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Algebraic Construction for Zero-Knowledge Sets

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Abstract

Zero knowledge sets is a new cryptographic primitive introduced by Micali, Rabin, and Kilian in FOCS 2003. It has been intensively studied recently. However all the existing ZKS schemes follow the basic structure by Micali et al. That is, the schemes employ the Merkle tree as a basic structure and mercurial commitments as the commitment units to nodes of the tree. The proof for any query consists of an authentication chain. We propose in this paper a new algebraic scheme that is completely different from all the existing schemes. Our new scheme is computationally secure under the standard strong RSA assumption. Neither mercurial commitments nor tree structure is used in the new construction. In fact, the prover in our construction commits the desired set without any trapdoor information, which is another key important difference from the previous approaches.

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Author information

Authors and Affiliations

  1. The State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Rui Xue

  2. Department of Computer Science, Purdue University, West Lafayette, U.S.A.

    Ning-Hui Li

  3. Software and Solutions Group, Intel Corporation, Hillsboro, U.S.A.

    Jiang-Tao Li

Authors
  1. Rui Xue
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  2. Ning-Hui Li
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  3. Jiang-Tao Li
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Corresponding author

Correspondence to Rui Xue.

Additional information

This work is supported by NSF of USA under Grant Nos. IIS-0430274, and CCR-0325951, and sponsors of CERIAS. Rui Xue is partially supported by the Fund of the China Scholarship Council, partially by National Natural Science Foundation of China under Grant No. 60773029, National Grand Fundamental Research 973 Program of China under Grant No. 2007CB311202, and the National High Technology Research and Development 863 Program of China under Grant No. 2006AA01Z427.

Most of this work was done while Jiang-Tao Li and Rui Xue were at Purdue University.

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Xue, R., Li, NH. & Li, JT. Algebraic Construction for Zero-Knowledge Sets. J. Comput. Sci. Technol. 23, 166–175 (2008). https://doi.org/10.1007/s11390-008-9119-x

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