ECCC-Report TR18-022https://eccc.weizmann.ac.il/report/2018/022Comments and Revisions published for TR18-022en-usThu, 01 Feb 2018 20:14:00 +0200
Paper TR18-022
| Efficient Batch Verification for UP |
Omer Reingold,
Guy Rothblum,
Ron Rothblum
https://eccc.weizmann.ac.il/report/2018/022Consider 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 $k^\delta \cdot poly( m )$, 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. Thu, 01 Feb 2018 20:14:00 +0200https://eccc.weizmann.ac.il/report/2018/022