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

Hongjian Yin, E Chen (), Yan Zhu (), Rongquan Feng and Stephen S. Yau
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Hongjian Yin: School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
E Chen: School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
Yan Zhu: School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
Rongquan Feng: School of Mathematical Science, Peking University, Beijing 100084, China
Stephen S. Yau: School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85281, USA

Mathematics, 2022, vol. 10, issue 17, 1-25

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.

Keywords: security protocol; aggregation function; subset representation; dual membership decision; zero-knowledge proof (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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