Non-interactive proofs of proximity

Gur, Tom; Rothblum, Ron D.

doi:10.1007/s00037-016-0136-9

Cited by 30 publications

(79 citation statements)

References 65 publications

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“…Introduced by Goldwasser et al [34], computation delegations are interactive proofs where the provers are also computationally bounded. These protocols have been studied by many ever since; see, for example, [15,16,38,39,44,45]. Recently, interactive proofs have also been studied in streaming settings [17,21,22,23].…”

Section: Related Workmentioning

confidence: 99%

Rational Proofs with Multiple Provers

Chen

McCauley

Singh

2016

Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

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Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation outsourcing, computation delegation, cloud computing, etc. In these applications, the verifier may pay the prover based on the quality of his work. Rational interactive proofs (RIP), introduced by Azar and Micali (2012), are an interactive-proof system with payments, in which the prover is rational rather than untrustworthy-he may lie, but only to increase his payment. Rational proofs leverage the prover's rationality to obtain simple and efficient protocols. Azar and Micali show that RIP=IP(=PSPACE), i.e., the set of provable languages stay the same with a single rational prover (compared to classic IP). They leave the question of whether multiple provers are more powerful than a single prover for rational and classical proofs as an open problem.In this paper we introduce multi-prover rational interactive proofs (MRIP). Here, a verifier cross-checks the provers' answers with each other and pays them according to the messages exchanged. The provers are cooperative and maximize their total expected payment if and only if the verifier learns the correct answer to the problem. We further refine the model of MRIP to incorporate utility gaps, which is the loss in payment suffered by provers who mislead the verifier to the wrong answer.We define the class of MRIP protocols with constant, noticeable and negligible utility gaps-the payment loss due to a wrong answer is O(1), 1/n O(1) and 1/2 n O(1) respectively, where n is the length of the input. We give tight characterization for all three MRIP classes. On the way, we resolve Azar and Micali's open problem-under standard complexity-theoretic assumptions, MRIP is not only more powerful than RIP, but also more powerful than MIP (classic multi-prover IP); and this is true even the utility gap is required to be constant. We further show that the full power of each MRIP class can be achieved using only two provers and three rounds of communication.

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Section: Related Workmentioning

confidence: 99%

Rational Proofs with Multiple Provers

Chen

McCauley

Singh

2016

Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

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“…Interactive proofs are largely concerned with verifiers that are computationally bounded, but are relevant for verifiers with any sort of limitation (e.g., finite automata [DS92,Con92]). They have been studied in other settings such as communication complexity [BFS86,GPW18] and their connection to circuit complexity [KW90, AW09,Wil16] and property testing [RVW13,GR18]. Of particular interest to us are interactive proofs for graph problems in P with a presumably weaker verifier (e.g.…”

Section: Introductionmentioning

confidence: 99%

The Power of Distributed Verifiers in Interactive Proofs

Naor

Parter

Yogev

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We explore the power of interactive proofs with a distributed verifier. In this setting, the verifier consists of n nodes and a graph G that defines their communication pattern. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph G belongs to some language in a small number of rounds, and with small communication bound, i.e., the proof size.This interactive model was introduced by Kol, Oshman and Saxena (PODC 2018) as a generalization of non-interactive distributed proofs. They demonstrated the power of interaction in this setting by constructing protocols for problems as Graph Symmetry and Graph Non-Isomorphism -both of which require proofs of Ω(n 2 )-bits without interaction.In this work, we provide a new general framework for distributed interactive proofs that allows one to translate standard interactive protocols (i.e., with a centralized verifier) to ones where the verifier is distributed with a proof size that depends on the computational complexity of the verification algorithm run by the centralized verifier. We show the following:• Every (centralized) computation that can be performed in time O(n) can be translated into three-round distributed interactive protocol with O(log n) proof size. This implies that many graph problems for sparse graphs have succinct proofs (e.g., testing planarity).• Every (centralized) computation implemented by either a small space or by uniform NC circuit can be translated into a distributed protocol with O(1) rounds and O(log n) bits proof size for the low space case and polylog(n) many rounds and proof size for NC.• We also demonstrate the power of our compilers for problems not captured by the above families. We show that for Graph Non-Isomorphism, one of the striking demonstrations of the power of interaction, there is a 4-round protocol with O(log n) proof size, improving upon the O(n log n) proof size of Kol et al.• For many problems we show how to reduce proof size below the naturally seeming barrier of log n. By employing our RAM compiler, we get a 5-round protocols with proof size O(log log n) for a family of problems including Fixed Automorphism, Clique and Leader Election (for the later two problems we actually get O(1) proof size).• Finally we discuss how to make these proofs non-interactive arguments via random oracles.Our compilers capture many natural problems and demonstrates the difficultly in showing lower bounds in these regimes.with the nodes of the network in rounds. In each round, a node u sends the prover a random challenge R u . Then, the prover responds by sending each node u its respond Y u . Nodes can exchange their proof Y u only with their immediate neighbors N(u) in the network in order to decide whether to accept the proof. For accepting a proof all nodes must accept and to reject it is enough that one node rejects. A simple example for a "distributed NP" proof is 3-coloring of a graph: the prover gives each node in the graph its color, and nodes exchange colors with their neigh...

