Delegation For Bounded Space

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(n + poly(s)) (where O 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 M I Ps that are sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is 6(8), and the running time of the verifier is 6(8 n). We then show how to use the method suggested by Aiello et al. (ICALP, 2000) to convert our M I P 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.