*13:17*[Pub][ePrint] How to Delegate Computations: The Power of No-Signaling Proofs, by Yael Tauman Kalai and Ran Raz and Ron Rothblum

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.