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

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 MIP s 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.