Lattice-Based Succinct Mercurial Functional Commitment for Circuits: Definitions and Constructions

Hongxiao Wang; Siu-Ming Yiu; Yanmin Zhao; Zoe L. Jiang; Min Xie

Paper 2024/617

Lattice-Based Succinct Mercurial Functional Commitment for Circuits: Definitions and Constructions

Hongxiao Wang

, The University of Hong Kong

Siu-Ming Yiu, The University of Hong Kong

Yanmin Zhao, The University of Hong Kong

Zoe L. Jiang, Harbin Institute of Technology, Shenzhen

Min Xie, Harbin Institute of Technology, Shenzhen

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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Vector commitment Mercurial commitment Lattice Zero-knowledge elementary database
Contact author(s): hxwang @ cs hku hk
smyiu @ cs hku hk
ymzhao @ cs hku hk
zoeljiang @ hit edu cn
minxie @ stu hit edu cn
History: 2024-04-26: approved; 2024-04-22: received; See all versions
Short URL: https://ia.cr/2024/617
License: CC BY

BibTeX

@misc{cryptoeprint:2024/617,
      author = {Hongxiao Wang and Siu-Ming Yiu and Yanmin Zhao and Zoe L. Jiang and Min Xie},
      title = {Lattice-Based Succinct Mercurial Functional Commitment for Circuits: Definitions and Constructions},
      howpublished = {Cryptology ePrint Archive, Paper 2024/617},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/617}},
      url = {https://eprint.iacr.org/2024/617}
}