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“…Interactive proofs (IP) are the most well-studied and widely-used theoretical framework to verify correctness of outsourced computation [8,9,12,13,14,20,21,22,29,32,38,39,46]. In an IP, a weak client (or verifier ) interacts with powerful ⋆ A preliminary version of this paper will appear in the proceedings of the 11th Interna the input size n. We also design single-round rational protocols that have only logarithmic overhead on the verifier's use of space and randomness.…”

Section: Introductionmentioning

confidence: 99%

Efficient Rational Proofs with Strong Utility-Gap Guarantees

Chen

McCauley

Singh

2018

Algorithmic Game Theory

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As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for verifiable computation delegation. Rational proofs are payment-based interactive proofs. The payments are designed to incentivize the provers to give correct answers. If the provers misreport the answer then they incur a payment loss of at least 1/u, where u is the utility gap of the protocol. In this work, we tightly characterize the power of rational proofs that are super efficient, that is, require only logarithmic time and communication for verification. We also characterize the power of single-round rational protocols that require only logarithmic space and randomness for verification. Our protocols have strong (that is, polynomial, logarithmic, and even constant) utility gap. Finally, we show when and how rational protocols can be converted to give the completeness and soundness guarantees of classical interactive proofs. service providers (or provers) to determine the correctness of their claim. At the end, the verifier probabilistically accepts or rejects the claim. 3 Interactive proofs guarantee that, roughly speaking, the verifier accepts a truthful claim with probability at least 2/3 (completeness) and no strategy of the provers can make the verifier accept a false claim with probability more than 1/3 (soundness). 4 .Rational proofs are payment-based interactive proofs for computation outsourcing which leverage the incentives of the service providers. In rational proofs, the provers act rationally in the game-theoretic sense, that is, they want to maximize their payment. The payment is designed such that when the provers maximize their payment, they also end up giving the correct answer. The model of rational proofs (RIP) was introduced by Azar and Micali in [3]. Since then, many simple and efficient rational protocols have been designed [4, 11, 17, 30, 31, 35, 48].While rational proofs provide strong theoretical guarantees, there are two main barriers that separate them from what is often desired in practice. First, many rational protocols require a polynomial-time verifier-but a "weak" client is unlikely to be able to spend (say) quadratic time or linear extra space on verification. Second, many of these protocols strongly rely on the rationality of the provers. An honest prover may receive only a fraction of a cent more than a dishonest prover, yet a rational prover is assumed to be incentivized by that small amount. However, service providers may not always be perfectly rational.The goal of this paper is to give protocols that overcome these barriers.Utility Gap. The strength of the guarantee provided by rational proofs is captured by the notion of utility gap. The high level idea behind utility gap is that provers who are not perfectly rational may not care about small losses in payments and may lazily give the incorrect answer. If a rational protocol has a utility gap...

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Non-interactive proofs of proximity

Cited by 30 publications

References 65 publications

Rational Proofs with Multiple Provers

Rational Proofs with Multiple Provers

The Power of Distributed Verifiers in Interactive Proofs

Efficient Rational Proofs with Strong Utility-Gap Guarantees

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