Welcome to the resource topic for 2024/617
Title:
Lattice-Based Succinct Mercurial Functional Commitment for Circuits: Definitions and Constructions
Authors: Hongxiao Wang, Siu-Ming Yiu, Yanmin Zhao, Zoe L. Jiang, Min Xie
Abstract:Vector commitments gain a lot of attention because of their wide usage in applications such as blockchain and accumulator. Mercurial vector commitments and mercurial functional commitments (MFC), as significant variants of VC, are the central techniques to construct more advanced cryptographic primitives such as zero-knowledge set and zero-knowledge functional elementary database (ZK-FEDB).
However, the current MFC only supports linear functions, limiting its application, i.e. building the ZK-FEDB that only supports linear function queries. Besides, to our best knowledge, the existing MFC and ZK-FEDBs, including the one proposed by Zhang and Deng (ASIACRYPT '23) using RSA accumulators, are all in the group model and cannot resist the attack of quantum computers.
To break these limitations, we formalize the first system model and security model of MFC for circuits. Then, we target some specific properties of a new falsifiable assumption, i.e. the \mathsf{BASIS} assumption proposed by Wee and Wu (EUROCRYPT '23) to construct the first lattice-based succinct mercurial functional commitment for circuits. To the application, we show that our constructions can be used to build the first lattice-based ZK-FEDB directly within the existing generic framework.
ePrint: https://eprint.iacr.org/2024/617
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