Counting Vampires: From Univariate Sumcheck to Updatable ZK-SNARK

Helger Lipmaa; Janno Siim; Michal Zajac

Paper 2022/406

Counting Vampires: From Univariate Sumcheck to Updatable ZK-SNARK

Helger Lipmaa, Simula UiB, Norway

Janno Siim, Simula UiB, Norway

Michal Zajac, Nethermind, UK

Abstract

We propose a univariate sumcheck argument $Count$ of essentially optimal communication efficiency of one group element. While the previously most efficient univariate sumcheck argument of Aurora is based on polynomial commitments, $Count$ is based on inner-product commitments. We use $Count$ to construct a new pairing-based updatable and universal zk-SNARK $Vampire$ with the shortest known argument length (four group and two finite field elements) for $NP$ . In addition, $Vampire$ uses the aggregated polynomial commitment scheme of Boneh \emph{et al}.

Note: This is version 2.0 of Vampire. The argument length is shorter by one more group element while the SRS is somewhat longer. Version 1.0 can be retrieved from eprint (see the first version of this eprint from March 2022).

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Aggregatable polynomial commitment inner-product commitment univariate sumcheck updatable and universal zk-SNARK
Contact author(s): helger lipmaa @ gmail com
jannosiim @ gmail com
m p zajac @ gmail com
History: 2022-06-23: revised; 2022-03-31: received; See all versions
Short URL: https://ia.cr/2022/406
License: CC BY

BibTeX

@misc{cryptoeprint:2022/406,
      author = {Helger Lipmaa and Janno Siim and Michal Zajac},
      title = {Counting Vampires: From Univariate Sumcheck to Updatable {ZK}-{SNARK}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/406},
      year = {2022},
      url = {https://eprint.iacr.org/2022/406}
}