[Resource Topic] 2019/808: 2-Message Publicly Verifiable WI from (Subexponential) LWE

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2-Message Publicly Verifiable WI from (Subexponential) LWE

Authors: Alex Lombardi, Vinod Vaikuntanathan, Daniel Wichs


We construct a 2-message publicly verifiable witness indistinguishable argument system for NP assuming that the Learning with Errors (LWE) problem is subexponentially hard. Moreover, the protocol is delayed input''; that is, the verifier message in this protocol does not depend on the instance. This means that a single verifier message can be reused many times. We construct two variants of this argument system: one variant is adaptively sound, while the other is public-coin (but only non-adaptively sound). We obtain our result via a generic transformation showing that the correlation intractable hash families constructed by Canetti et al. (STOC 2019) and Peikert and Shiehian (CRYPTO 2019) suffice to construct such 2-message WI arguments when combined with an appropriately chosen trapdoor Sigma-protocol.‘’ Our construction can be seen as an adaptation of the Dwork-Naor ``reverse randomization’’ paradigm (FOCS '00) for constructing ZAPs to the setting of computational soundness rather than statistical soundness. Our adaptation of the Dwork-Naor transformation crucially relies on complexity leveraging to prove that soundness is preserved.

ePrint: https://eprint.iacr.org/2019/808

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