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Paper 2022/406

Counting Vampires: From Univariate Sumcheck to Updatable ZK-SNARK

Helger Lipmaa and Janno Siim and Michal Zajac

Abstract

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 (five group elements and two integers) for $\mathsf{NP}$. In addition, $\mathfrak{Vampire}$ uses the aggregated polynomial commitment scheme of Boneh et al. Differently from the previous (efficient) work, both $\mathfrak{Count}$ and $\mathfrak{Vampire}$ have an updatable SRS that consists of non-consequent monomials.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Preprint. MINOR revision.
Keywords
Aggregatable polynomial commitmentinner-product commitmentunivariate sumcheckupdatable and universal zk-SNARK
Contact author(s)
helger lipmaa @ gmail com
History
2022-06-23: revised
2022-03-31: received
See all versions
Short URL
https://ia.cr/2022/406
License
Creative Commons Attribution
CC BY
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