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Concise ID-based mercurial functional commitments and applications to zero-knowledge sets

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Abstract

Zero-knowledge sets (ZKS) is a basic cryptographic primitive that can be used to commit to a set S and prove statements such as \(x\in S\) or \(x\notin S\), without revealing anything else on S. Mercurial commitment is a useful tool to construct ZKS. Trapdoor q-mercurial commitment, an extension of normal mercurial commitment, results in more efficient ZKS with much shorter proofs when combining with a q-arity Merkle tree. ID-based trapdoor mercurial commitment is proposed by Chen et al. in 2011 to mainly solve the conflicts between propagation and plagiarism of non-interactive zero-knowledge proofs in ZKS, but it only supports binary Merkle tree. In this paper, we present the first ID-based mercurial functional commitment which provides more efficient ZKS than Chen et al.’s scheme by extending it to vector commitment. Moreover, our mercurial functional commitment supports the functionality of linear functions, where commitment to a message vector (e.g., \(\mathbf {m}=(m_1,m_2,\ldots ,m_n)\in {\mathcal {D}}^n\)) can later be de-committed to a linear function \(\sum _{i=1}^n m_i x_i=y\in {\mathcal {R}}\) of some vector coordinates. It has applications in generalized ZKS which allows us to provide proof of a linear computation on values in a database other than just membership/non-membership statements. Besides, the proposed mercurial functional commitment, as an extension of mercurial vector commitment, is concise (the sizes of the commitments and hard/soft openings are independent of the length of the function description or messages) and achieves both linear-size public keys and constant-size assumptions.

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Notes

  1. \(ID_S,ID_R,ID_T\) denote the identity of the sender, receiver and time, respectively.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Nos. 61902081 and 61960206014), the Natural Science Foundation of Guangdong Province, China (No. 2018A030313974), and the Science and Technology Planning Project of Guangdong (No. 2018A050506087). W. Susilo is partially supported by the Australian Research Council Discovery Project (DP180100665).

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Authors and Affiliations

  1. School of Internet Finance and Information Engineering, Guangdong University of Finance, Guangzhou, 510521, People’s Republic of China

    Chunhui Wu

  2. State Key Laboratory of Integrated Service Networks (ISN), Xidian University, Xi’an, 710071, People’s Republic of China

    Xiaofeng Chen

  3. School of Computer Science and Software Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia

    Willy Susilo

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  1. Chunhui Wu
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  2. Xiaofeng Chen
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  3. Willy Susilo
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Correspondence to Willy Susilo.

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Wu, C., Chen, X. & Susilo, W. Concise ID-based mercurial functional commitments and applications to zero-knowledge sets. Int. J. Inf. Secur. 19, 453–464 (2020). https://doi.org/10.1007/s10207-019-00466-7

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