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VSS Made Simpler

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Advances in Information and Computer Security (IWSEC 2019)

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Abstract

Verifiable secret sharing (VSS) allows honest parties to ensure consistency of their shares even if a dealer and/or a subset of parties are corrupt. We focus on perfect VSS, i.e., those providing perfect privacy, correctness and commitment with zero error, in the unconditional (information-theoretic) security setting where no assumption on the computational power of the participants is imposed.

Our study is motivated by both practical and theoretical considerations. For the practical side, MPC with perfect security is now being implemented. Multi-cloud storage has been implemented by IBM. Modern users rely on smartphones with limited internet connectivity, limited battery power, etc. We focus on such a user outsourcing her data to multi-clouds with the capability to have these multi-clouds participate on her behalf in MPC protocols. We show that in the case of VSS based on the replicated secret sharing scheme, there is no need for that user to be involved in any interaction. In addition, this scheme has an optimal number of rounds. This construction is derived from Maurer’s VSS based on the replicated secret sharing scheme.

A disadvantage of the replicated scheme is that it generally requires a considerable amount of randomness. We address this issue by showing a VSS scheme based on Shamir’s secret sharing, where the dealer does not need any randomness at all.

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Notes

  1. 1.

    In fact, \(Q^3\) is also necessary for perfect VSS [22].

  2. 2.

    In the current literature on VSS and MPC, it is common to allow the dealer to be one of the parties that later takes part in the protocol.

  3. 3.

    In asynchronous network, the global clocking is present so that the protocol execution can be divided into rounds, and hereby, a failure to send a message is easy to detect, for every player. Note that to prevent malleability type of attacks, parties should not be able to see data sent by others before they sent theirs. A strict synchronization enforces this in an obvious way.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of North Texas, Denton, USA

    Kirill Morozov

  2. Department of Computer Science, The University of Texas at Dallas, Richardson, USA

    Yvo Desmedt

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  1. Yvo Desmedt
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  2. Kirill Morozov
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Correspondence to Kirill Morozov .

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Editors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Nuttapong Attrapadung

  2. NTT Security (Japan) KK, Tokyo, Japan

    Takeshi Yagi

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Desmedt, Y., Morozov, K. (2019). VSS Made Simpler. In: Attrapadung, N., Yagi, T. (eds) Advances in Information and Computer Security. IWSEC 2019. Lecture Notes in Computer Science(), vol 11689. Springer, Cham. https://doi.org/10.1007/978-3-030-26834-3_19

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  • DOI: https://doi.org/10.1007/978-3-030-26834-3_19

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