On Succinct Non-Interactive Arguments in Relativized Worlds

Megan Chen; Alessandro Chiesa; Nicholas Spooner

Paper 2022/383

On Succinct Non-Interactive Arguments in Relativized Worlds

Megan Chen, Alessandro Chiesa, and Nicholas Spooner

Abstract

Succinct non-interactive arguments of knowledge (SNARKs) are cryptographic proofs with strong efficiency properties. Applications of SNARKs often involve proving computations that include the SNARK verifier, a technique called recursive composition. Unfortunately, SNARKs with desirable features such as a transparent (public-coin) setup are known only in the random oracle model (ROM). In applications this oracle must be heuristically instantiated and used in a non-black-box way. In this paper we identify a natural oracle model, the low-degree random oracle model, in which there exist transparent SNARKs for all NP computations relative to this oracle. Informally, letting be a low-degree encoding of a random oracle, and assuming the existence of (standard-model) collision-resistant hash functions, there exist SNARKs relative to for all languages in . Such a SNARK can directly prove a computation about its own verifier. This capability leads to proof-carrying data (PCD) in the oracle model based solely on the existence of (standard-model) collision-resistant hash functions. To analyze this model, we introduce a more general framework, the linear code random oracle model (LCROM). We show how to obtain SNARKs in the LCROM for computations that query the oracle, given an accumulation scheme for oracle queries in the LCROM. Then we construct such an accumulation scheme for the special case of a low degree random oracle.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: A major revision of an IACR publication in EUROCRYPT 2022
Keywords: succinct arguments proof-carrying data random oracles
Contact author(s): megchen @ bu edu
alessandro chiesa @ epfl ch
nicholas spooner @ warwick ac uk
History: 2022-03-28: received
Short URL: https://ia.cr/2022/383
License: CC BY

BibTeX

@misc{cryptoeprint:2022/383,
      author = {Megan Chen and Alessandro Chiesa and Nicholas Spooner},
      title = {On Succinct Non-Interactive Arguments in Relativized Worlds},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/383},
      year = {2022},
      url = {https://eprint.iacr.org/2022/383}
}