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Two-Server Verifiable Homomorphic Secret Sharing for High-Degree Polynomials

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Information Security (ISC 2020)

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Abstract

Homomorphic secret sharing (HSS) allows multiple input clients to secret-share their data among multiple servers such that each server is able to locally compute a function on its shares to obtain a partial result and all partial results enable the reconstruction of the function’s value on the outsourced data by an output client. The existing HSS schemes for high-degree polynomials either require a large number of servers or lack verifiability, which is essential for ensuring the correctness of the outsourced computations. In this paper, we propose a two-server verifiable HSS (VHSS) model and construct a scheme that supports the computation of high-degree polynomials. The degree of the outsourced polynomials can be as high as a polynomial in the system’s security parameter. Despite of using only 2 servers, our VHSS ensures that each single server learns no information about the outsourced data and no single server is able to persuade the client to output a wrong function value. Our VHSS is significantly more efficient. When computing degree-7 polynomials, our scheme could be 3–10 times faster than the previously best construction.

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Acknowledgments

The research was supported by Singapore Ministry of Education under Research Grant RG12/19 and National Natural Science Foundation of China (No. 61602304).

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Authors and Affiliations

  1. School of Information Science and Technology, ShanghaiTech University, Shanghai, China

    Xin Chen & Liang Feng Zhang

  2. Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China

    Xin Chen

  3. University of Chinese Academy of Sciences, Beijing, China

    Xin Chen

Authors
  1. Xin Chen
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  2. Liang Feng Zhang
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Corresponding author

Correspondence to Liang Feng Zhang .

Editor information

Editors and Affiliations

  1. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  3. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  4. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Yannan Li

  5. Informatics, Petra Christian University, Surabaya, Indonesia

    Rolly Intan

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Chen, X., Zhang, L.F. (2020). Two-Server Verifiable Homomorphic Secret Sharing for High-Degree Polynomials. In: Susilo, W., Deng, R.H., Guo, F., Li, Y., Intan, R. (eds) Information Security. ISC 2020. Lecture Notes in Computer Science(), vol 12472. Springer, Cham. https://doi.org/10.1007/978-3-030-62974-8_5

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  • DOI: https://doi.org/10.1007/978-3-030-62974-8_5

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