GOMSS: A Simple Group Oriented (<i>t, m, n</i>) Multi-secret Sharing Scheme

MIAO Fuyou; WANG Li; JI Yangyang; XIONG Yan

doi:10.1049/cje.2016.08.014

Volume 26 Issue 3

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MIAO Fuyou, WANG Li, JI Yangyang, et al., “GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme,” Chinese Journal of Electronics, vol. 26, no. 3, pp. 557-563, 2017, doi: 10.1049/cje.2016.08.014

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MIAO Fuyou, WANG Li, JI Yangyang, et al., “GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme,” Chinese Journal of Electronics, vol. 26, no. 3, pp. 557-563, 2017, doi: 10.1049/cje.2016.08.014

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GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme

doi: 10.1049/cje.2016.08.014

School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, China

Funds: This work is supported in part by the National Natural Science Foundation of China (No.61572454, No.61472382, No.61572453, No.61520106007), and Open Project of Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University.

Received Date: 2015-03-30
Rev Recd Date: 2015-07-22
Publish Date: 2017-05-10

Abstract

Abstract

In most (t, n)-Multi-secret sharing ((t, n)-MSS) schemes, an illegal participant, even without any valid share, may recover secrets when there are over t participants in secret reconstructions. To address this problem, the paper presents the notion of Group oriented (t, m, n)-multi-secret sharing (or (t, m, n)-GOMSS), in which recovering each secret requires all m (n≥m≥t) participants to have valid shares and actually participate in secret reconstruction. As an example, the paper then proposes a simple (t, m, n)-GOMSS scheme. In the scheme, every shareholder has only one share; to recover a secret, m shareholders construct a Polynomial-based randomized component (PRC) each with the share to form a tightly coupled group, which forces the secret to be recovered only with all m valid PRCs. As a result, the scheme can thwart the above illegal participant attack. The scheme is simple as well as flexible and does not depend on conventional hard problems or one way functions.
- Multi-secret sharing,
- Shamirs scheme,
- Tightly coupled group,
- Polynomial-based randomized component (PRC)

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References(18)

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