Arguments of proximity [Extended Abstract]

An interactive proof of proximity (IPP) is an interactive protocol in which a prover tries to convince a sublinear-time verifier that x ∈ L. Since the verifier runs in sublinear-time, following the property testing literature, the verifier is only required to reject inputs that are far from L. In a recent work, Rothblum et. al (STOC, 2013) constructed an IPP for every language computable by a low depth circuit. In this work, we study the computational analogue, where soundness is required to hold only against a computationally bounded cheating prover. We call such protocols interactive arguments of proximity. Assuming the existence of a sub-exponentially secure FHE scheme, we construct a one-round argument of proximity for every language computable in time t, where the running time of the verifier is o(n)+polylog(t) and the running time of the prover is poly(t). As our second result, assuming sufficiently hard cryptographic PRGs, we give a lower bound, showing that the parameters obtained both in the IPPs of Rothblum et al., and in our arguments of proximity, are close to optimal. Finally, we observe that any one-round argument of proximity immediately yields a one-round delegation scheme (without proximity) where the verifier runs in linear time.