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

Yael Tauman Kalai, Ran Raz, and Ron D. Rothblum

##### 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.

Note: Corrected minor error in verifier's running time.

Available format(s)
Publication info
Preprint. MINOR revision.
Keywords
DelegationProbabilistic Proof SystemsInteractive Arguments
Contact author(s)
ron rothblum @ weizmann ac il
History
2015-05-01: revised
See all versions
Short URL
https://ia.cr/2013/862

CC BY

BibTeX

@misc{cryptoeprint:2013/862,
author = {Yael Tauman Kalai and Ran Raz and Ron D.  Rothblum},
title = {How to Delegate Computations: The Power of No-Signaling Proofs},
howpublished = {Cryptology ePrint Archive, Paper 2013/862},
year = {2013},
note = {\url{https://eprint.iacr.org/2013/862}},
url = {https://eprint.iacr.org/2013/862}
}

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