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

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

Available format(s)
Cryptographic protocols
Publication info
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
2022-06-23: revised
2022-03-31: received
See all versions
Short URL
Creative Commons Attribution


      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},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.