[Resource Topic] 2023/346: How to achieve bidirectional zero-knowledge authentication?

Welcome to the resource topic for 2023/346

How to achieve bidirectional zero-knowledge authentication?

Authors: Jin Li, Xingyu Li, Chang Chen, Guoyu Yang, Junyang Li, Qi Chen, Hongyang Yan


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.

ePrint: https://eprint.iacr.org/2023/346

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