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On Interactive Proofs of Proximity with Proof-Oblivious Queries

Authors Oded Goldreich, Guy N. Rothblum, Tal Skverer

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Author Details

Oded Goldreich
  • Weizmann Institute of Science, Rehovot, Israel
Guy N. Rothblum
  • Apple, Cupertino, CA, USA
Tal Skverer
  • Weizmann Institute of Science, Rehovot, Israel

Funding

  • Goldreich, Oded: Partially supported by the Israel Science Foundation (grant No. 1041/18) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819702).
  • Rothblum, Guy N.: Received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819702), from the Israel Science Foundation (grant number 5219/17), and from the Simons Foundation Collaboration on the Theory of Algorithmic Fairness.
  • Skverer, Tal: Partially supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness.

Acknowledgements

We are grateful to Ron Rothblum for helpful discussions.

Cite As Get BibTex

Oded Goldreich, Guy N. Rothblum, and Tal Skverer. On Interactive Proofs of Proximity with Proof-Oblivious Queries. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 59:1-59:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ITCS.2023.59

Abstract

Interactive proofs of proximity (IPPs) offer ultra-fast approximate verification of assertions regarding their input, where ultra-fast means that only a small portion of the input is read and approximate verification is analogous to the notion of approximate decision that underlies property testing. Specifically, in an IPP, the prover can make the verifier accept each input in the property, but cannot fool the verifier into accepting an input that is far from the property (except for with small probability).
The verifier in an IPP system engages in two very different types of activities: interacting with an untrusted prover, and querying its input. The definition allows for arbitrary coordination between these two activities, but keeping them separate is both conceptually interesting and necessary for important applications such as addressing temporal considerations (i.e., at what time is each of the services available) and facilitating the construction of zero-knowledge schemes. In this work we embark on a systematic study of IPPs with proof-oblivious queries, where the queries should not be affected by the interaction with the prover. We assign the query and interaction activities to separate modules, and consider different limitations on their coordination.
The most strict limitation requires these activities to be totally isolated from one another; they just feed their views to a separate deciding module. We show that such systems can be efficiently emulated by standard testers.
Going to the other extreme, we only disallow information to flow from the interacting module to the querying module, but allow free information flow in the other direction. We show that extremely efficient one-round (i.e., two-message) systems of such type can be used to verify properties that are extremely hard to test (without the help of a prover). That is, the complexity of verifying can be polylogarithmic in the complexity of testing. This stands in contrast the MAPs (viewed as 1/2-round systems) in which proof-oblivious queries are as limited as our isolated model.
Our focus is on an intermediate model that allows shared randomness between the querying and interacting modules but no information flow between them. In this case we show that 1-round systems are efficiently emulated by standard testers but 3/2-round systems of extremely low complexity exist for properties that are extremely hard to test. One additional result about this model is that it can efficiently emulate any IPP for any property of low-degree polynomials.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Interactive proof systems
Keywords
  • Complexity Theory
  • Property Testing
  • Interactive Proofs
  • Interactive Proofs of Proximity
  • Proof-Oblivious Queries

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