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Distributed Implementation of SM4 Block Cipher Algorithm Based on SPDZ Secure Multi-party Computation Protocol

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Data Science (ICPCSEE 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1879))

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Abstract

SM4 is a block cipher algorithm among Chinese commercial cryptographic algorithms, which is advanced in terms of efficiency and theoretical security and has become national and international standards successively. However, existing literature shows that SM4 was not designed with an emphasis on key storage, which means that in today’s world where a single trusted hardware device with the built-in key faces challenges such as vulnerability, high cost, and unreliability, the usability of SM4 may be limited. Therefore, this paper proposes an implementation scheme for SM4 based on secure multi-party computation (MPC) technology. The scheme involves dispensing the key among multiple users’ devices in a distributed manner, and when using the SM4 algorithm for encryption, multiple users perform joint computation without opening the full key. Specifically, this paper employs the MP-SPDZ framework, which satisfies security requirements in the presence of a dishonest majority of active adversaries. In view of the fact that this framework can only perform basic linear operations such as addition and multiplication, this paper focuses on the algebraic analysis of Sbox, which is the only non-linear component in SM4, and reconstructs it using the bit decomposition method. Furthermore, this paper demonstrates the conversion between the SM4-Sbox field \(GF(2^8)\) and the SPDZ parameter field \(GF(2^{40})\) through the isomorphic mapping, making it possible to perform joint calculations throughout the entire SM4 algorithm. Complexity analysis shows that this scheme has advantages in terms of data storage and communication volume, reaching a level of usability.

Supported by the National Natural Science Foundation of China under Grant No. 61907042 and Beijing Natural Science Foundation under Grant No.4194090.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61907042 and Beijing Natural Science Foundation under Grant No.4194090.

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Authors and Affiliations

  1. School of Information, Central University of Finance and Economics, Beijing, 100081, China

    Xiaowen Ma, Maoning Wang & Zhong Kang

  2. Engineering Research Center of State Financial Security, Ministry of Education, Central University of Finance and Economics, Beijing, 102206, China

    Maoning Wang

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  1. Xiaowen Ma
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  2. Maoning Wang
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  3. Zhong Kang
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Corresponding author

Correspondence to Maoning Wang .

Editor information

Editors and Affiliations

  1. Harbin Engineering University, Harbin, China

    Zhiwen Yu

  2. Harbin Engineering University, Harbin, China

    Qilong Han

  3. Harbin Institute of Technology, Harbin, China

    Hongzhi Wang

  4. Northwestern Polytechnical University, Xi'an, China

    Bin Guo

  5. Shiga University, Shiga, Japan

    Xiaokang Zhou

  6. Harbin University of Science and Technology, Harbin, China

    Xianhua Song

  7. National Academy of Guo Ding Institute of Data Science, Beijing, China

    Zeguang Lu

A Appendix

A Appendix

Table 2. Algebraic Expression of Sbox
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Ma, X., Wang, M., Kang, Z. (2023). Distributed Implementation of SM4 Block Cipher Algorithm Based on SPDZ Secure Multi-party Computation Protocol. In: Yu, Z., et al. Data Science. ICPCSEE 2023. Communications in Computer and Information Science, vol 1879. Springer, Singapore. https://doi.org/10.1007/978-981-99-5968-6_20

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  • DOI: https://doi.org/10.1007/978-981-99-5968-6_20

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  • Print ISBN: 978-981-99-5967-9

  • Online ISBN: 978-981-99-5968-6

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