Complexity Measures for Public-Key Cryptosystems

Grollmann, Joachim; Selman, Alan L.

doi:10.1137/0217018

Cited by 251 publications

(119 citation statements)

References 40 publications

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“…A pair (A, B) is called a disjoint NP-pair if A, B ∈ NP and A ∩ B = ∅. Grollmann and Selman [15] first defined the notion of a many-one reduction between disjoint NP-pairs, which can be equivalently stated as follows (cf. [20]): a disjoint NP-pair (A, B) many-one reduces to a pair (C,…”

Section: Preliminariesmentioning

confidence: 99%

“…Although disjoint NP-pairs were already introduced into complexity theory in the 80's by Grollmann and Selman [15], it was only during recent years that disjoint NP-pairs have fully come into the focus of complexitytheoretic research [20, 11-14, 1, 4]. This interest mainly stems from the application of disjoint NP-pairs to such different areas as cryptography [15,16] and propositional proof complexity [21,20,1].…”

Section: Introductionmentioning

confidence: 99%

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The Deduction Theorem for Strong Propositional Proof Systems

Beyersdorff

2007

FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science

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Abstract. This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Deduction Theorem for Strong Propositional Proof Systems

Beyersdorff

2007

FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science

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“…Obviously, P ⊆ UP ⊆ NP, and it is not known whether either inclusion is proper. One reason UP is an interesting complexity class is because there exists a one-to-one, honest function f ∈ PF whose inverse f −1 is not computable in polynomial time if and only if P = UP [GS88].…”

Section: Preliminariesmentioning

confidence: 99%

Survey of Disjoint NP-pairs and Relations to Propositional Proof Systems

Glaßer

Selman

Zhang

2006

Lecture Notes in Computer Science

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“…Finally, let us state the definitions of the function classes UPSV t and UPSV p [GS88,Kos99], which are the (respectively total and partial) unambiguous versions of the central, single-valued nondeterministic function classes NPSV t and NPSV p [BLS84, BLS85,Sel94]. When speaking of nondeterministic machines as computing (possibly partial) functions from Σ * to Σ * , we view each path as having no output if the path is a rejecting path, and if a path is an accepting path then it is viewed as outputting whatever string s ∈ Σ * is on the output tape (along that path) when that path halts.…”

Section: F (X) = #Acc M (X)mentioning

confidence: 99%

Cluster Computing and the Power of Edge Recognition

Hemaspaandra

Homan

Kosub

2006

Lecture Notes in Computer Science

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We study the robustness-the invariance under definition changes-of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with respect to some length-respecting total order with efficient adjacency checks. The definition of CL#P is heavily influenced by the defining paper's focus on (global) orders. In contrast, we define a cluster class, CLU#P, to capture what seems to us a more natural model of cluster computing. We prove that the naturalness is costless: CL#P = CLU#P. Then we exploit the more natural, flexible features of CLU#P to prove new robustness results for CL#P and to expand what is known about the closure properties of CL#P.The complexity of recognizing edges-of an ordered collection of computation paths or of a cluster of accepting computation paths-is central to this study. Most particularly, our proofs exploit the power of unique discovery of edges-the ability of nondeterministic functions to, in certain settings, discover on exactly one (in some cases, on at most one) computation path a critical piece of information regarding edges of orderings or clusters.

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Complexity Measures for Public-Key Cryptosystems

Cited by 251 publications

References 40 publications

The Deduction Theorem for Strong Propositional Proof Systems

The Deduction Theorem for Strong Propositional Proof Systems

Survey of Disjoint NP-pairs and Relations to Propositional Proof Systems

Cluster Computing and the Power of Edge Recognition

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