An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision
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 arb...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/17/3217 |
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| author | Hongjian Yin E Chen Yan Zhu Rongquan Feng Stephen S. Yau |
| author_facet | Hongjian Yin E Chen Yan Zhu Rongquan Feng Stephen S. Yau |
| author_sort | Hongjian Yin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T01:31:43Z |
| format | Article |
| id | doaj.art-816dfa05eec74b23b30139c5252a7de9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:31:43Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-816dfa05eec74b23b30139c5252a7de92023-11-23T13:40:32ZengMDPI AGMathematics2227-73902022-09-011017321710.3390/math10173217An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership DecisionHongjian Yin0E Chen1Yan Zhu2Rongquan Feng3Stephen S. Yau4School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematical Science, Peking University, Beijing 100084, ChinaSchool of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85281, USAIn 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.https://www.mdpi.com/2227-7390/10/17/3217security protocolaggregation functionsubset representationdual membership decisionzero-knowledge proof |
| spellingShingle | Hongjian Yin E Chen Yan Zhu Rongquan Feng Stephen S. Yau An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision Mathematics security protocol aggregation function subset representation dual membership decision zero-knowledge proof |
| title | An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision |
| title_full | An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision |
| title_fullStr | An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision |
| title_full_unstemmed | An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision |
| title_short | An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision |
| title_sort | efficient zero knowledge dual membership proof supporting pos and neg membership decision |
| topic | security protocol aggregation function subset representation dual membership decision zero-knowledge proof |
| url | https://www.mdpi.com/2227-7390/10/17/3217 |
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