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A proactive secret sharing scheme based on Chinese remainder theorem

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Abstract

If an adversary tries to obtain a secret s in a (t, n) threshold secret sharing (SS) scheme, it has to capture no less than t shares instead of the secret s directly. However, if a shareholder keeps a fixed share for a long time, an adversary may have chances to filch some shareholders’ shares. In a proactive secret sharing (PSS) scheme, shareholders are supposed to refresh shares at fixed period without changing the secret. In this way, an adversary can recover the secret if and only if it captures at least t shares during a period rather than any time, and thus PSS provides enhanced protection to long-lived secrets. The existing PSS schemes are almost based on linear SS but no Chinese Remainder Theorem (CRT)-based PSS scheme was proposed. This paper proposes a PSS scheme based on CRT for integer ring to analyze the reason why traditional CRT-based SS is not suitable to design PSS schemes. Then, an ideal PSS scheme based on CRT for polynomial ring is also proposed. The scheme utilizes isomorphism of CRT to implement efficient share refreshing.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61572454), National Key R&D Project (2018YFB2100301, 2018YFB0803400) and the National Natural Science Foundation of China (Grant Nos. 61572453, 61520106007).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230026, China

    Keju Meng, Fuyou Miao, Yu Ning, Wenchao Huang & Yan Xiong

  2. Department of Information Engineering and Computer Science, Feng Chia University, Taichung, 40724, China

    Chin-Chen Chang

  3. School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China

    Chin-Chen Chang

Authors
  1. Keju Meng
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  2. Fuyou Miao
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  3. Yu Ning
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  4. Wenchao Huang
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  5. Yan Xiong
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  6. Chin-Chen Chang
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Corresponding author

Correspondence to Fuyou Miao.

Additional information

Keju Meng is a PhD student studying in the School of Computer Science and Technology (USTC), China. He received bachelor’s degree from Dalian Universiry of Technology (DLUT), China in 2016. His research interests include Internet of things, network security and secret sharing.

Fuyou Miao received the PhD degree in computer science from USTC, China, where he is an associate professor currently with school of computer science and technolog. His research interests include information security, information coding key management in WSN, and network security.

Yu Ning is a PhD student with the School of Computer Science and Technology in USTC, China. He received bachelor’s degree in electronics engineering from USTC, China in 2016. His research interests include pure mathematics and secret sharing.

Wenchao Huang received BS and PhD degrees from USTC, China in 2006 and 2011 respectively. Now, he is an associate professor currently with school of computer science and technology, USTC, China. His current research interests include mobile computing, information security, trusted computing, and formal methods.

Yan Xiong received the BS, MS, and PhD degrees from USTC, China in 1983, 1986, and 1990, respectively. He is currently a professor with the School of Computer Science and Technology. His research interests include distributed processing, mobile computing, and information security.

Chin-Chen Chang is a fellow of IEEE and IET. His current title is Chair Professor in Department of Information Engineering and Computer Science, Feng Chia University, China. His specialties include, but not limited to, data engineering, computer cryptography and information security.

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Meng, K., Miao, F., Ning, Y. et al. A proactive secret sharing scheme based on Chinese remainder theorem. Front. Comput. Sci. 15, 152801 (2021). https://doi.org/10.1007/s11704-019-9123-z

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