SNARGs for Monotone Policy Batch NP.

We construct a succinct non-interactive argument ( SNARG ) for the class of monotone policy batch NP languages, under the Learning with Errors ( LWE ) assumption. This class is a subclass of NP that is associated with a monotone function f : { 0 , 1 } k → { 0 , 1 } and an NP language L , and contains instances ( x 1 , … , x k ) such that f ( b 1 , … , b k ) = 1 where b j = 1 if and only if x j ∈ L . Our SNARG s are arguments of knowledge in the non-adaptive setting, and satisfy a new notion of somewhere extractability against adaptive adversaries. This is the first SNARG under standard hardness assumptions for a sub-class of NP that is not known to have a (computational) non-signaling PCP with parameters compatible with the standard framework for constructing SNARG s dating back to [Kalai-Raz-Rothblum, STOC ’13]. Indeed, our approach necessarily departs from this framework. Our construction combines existing quasi-arguments for NP (based on batch arguments for NP ) with a new type of cryptographic encoding of the instance and a new analysis going from local to global soundness. The main novel ingredient used in our encoding is a predicate-extractable hash ( PEHash ) family, which is a primitive that generalizes the notion of a somewhere extractable hash. Whereas a somewhere extractable hash allows to extract a single input coordinate, our PEHash extracts a global property of the input. We view this primitive to be of independent interest, and believe that it will find other applications.