardness*
"... Using random walks on constructive expanders, we transform any regular (e.g., onetoone) weak oneway function into a strong one, while preserving security. The resulting function F (x) applies the weak oneway f to strings of length \Theta (x). Our security preserving constructions yield efficien ..."
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Using random walks on constructive expanders, we transform any regular (e.g., onetoone) weak oneway function into a strong one, while preserving security. The resulting function F (x) applies the weak oneway f to strings of length \Theta (x). Our security preserving constructions yield efficient pseudorandom generators and signatures based on any regular oneway function.
Texts in Computational Complexity: Amplification of Hardness
, 2006
"... The existence of natural computational problems that are (or seem to be) infeasible to solve is usually perceived as bad news, because it means that we cannot do things we wish to do. But these bad news have a positive side, because hard problem can be "put to work " to our benefit ..."
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). Much of the current chapter is devoted to this issue, which is known by the term hardness amplification. Summary: We consider two conjectures that are related to P 6 = N P. The first conjecture is that there are problems that are solvable in exponentialtime but are not solvable by (non
Counterexamples to Hardness Amplification Beyond Negligible
, 2012
"... If we have a problem that is mildly hard, can we create a problem that is significantly harder? A natural approach to hardness amplification is the “direct product”; instead of asking an attacker to solve a single instance of a problem, we ask the attacker to solve several independently generated on ..."
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Cited by 1 (0 self)
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If we have a problem that is mildly hard, can we create a problem that is significantly harder? A natural approach to hardness amplification is the “direct product”; instead of asking an attacker to solve a single instance of a problem, we ask the attacker to solve several independently generated
Note Improved hardness amplification in NP
, 2006
"... We study the problem of hardness amplification in NP. We prove that if there is a balanced function in NP such that any circuit of size s(n) = 2Ω(n) fails to compute it on a 1/poly(n) fraction of inputs, then there is a function in NP such that any circuit of size s′(n) fails to compute it on a 1/2 ..."
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We study the problem of hardness amplification in NP. We prove that if there is a balanced function in NP such that any circuit of size s(n) = 2Ω(n) fails to compute it on a 1/poly(n) fraction of inputs, then there is a function in NP such that any circuit of size s′(n) fails to compute it on a 1
Query Complexity in Errorless Hardness Amplification
, 2010
"... An errorless circuit for a boolean function is one that outputs the correct answer or “don’t know ” on each input (and never outputs the wrong answer). The goal of errorless hardness amplification is to show that if f has no size s errorless circuit that outputs “don’t know ” on at most a δ fraction ..."
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Cited by 2 (1 self)
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An errorless circuit for a boolean function is one that outputs the correct answer or “don’t know ” on each input (and never outputs the wrong answer). The goal of errorless hardness amplification is to show that if f has no size s errorless circuit that outputs “don’t know ” on at most a δ
Results 1  10
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