Lattice-Based Succinct Mercurial Functional Commitment for Boolean 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 Boolean 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 (VC) have gained significant attention due to their extensive use in applications such as blockchain and accumulators. Mercurial vector commitments (MVC) and mercurial functional commitments (MFC), as variants of VC, are central techniques for constructing more advanced cryptographic primitives, such as zero-knowledge sets and zero-knowledge functional elementary databases (ZK-FEDB). However, existing MFCs , which limits their applicability—for instance, in building ZK-FEDBs that support only linear function queries. Moreover, to the best of our knowledge, the current MFCs and ZK-FEDBs, including the state-of-the-art proposed by Zhang and Deng (ASIACRYPT '23) using RSA accumulators, are all based on group-based assumptions and . To address these limitations, we formalize the system and security models of MFC to support Boolean circuits. Then, we target specific properties of a new falsifiable assumption, namely the assumption proposed by Wee and Wu (EUROCRYPT '23), to construct the lattice-based succinct mercurial functional commitment for Boolean circuits. As an application of our construction, we demonstrate how it can be used to build the lattice-based ZK-FEDB 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: 2024-08-20: revised; 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 Boolean Circuits: Definitions and Constructions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/617},
      year = {2024},
      url = {https://eprint.iacr.org/2024/617}
}