A collaborative secret sharing scheme based on the Chinese Remainder Theorem

Xingxing Jia; Yixuan Song; Daoshun Wang; Daxin Nie; Jinzhao Wu; Xingxing Jia; Yixuan Song; Daoshun Wang; Daxin Nie; Jinzhao Wu

doi:10.3934/mbe.2019062

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 3: 1280-1299. doi: 10.3934/mbe.2019062

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Research article Special Issues

A collaborative secret sharing scheme based on the Chinese Remainder Theorem

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
2.
School of Computing, Tsinghua University, Beijing 100084, China
3.
School of Software, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received: 25 November 2018 Accepted: 18 January 2019 Published: 19 February 2019

Secret sharing (SS) can be used as an important group key management technique for distributed cloud storage and cloud computing. In a traditional threshold SS scheme, a secret is shared among a number of participants and each participant receives one share. In many real-world applications, some participants are involved in multiple SS schemes with group collaboration supports thus have more privileges than the others. To address this issue, we could assign multiple shares to such participants. However, this is not a bandwidth efficient solution. Therefore, a more sophisticated mechanism is required. In this paper, we propose an efficient collaborative secret sharing (CSS) scheme specially tailored for multi-privilege participants in group collaboration. The CSS scheme between two or among more SS schemes is constructed by rearranging multi-privilege participants in each participant set and then formulated into several independent SS schemes with multi-privilege shares that precludes information leakage. Our scheme is based on the Chinese Remainder Theorem with lower recovery complexity and it allows each multi-privilege participant to keep only one share. It can be formally proved that our scheme achieves asymptotically perfect security. The experimental results demonstrate that it is efficient to achieve group collaboration, and it has computational advantages, compared with the existing works in the literature.
- group collaboration,
- collaborative secret sharing,
- Chinese Remainder Theorem,
- secret sharing
Citation: Xingxing Jia, Yixuan Song, Daoshun Wang, Daxin Nie, Jinzhao Wu. A collaborative secret sharing scheme based on the Chinese Remainder Theorem[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1280-1299. doi: 10.3934/mbe.2019062

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Abstract

Secret sharing (SS) can be used as an important group key management technique for distributed cloud storage and cloud computing. In a traditional threshold SS scheme, a secret is shared among a number of participants and each participant receives one share. In many real-world applications, some participants are involved in multiple SS schemes with group collaboration supports thus have more privileges than the others. To address this issue, we could assign multiple shares to such participants. However, this is not a bandwidth efficient solution. Therefore, a more sophisticated mechanism is required. In this paper, we propose an efficient collaborative secret sharing (CSS) scheme specially tailored for multi-privilege participants in group collaboration. The CSS scheme between two or among more SS schemes is constructed by rearranging multi-privilege participants in each participant set and then formulated into several independent SS schemes with multi-privilege shares that precludes information leakage. Our scheme is based on the Chinese Remainder Theorem with lower recovery complexity and it allows each multi-privilege participant to keep only one share. It can be formally proved that our scheme achieves asymptotically perfect security. The experimental results demonstrate that it is efficient to achieve group collaboration, and it has computational advantages, compared with the existing works in the literature.

References

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