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Where Delegation Meets Einstein

Presented by: 
Y Tauman Kalai
Date: 
Thursday 12th April 2012 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
We show a curious connection between the problem of *computation delegation* and the model of *no-signalling multi-prover interactive proofs*, 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 law that information cannot travel instantly (and is, like matter, limited by the speed of light).

We consider the method suggested by Aiello et. al. for converting a 1-round multi-prover interactive proof (MIP) into a 1-round delegation scheme, by using a computational private information retrieval (PIR) scheme. On one direction, we show that if the underlying MIP protocol is sound against statistically no-signalling cheating provers then the resulting delegation protocol is secure (under the assumption that the underlying PIR is secure for attackers of sub-exponential size). On the other direction, we show that if the resulting delegation protocol is secure for every PIR scheme, and the proof of security is a black-box reduction that reduces the security of the protocol to the security of any ``standard'' cryptographic assumption, and such that the number of calls made by the reduction to the cheating prover is independent of the security parameter, then the underlying MIP protocol is sound against statistically no-signalling cheating provers.

This is joint work with Ran Raz and Ron Rothblum.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons