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- W2337421628 abstract "An interactive proof of proximity ( $$mathsf{{IPP}}$$ ) is an interactive protocol in which a prover tries to convince a sublinear-time verifier that $$x in mathcal {L}$$ . Since the verifier runs in sublinear-time, following the property testing literature, the verifier is only required to reject inputs that are far from $$mathcal {L}$$ . In a recent work, Rothblum et. al (STOC, 2013) constructed an $$mathsf{{IPP}}$$ 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 $$mathsf{{FHE}}$$ scheme, we construct a one-round argument of proximity for every language computable in time t, where the running time of the verifier is $$o(n) + mathsf{polylog}(t)$$ and the running time of the prover is $$mathsf{poly}(t)$$ . As our second result, assuming sufficiently hard cryptographic $$mathsf{PRG }$$ s, we give a lower bound, showing that the parameters obtained both in the $$mathsf{{IPP}}$$ s 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." @default.
- W2337421628 created "2016-06-24" @default.
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- W2337421628 date "2015-01-01" @default.
- W2337421628 modified "2023-10-01" @default.
- W2337421628 title "Arguments of Proximity" @default.
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- W2337421628 doi "https://doi.org/10.1007/978-3-662-48000-7_21" @default.
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