Cryptocomplexity and NP-completeness

Even, Shimon; Yacobi, Yacov

doi:10.1007/3-540-10003-2_71

Cited by 43 publications

(21 citation statements)

References 9 publications

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“…6 Even, Yacobi and Lempel [22,51] devised a public key cryptosystem such that an efficient adversary that breaks the system for every key implies an efficient algorithm for an NP-complete problem. An efficient adversary that breaks the system on almost all keys, however, is also discussed.…”

Section: One-way Functions and Cryptographymentioning

confidence: 99%

Average-Case Complexity

Bogdanov

Trevisan

2006

FNT in Theoretical Computer Science

112

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We survey the average-case complexity of problems in NP.We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easy-on-average with respect to the uniform distribution, then all problems in NP are easy-on-average with respect to all samplable distributions. Applying the theory to natural distributional problems remain an outstanding open question. We review some natural distributional problems whose average-case complexity is of particular interest and that do not yet fit into this theory.A major open question is whether the existence of hard-on-average problems in NP can be based on the P = NP assumption or on related worst-case assumptions. We review negative results showing that certain proof techniques cannot prove such a result. While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case complexity. We discuss some of these "hardness amplification" results.

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Section: One-way Functions and Cryptographymentioning

confidence: 99%

Average-Case Complexity

Bogdanov

Trevisan

2006

FNT in Theoretical Computer Science

112

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“…Contract signing [1] is an important security task with many applications, namely to stock market and others [2]. It is a two party protocol between Alice and Bob who share a common contract and want to exchange each others' commitments to it, thus binding to the terms of the contract.…”

Section: Introductionmentioning

confidence: 99%

“…However, Trent's time and resources are expensive and should be avoided as much as possible. Unfortunately, it has been shown that there is no fair and viable contract signing protocol [1,3], unless during the signature exchange phase the signing parties communicate with a common trusted agent, i.e., Trent. By fair protocol we mean that either both parties get each other's commitment or none gets.…”

Section: Introductionmentioning

confidence: 99%

Fair and optimistic quantum contract signing

2011

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We present a fair and optimistic [7,8] quantum contract signing protocol between two clients that requires no communication with the third trusted party during the exchange phase. We discuss its fairness and show that it is possible to design such a protocol for which the probability of a dishonest client to cheat becomes negligible, and scales as N −1/2 , where N is the number of messages exchanged between the clients. Our protocol is not based on the exchange of signed messages: its fairness is based on the laws of quantum mechanics. Thus, it is abuse-free [9], and the clients do not have to generate new keys for each message during the Exchange phase. We discuss a real-life scenario when the measurement errors and qubit state corruption due to noisy channels occur and argue that for real, good enough measurement apparatus and transmission channels, our protocol would still be fair. Our protocol could be implemented by today's technology, as it requires in essence the same type of apparatus as the one needed for BB84 cryptographic protocol [12]. Finally, we briefly discuss two alternative versions of the protocol, one that uses only two states (based on B92 protocol [24]) and the other that uses entangled pairs (based on [20]), and show that it is possible to generalize our protocol to an arbitrary number of clients.

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“…Cryptosystems reliant on N P-complete problems [22] have been previously studied, e.g., the Merkle-Hellman cryptosystem [36], which is based on the general knapsack problem. These systems rely on a series of tricks to conceal the existence of a "trapdoor" that permits retrieving the hidden information efficiently (N DBs have no trapdoors); however, almost all knapsack cryptosystems have been broken [40].…”

Section: Related Workmentioning

confidence: 99%

Protecting Data Privacy Through Hard-to-Reverse Negative Databases

Esponda

Ackley

Helman

et al. 2006

Lecture Notes in Computer Science

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A set DB of data elements can be represented in terms of its complement set, known as a negative database. That is, all of the elements not in DB are represented, and DB itself is not explicitly stored. This method of representing data has certain properties that are relevant for privacy enhancing applications.The paper reviews the negative database (N DB) representation scheme for storing a negative image compactly, and it proposes using a collection of N DBs to represent a single DB, that is, one N DB is assigned for each record in DB. This method has the advantage of producing negative databases that are hard to reverse in practice, i.e., from which it is hard to obtain DB. This result is obtained by adapting a technique for generating hard-to-solve 3-SAT formulas. Finally we suggest potential avenues of application.

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Cryptocomplexity and NP-completeness

Cited by 43 publications

References 9 publications

Average-Case Complexity

Average-Case Complexity

Fair and optimistic quantum contract signing

Protecting Data Privacy Through Hard-to-Reverse Negative Databases

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