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Efficient proofs that a committed number lies in an interval
, 2000
"... Abstract. Alice wants to prove that she is young enough to borrow money from her bank, without revealing her age. She therefore needs a tool for proving that a committed number lies in a specific interval. Up to now, such tools were either inefficient (too many bits to compute and to transmit) or in ..."
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Cited by 166 (0 self)
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) or inexact (i.e. proved membership to a much larger interval). This paper presents a new proof, which is both efficient and exact. Here, “efficient ” means that there are less than 20 exponentiations to perform and less than 2 Kbytes to transmit. The potential areas of application of this proof are numerous
Towards Efficient Proofs of Retrievability
"... Proofs of Retrievability (POR) is a cryptographic formulation for remotely auditing the integrity of files stored in the cloud, without keeping a copy of the original files in local storage. In a POR scheme, a user Alice backups her data file together with some authentication data to a potentially d ..."
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Cited by 2 (2 self)
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is indeed efficient and practical. Our security proof is based on Strong DiffieHellman Assumption.
The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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for the languages of quadratic residuosity and quadratic nonresiduosity. These are the first examples of zeroknowledge proofs for languages not known to be efficiently recognizable.
Secure and efficient proof of storage with deduplication
 in Proceedings of the second ACM conference on Data and Application Security and Privacy, ser. CODASPY ’12
"... Both security and efficiency are crucial to the success of cloud storage. So far, security and efficiency of cloud storage have been separately investigated as follows: On one hand, security notions such as Proof of Data Possession (PDP) and Proof of Retrievability (POR) have been introduced for det ..."
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Cited by 13 (1 self)
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Both security and efficiency are crucial to the success of cloud storage. So far, security and efficiency of cloud storage have been separately investigated as follows: On one hand, security notions such as Proof of Data Possession (PDP) and Proof of Retrievability (POR) have been introduced
Random Oracles are Practical: A Paradigm for Designing Efficient Protocols
, 1995
"... We argue that the random oracle model  where all parties have access to a public random oracle  provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol P R for the ..."
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Cited by 1645 (70 self)
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for the random oracle model, and then replacing oracle accesses by the computation of an "appropriately chosen" function h. This paradigm yields protocols much more efficient than standard ones while retaining many of the advantages of provable security. We illustrate these gains for problems including
Proofs that Yield Nothing but Their Validity or All Languages in NP Have ZeroKnowledge Proof Systems
 JOURNAL OF THE ACM
, 1991
"... In this paper the generality and wide applicability of Zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without convey ..."
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Cited by 426 (43 self)
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In this paper the generality and wide applicability of Zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without
Entity Authentication and Key Distribution
, 1993
"... Entity authentication and key distribution are central cryptographic problems in distributed computing  but up until now, they have lacked even a meaningful definition. One consequence is that incorrect and inefficient protocols have proliferated. This paper provides the first treatment of these p ..."
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Cited by 576 (13 self)
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of these problems in the complexitytheoretic framework of modern cryptography. Addressed in detail are two problems of the symmetric, twoparty setting: mutual authentication and authenticated key exchange. For each we present a definition, protocol, and proof that the protocol meets its goal, assuming
Automatic verification of finitestate concurrent systems using temporal logic specifications
 ACM Transactions on Programming Languages and Systems
, 1986
"... We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent ..."
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Cited by 1387 (62 self)
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We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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BPP. The class BQP of languages that are efficiently decidable (with small errorprobability) on a quantum Turing machine satisfies BPP ⊆ BQP ⊆ P ♯P. Therefore, there is no possibility of giving a mathematical proof that quantum Turing machines are more powerful than classical probabilistic Turing
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