Paper 2023/346

How to achieve bidirectional zero-knowledge authentication?

Jin Li, Guangzhou University
Xingyu Li, Guangzhou University
Chang Chen, Beijing Jiaotong University
Guoyu Yang, Guangzhou University
Junyang Li, Guangzhou University
Qi Chen, Guangzhou University
Hongyang Yan, Guangzhou University

Due to the completeness, reliability and zero-knowledge nature, the zero-knowledge proof is widely used to designed various protocols, including zero-knowledge authentication protocols. However, the existing zero-knowledge proof scheme cannot realize bidirectional authentication. In this paper, we design a series of bidirectional zero-knowledge protocols based on two new flavors of operations applicable to multiplicative cyclic group. The two notions are formally defined in this paper. We also provide some formal definitions and properties for the two notions. According to our definitions, any bounded polynomial function defined on multiplicative cyclic group has duality and mirror. Based on the two operations, we introduce and formally define dual commitment scheme and mirror commitment scheme. Besides, we provide two efficient constructions for dual commitment and mirror commitment respectively based on CDH assumption and RSA assumption, and named DCCDH, DCRSA, MCCDH and MCRSA respectively. We also provide the extended version supporting multiple messages in the appendix. Then, we design some efficient non-interactive as well as interactive zero-knowledge authentication protocols based on these commitments. The protocols allow two participants to submit commitments to each other so that they can achieve mutual zero-knowledge authentication only a communication initialization needed. Moreovere , similar to other commitment schemes, our schemes also can be widely used to construction of other schemes for cryptography, such as, verifiable secret sharing, zero-knowledge sets, credentials and content extraction signatures.

Note: We have corrected two symbols.

Available format(s)
Cryptographic protocols
Publication info
dualitymirrordual commitmentmirror commitmentzero-knowledge authenticationnon-interactive protocol
Contact author(s)
lijin @ gzhu edu cn
XYLhdu19 @ 163 com
neucc1997 @ gmail com
yangguoyu1020 @ 163 com
jhouse nr @ qq com
chenqi @ gzhu edu cn
hyang_yan @ gzhu edu cn
2023-05-30: last of 2 revisions
2023-03-09: received
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      author = {Jin Li and Xingyu Li and Chang Chen and Guoyu Yang and Junyang Li and Qi Chen and Hongyang Yan},
      title = {How to achieve bidirectional zero-knowledge authentication?},
      howpublished = {Cryptology ePrint Archive, Paper 2023/346},
      year = {2023},
      note = {\url{}},
      url = {}
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