Efficient batch verification for UP

Omer Reingold, Guy N. Rothblum, Ron D. Rothblum

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Consider a setting in which a prover wants to convince a verifier of the correctness of k NP statements. For example, the prover wants to convince the verifier that k given integers N1,⋯, Nk are all RSA moduli (i.e., products of equal length primes). Clearly this problem can be solved by simply having the prover send the k NP witnesses, but this involves a lot of communication. Can interaction help? In particular, is it possible to construct interactive proofs for this task whose communication grows sub-linearly with k? Our main result is such an interactive proof for verifying the correctness of any k UP statements (i.e., NP statements that have a unique witness). The proof-system uses only a constant number of rounds and the communication complexity is kδ · poly (m), where δ > 0 is an arbitrarily small constant, m is the length of a single witness, and the poly term refers to a fixed polynomial that only depends on the language and not on δ. The (honest) prover strategy can be implemented in polynomial-time given access to the k (unique) witnesses. Our proof leverages "interactive witness verification" (IWV), a new type of proof-system that may be of independent interest. An IWV is a proof-system in which the verifier needs to verify the correctness of an NP statement using: (i) a sublinear number of queries to an alleged NP witness, and (ii) a short interaction with a powerful but untrusted prover. In contrast to the setting of PCPs and Interactive PCPs, here the verifier only has access to the raw NP witness, rather than some encoding thereof.

Original languageEnglish
Title of host publication33rd Computational Complexity Conference, CCC 2018
EditorsRocco A. Servedio
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages23
ISBN (Electronic)9783959770699
StatePublished - 1 Jun 2018
Event33rd Computational Complexity Conference, CCC 2018 - San Diego, United States
Duration: 22 Jun 201824 Jun 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference33rd Computational Complexity Conference, CCC 2018
Country/TerritoryUnited States
CitySan Diego

All Science Journal Classification (ASJC) codes

  • Software


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