From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again

Nir Bitansky, Ran Canetti, Alessandro Chiesa, Eran Tromer

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

Abstract

The existence of succinct non-interactive arguments for NP (i.e., non-interactive computationally-sound proofs where the verifier's work is essentially independent of the complexity of the NP nondeterministic verifier) has been an intriguing question for the past two decades. Other than CS proofs in the random oracle model [Micali, FOCS '94], the only existing candidate construction is based on an elaborate assumption that is tailored to a specific protocol [Di Crescenzo and Lipmaa, CiE '08]. We formulate a general and relatively natural notion of an extractable collision-resistant hash function (ECRH) and show that, if ECRHs exist, then a modified version of Di Crescenzo and Lipmaa's protocol is a succinct non-interactive argument for NP. Furthermore, the modified protocol is actually a succinct non-interactive adaptive argument of knowledge (SNARK). We then propose several candidate constructions for ECRHs and relaxations thereof. We demonstrate the applicability of SNARKs to various forms of delegation of computation, to succinct non-interactive zero knowledge arguments, and to succinct two-party secure computation. Finally, we show that SNARKs essentially imply the existence of ECRHs, thus demonstrating the necessity of the assumption.

Original languageEnglish
Title of host publicationITCS 2012 - Innovations in Theoretical Computer Science Conference
Pages326-349
Number of pages24
DOIs
StatePublished - 2012
Event3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012 - Cambridge, MA, United States
Duration: 8 Jan 201210 Jan 2012

Publication series

NameITCS 2012 - Innovations in Theoretical Computer Science Conference

Conference

Conference3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012
Country/TerritoryUnited States
CityCambridge, MA
Period8/01/1210/01/12

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