TY - GEN

T1 - Efficient batch verification for UP

AU - Reingold, Omer

AU - Rothblum, Guy N.

AU - Rothblum, Ron D.

N1 - We thank Oded Goldreich for illuminating conversations and particularly for his insights that helped us crystallize the notion of Interactive Witness Verification. Supported by NSF grant CCF-1749750. 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.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

U2 - https://doi.org/10.4230/LIPIcs.CCC.2018.22

DO - https://doi.org/10.4230/LIPIcs.CCC.2018.22

M3 - منشور من مؤتمر

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 22:1-22:23

BT - 33rd Computational Complexity Conference, CCC 2018

A2 - Servedio, Rocco A.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 33rd Computational Complexity Conference, CCC 2018

Y2 - 22 June 2018 through 24 June 2018

ER -