Arguments Of Proximity [Extended Abstract]
ADVANCES IN CRYPTOLOGY, PT II(2015)
摘要
An interactive proof of proximity (IPP) is an interactive protocol in which a prover tries to convince a sublinear-time verifier that x is an element of 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.
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