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International Conference on Information Security and Cryptology

Inscrypt 2021: Information Security and Cryptology pp 281–298Cite as

Improved Zero-Knowledge Argument of Encrypted Extended Permutation

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 13007)

Abstract

Extended permutation (EP) is a generalized notion of the standard permutation. Unlike the one-to-one correspondence mapping of the standard permutation, EP allows to replicate or omit elements as many times as needed during the mapping. EP is useful in the area of secure multi-party computation (MPC), especially for the problem of private function evaluation (PFE). As a special class of MPC problems, PFE focuses on the scenario where a party holds a private circuit C while all other parties hold their private inputs \(x_1, \ldots , x_n\), respectively. The goal of PFE protocols is to securely compute the evaluation result \(C(x_1, \ldots , x_n)\), while any other information beyond \(C(x_1, \ldots , x_n)\) is hidden. EP here is introduced to describe the topological structure of the circuit C, and it is further used to support the evaluation of C privately.

For an actively secure PFE protocol, it is crucial to guarantee that the private circuit provider cannot deviate from the protocol to learn more information. Hence, we need to ensure that the private circuit provider correctly performs an EP. This seeks the help of the so-called zero-knowledge argument of encrypted extended permutation protocol. In this paper, we provide an improvement of this protocol. Our new protocol can be instantiated to be non-interactive while the previous protocol should be interactive. Meanwhile, compared with the previous protocol, our protocol is significantly (e.g., more than \(3.4\times \)) faster, and the communication cost is only around \(24\%\) of that of the previous one.

Keywords

  • Elgamal encryption
  • Extended permutation
  • Private function evaluation
  • Zero-knowledge

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Fig. 1.
Fig. 2.
Fig. 3.

Notes

  1. 1.

    Since \(\mathsf{OW}_8\) and \(\mathsf{OW}_9\), as output wires of the circuit C, have no connections to other wires, we can simply omit them in the EP.

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Acknowledgments

We thank the reviewers for their detailed and helpful comments. Y. Liu and Q. Wang partially supported by the Shenzhen fundamental research programs under Grant no. 20200925154814002 and Guangdong Provincial Key Laboratory (Grant No. 2020B121201001). Y. Liu and S.-M. Yiu were also partially supported by ITF, Hong Kong (ITS/173/18FP).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Yi Liu & Qi Wang

  2. National Center for Applied Mathematics (Shenzhen), Southern University of Science and Technology, Shenzhen, 518055, China

    Qi Wang

  3. Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Yi Liu & Siu-Ming Yiu

Authors
  1. Yi Liu
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Correspondence to Qi Wang .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Yu Yu

  2. Columbia University, New York, NY, USA

    Moti Yung

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Liu, Y., Wang, Q., Yiu, SM. (2021). Improved Zero-Knowledge Argument of Encrypted Extended Permutation. In: Yu, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2021. Lecture Notes in Computer Science(), vol 13007. Springer, Cham. https://doi.org/10.1007/978-3-030-88323-2_15

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