TY - JOUR
T1 - An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision
AU - Yin, Hongjian
AU - Chen, E.
AU - Zhu, Yan
AU - Feng, Rongquan
AU - Yau, Stephen S.
N1 - Funding Information:
This research was funded by the National Key Technologies Research and Development Programs of China grant number 2018YFB1402702; and the National Natural Science Foundation of China grant number 61972032.
Publisher Copyright:
© 2022 by the authors.
PY - 2022/9
Y1 - 2022/9
N2 - 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.
AB - 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.
KW - aggregation function
KW - dual membership decision
KW - security protocol
KW - subset representation
KW - zero-knowledge proof
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U2 - 10.3390/math10173217
DO - 10.3390/math10173217
M3 - Article
AN - SCOPUS:85137796191
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 17
M1 - 3217
ER -