Efficient Rational Proofs with Strong Utility-Gap Guarantees

TL;DR

This paper characterizes the capabilities of highly efficient rational proof systems with strong utility-gap guarantees, enabling verifiable computation with minimal resources and linking them to classical proof models.

Contribution

It provides a tight characterization of super-efficient rational proofs with strong utility gaps and explores conversions to classical interactive proof guarantees.

Findings

Super-efficient rational proofs require only logarithmic time and communication.

Single-round rational protocols can operate with logarithmic space and randomness.

Protocols achieve polynomial, logarithmic, and constant utility gaps.

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.