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Revision #1 to TR13-183 | 5th April 2015 20:32

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

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Revision #1
Authors: Ran Raz, Ron Rothblum, Yael Tauman Kalai
Accepted on: 5th April 2015 20:32
Downloads: 835
Keywords: 


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.



Changes to previous version:

Corrected the verifier's running time.


Paper:

TR13-183 | 22nd December 2013 22:55

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





TR13-183
Authors: Yael Tauman Kalai, Ran Raz, Ron Rothblum
Publication: 22nd December 2013 23:03
Downloads: 1672
Keywords: 


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.



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