We construct a 1-round delegation scheme for every language computable in time t = t(n) and space s = s(n), where the running time of the prover is poly(t) and the running time of the verifier is O\u02dc(n + poly(s)) (where O\u02dc hides polylog(t) factors). 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) and space s = s(n), we construct MIPs that are sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is O\u02dc(s), and the running time of the verifier is O\u02dc(s + n). We then show how to use the method suggested by Aiello et al. (ICALP, 2000) to convert our MIP into a 1-round delegation scheme, by using a computational private information retrieval (PIR) scheme. Thus, assuming the existence of a sub-exponentially secure PIR scheme, we get our 1-round delegation scheme.<\/p>\n","protected":false},"excerpt":{"rendered":"
We construct a 1-round delegation scheme for every language computable in time t = t(n) and space s = s(n), where the running time of the prover is poly(t) and the running time of the verifier is O\u02dc(n + poly(s)) (where O\u02dc hides polylog(t) factors). 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