SNARGs for Monotone Policy Batch NP

Zvika Brakerski*, Maya Farber Brodsky, Yael Tauman Kalai, Alex Lombardi, Omer Paneth

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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 (x1, …, xk) such that f(b1, …, bk) = 1 where bj= 1 if and only if xj∈ 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.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
EditorsHelena Handschuh, Anna Lysyanskaya
PublisherSpringer Science and Business Media Deutschland GmbH
Pages252-283
Number of pages32
ISBN (Print)9783031385445
DOIs
StatePublished - 2023
EventAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings - Santa Barbara, United States
Duration: 20 Aug 202324 Aug 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14082 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Country/TerritoryUnited States
CitySanta Barbara
Period20/08/2324/08/23

Funding

FundersFunder number
Checkpoint Institute of Information Security
Defense Advanced Research Projects AgencyHR00112020023
European Research Council756482
Israel Science Foundation3426/21, 1789/19
Horizon 2020

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