2026-07-25T08:26:43Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8868 2024-03-06T10:42:52Z ddc:004 open_access

Efficient Batch Verification for UP Reingold, Omer Rothblum, Guy N. Rothblum, Ron D. Interactive Proof Batch Verification Unique Solution 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 N_1,...,N_k 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 k^delta * poly(m), where delta>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 delta. 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Omer Reingold and Guy N. Rothblum and Ron D. Rothblum 2018 Is Part Of LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2018.22 urn:nbn:de:0030-drops-88681 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.22 eng https://creativecommons.org/licenses/by/3.0/legalcode