How to delegate computations: The power of no-signaling proofs

Yael Tauman Kalai, Ran Razy, Ron D. Rothblumz

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

55 Scopus citations

Abstract

We construct a 1-round delegation scheme (i.e., argumentsystem) for every language computable in time t = t(n), where the running time of the prover is poly(t) and the running time of the verifier is n · polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval (PIR) scheme. The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies, a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time t = t(n), we construct a multi-prover interactive proof (MIP) that is sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is polylog(t), and the running time of the verifier is n · polylog(t). In particular, this shows that the class of languages that have polynomial-time MIPs that are sound against no-signaling strategies, is exactly EXP. Previously, this class was only known to contain PSPACE. To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et al : (ICALP, 2000). This method relies on the existence of a sub-exponentially secure PIR scheme, and was proved secure by Kalai et al : (STOC, 2013) assuming the underlying MIP is secure against no-signaling provers.

Original languageEnglish (US)
Title of host publicationSTOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages485-494
Number of pages10
ISBN (Print)9781450327107
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States
Duration: May 31 2014Jun 3 2014

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other4th Annual ACM Symposium on Theory of Computing, STOC 2014
CountryUnited States
CityNew York, NY
Period5/31/146/3/14

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Interactive arguments
  • No-signaling proof-systems
  • Verifiable delegation

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