Cryptology ePrint Archive: Report 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.

Category / Keywords: cryptographic protocols / Aggregatable polynomial commitment, inner-product commitment, univariate sumcheck, updatable and universal zk-SNARK

Date: received 29 Mar 2022, last revised 29 Mar 2022

Contact author: helger lipmaa at gmail com

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Version: 20220331:072859 (All versions of this report)

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