Universal Samplers with Fast Verification

Recently, Hofheinz, Jager, Khurana, Sahai, Waters and Zhandry [9] proposed a new primitive called universal samplers that allows oblivious sampling from arbitrary distributions, and showed how to construct universal samplers using indistinguishability obfuscation (iO) in the ROM. One important limitation for applying universal samplers in practice is that the constructions are built upon indistinguishability obfuscation. The costs of using current iO constructions is prohibitively large. We ask is whether the cost of a (universal) sampling could be paid by one party and then shared (soundly) with all other users? We address this question by introducing the notion of universal samplers with verification. Our notion follows the general path of [9], but has additional semantics that allows for validation of a sample. In this work we define and give a construction for universal samplers with verification. Our verification procedure is simple and built upon one-time signatures, making verification of a sample much faster than computing it. Security is proved under the sub exponential hardness of indistinguishability obfuscation, puncturable pseudorandom functions, and one-time signatures.