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Provably Secure Proactive Secret Sharing Without the Adjacent Assumption

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Provable Security (ProvSec 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11821))

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Abstract

In secret sharing (SS), the secret is shared among a number of parties so that only a quorum of these parties can recover the secret, but a smaller set of parties cannot learn any information about the secret. However, the traditional SS technique is insufficient to protect the secret with a long lifetime, because the adversary may gradually compromise enough parties to retrieve the secret over the long time. To solve this issue, proactive secret sharing (PSS) divides the lifetime of the secret into many short time periods and the parties jointly update their secret shares in each time period. The benefit is that if the adversary cannot break into enough parties in a single time period, her compromised shares will become obsolete after the shares being updated.

In the last two decades, many PSS schemes have been proposed and they are widely used in various security protocols. However, the majority of existing PSS schemes require the adjacent assumption, i.e. if a party is corrupted during an update phase, it is corrupted in both time periods adjacent to that update phase. Note that this assumption not only hinders the security model to capture the mobile adversary’s abilities, but also prevents PSS schemes being used in many real-world applications. In this paper, we revisit the research of PSS, and our work contributes in the following aspects. Firstly, we discuss why some existing schemes (including Herzberg’s PSS scheme) cannot maintain their security when the adjacent assumption is removed. Secondly, we use the polynomial truncation method to improve Herzberg’s PSS scheme. To the best of our knowledge, our proposed scheme is the first provably secure PSS scheme without the adjacent assumption.

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Notes

  1. 1.

    It is crucial that nobody knows the value \(\log _gh\). To generate g and h, we first select g in the group G. Then, a distributed coin flipping protocol [3] can be used to generate a random value \(r \in \mathbb {Z}_p^*\). Finally, h can be computed as \(h = r^{(p-1)/q}\). In case if \(h = 1\), we can go back to select another random value \(r \in \mathbb {Z}_p^*\) until \(h \ne 1\).

  2. 2.

    Note that a similar problem has been independently discovered by Nikov and Nikova in [22]. But its consequences were not elaborated and no solution of this problem was proposed in that work.

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Acknowledgement

This work was partially supported by the National Natural Science Foundation of China (Grant No. 61572303, 61772326, 61822202, 61672010, 61702168, 61872087). We are very grateful to the anonymous reviewers for pointing out an error in a previous version of this paper as well as many valuable comments.

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Authors and Affiliations

  1. School of Computer Science and Technology, Wuhan University of Technology, Wuhan, China

    Zhe Xia

  2. School of Computer Science, Shaanxi Normal University, Xi’an, China

    Bo Yang & Yanwei Zhou

  3. School of Computers, Hubei University of Technology, Wuhan, China

    Mingwu Zhang & Hua Shen

  4. State Key Laboratory of Cryptology, Beijing, China

    Mingwu Zhang

  5. Fujian Provincial Key Laboratory of Network Security and Cryptology, College of Mathematics and Informatics, Fujian Normal University, Fuzhou, China

    Yi Mu

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  1. Zhe Xia
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Correspondence to Bo Yang .

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Editors and Affiliations

  1. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

  2. The University of Hong Kong, Pok Fu Lam, Hong Kong

    Tsz Hon Yuen

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Xia, Z., Yang, B., Zhou, Y., Zhang, M., Shen, H., Mu, Y. (2019). Provably Secure Proactive Secret Sharing Without the Adjacent Assumption. In: Steinfeld, R., Yuen, T. (eds) Provable Security. ProvSec 2019. Lecture Notes in Computer Science(), vol 11821. Springer, Cham. https://doi.org/10.1007/978-3-030-31919-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-31919-9_14

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