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Efficient Batch Verification for UP

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

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ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Interactive Proof
  • Batch Verification
  • Unique Solution

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Abstract

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.

Cite As Get BibTex

Omer Reingold, Guy N. Rothblum, and Ron D. Rothblum. Efficient Batch Verification for UP. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 22:1-22:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CCC.2018.22

Author Details

Omer Reingold
  • Stanford University, Palo Alto CA, USA
Guy N. Rothblum
  • Weizmann Institute, Rehovot, Israel
Ron D. Rothblum
  • MIT and Northeastern University, Cambridge and Boston MA, USA

Funding

  • Reingold, Omer: Supported by NSF grant CCF-1749750.
  • Rothblum, Ron D.: Research supported in part by NSF Grants CNS-1350619 and CNS-1414119, Alfred P. Sloan Research Fellowship, Microsoft Faculty Fellowship and in part by the Defense Advanced Research Projects Agency (DARPA), the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236 and by the Cybersecurity and Privacy Institute at Northeastern University.

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