How to Delegate Computations: The Power of No-Signaling Proofs

Yael Tauman Kalai, Ran Raz, Ron D. Rothblum

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a 1-round delegation scheme (i.e., argument-system) 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), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.

Original languageEnglish (US)
Article number1
JournalJournal of the ACM
Volume69
Issue number1
DOIs
StatePublished - Feb 2022

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Hardware and Architecture
  • Artificial Intelligence

Keywords

  • Delegating computations
  • no-signaling proofs

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