International Association
for Cryptologic Research

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

\\emph{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 \\emph{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.

Going beyond $\\ECRH$s, we formulate the notion of {\\em extractable

one-way functions ($\\EOWF$s)}. Assuming the existence of a natural

variant of $\\EOWF$s, we construct a $2$-message

selective-opening-attack secure commitment scheme and a 3-round

zero-knowledge argument of knowledge. Furthermore, if the $\\EOWF$s are

concurrently extractable, the 3-round zero-knowledge protocol is also

concurrent zero-knowledge.

Our constructions circumvent previous black-box impossibility

results regarding these protocols by relying on $\\EOWF$s as the non-black-box component in the security reductions.