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A simple construction of CRT-based ideal secret sharing scheme and its security extension based on common factor

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Abstract

Secret sharing (SS) is part of the essential techniques in cryptography but still faces many challenges in efficiency and security. Currently, SS schemes based on the Chinese Remainder Theorem (CRT) are either low in the information rate or complicated in construction. To solve the above problems, 1) a simple construction of an ideal (t, n)-SS scheme is proposed based on CRT for a polynomial ring. Compared with Ning’s scheme, it is much more efficient in generating n pairwise coprime modular polynomials during the scheme construction phase. Moreover, Shamir’s scheme is also a special case of our scheme. To further improve the security, 2) a common-factor-based (t, n)-SS scheme is proposed in which all shareholders share a common polynomial factor. It enables both the verification of received shares and the establishment of a secure channel among shareholders during the reconstruction phase. As a result, the scheme is resistant to eavesdropping and modification attacks by outside adversaries.

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Acknowledgements

This work was supported by National Key R&D Project 2018YFB2100300 and the National Natural Science Foundation of China (Grant No. 61520106007).

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Authors and Affiliations

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

    Lei Wu, Fuyou Miao, Keju Meng & Xu Wang

Authors
  1. Lei Wu
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  2. Fuyou Miao
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  3. Keju Meng
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  4. Xu Wang
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Corresponding author

Correspondence to Fuyou Miao.

Additional information

Lei Wu is a master student studying in the School of Computer Science and Technology in University of Science and Technology of China, China. She received bachelor’s degree in information security from Hefei University of Technology, China in 2018. Her research interests include secret sharing and Internet of Things.

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

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

Xu Wang received her bachelor’s degree from China University of Geosciences, China in 2019. After that, she has been studying for a master’s degree at the University of Science and Technology of China, China. Her main research interests are secret sharing and coding.

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Wu, L., Miao, F., Meng, K. et al. A simple construction of CRT-based ideal secret sharing scheme and its security extension based on common factor. Front. Comput. Sci. 16, 161811 (2022). https://doi.org/10.1007/s11704-021-0483-9

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  • DOI: https://doi.org/10.1007/s11704-021-0483-9

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