An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision

Hongjian Yin, E. Chen, Yan Zhu, Rongquan Feng, Stephen S. Yau

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we address the problem of secure decision of membership. We present a Zero-Knowledge Dual Membership Proof (ZKDMP) protocol, which can support positive and negative (Pos-and-Neg) membership decisions simultaneously. To do it, two secure aggregation functions are used to compact an arbitrarily-sized subset into an element in a cryptographic space. By using these aggregation functions, a subset can achieve a secure representation, and the representation size of the subsets is reduced to the theoretical lower limit. Moreover, the zeros-based and poles-based secure representation of the subset are used to decide Pos-and-Neg membership, respectively. We further verify the feasibility of combining these two secure representations of the subset, so this result is used to construct our dual membership decision cryptosystem. Specifically, our ZKDMP protocol is proposed for dual membership decisions, which can realize a cryptographic proof of strict Pos-and-Neg membership simultaneously. Furthermore, the zero-knowledge property of our construction ensures that the information of the tested element will not be leaked during the implementation of the protocol. In addition, we provide detailed security proof of our ZKDMP protocol, including positive completeness, negative completeness, soundness and zero-knowledge.

Original languageEnglish (US)
Article number3217
JournalMathematics
Volume10
Issue number17
DOIs
StatePublished - Sep 2022
Externally publishedYes

Keywords

  • aggregation function
  • dual membership decision
  • security protocol
  • subset representation
  • zero-knowledge proof

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Mathematics(all)
  • Engineering (miscellaneous)

Fingerprint

Dive into the research topics of 'An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision'. Together they form a unique fingerprint.

Cite this