Efficient Rational Proofs with Strong Utility-Gap Guarantees

Abstract

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...

Sumcheck-based delegation of quantum computing to rational server

“…Finally, we show, under the certain condition introduced in Ref. [41], that rational and ordinary delegated quantum computing protocols can be converted each other. To convert ordinary delegated quantum computing protocols to rational ones, we show that the construction in the previous paragraph can be used even under the condition.…”

“…Apart from these results, we also give, under the certain condition introduced in Ref. [41], a relation between rational and ordinary delegated quantum computing protocols. More precisely, we show that under the certain condition, these two types of delegated quantum computing protocols can be converted each other.…”

“…The first condition was introduced in Ref. [41]. It is worth mentioning that the second condition is satisfied in our sumcheck-based rational protocols, while the first condition is not satisfied.…”

“…As a reverse conversion, we utilize the construction in Ref. [41]. By combining these two constructions, we convert the two types of delegated quantum computing protocols each other.…”

“…Guo et al have introduced the reward gap [38], which is also called the utility gap [41,44]. For decision problems, the reward gap is defined as follows: Definition 4 Let a strategy s be defined as a set {a i } i of the server's messages.…”