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International Conference on Information Security and Cryptology

ICISC 2019: Information Security and Cryptology – ICISC 2019 pp 115–132Cite as

Sum It Up: Verifiable Additive Homomorphic Secret Sharing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11975))

Abstract

In many situations, clients (e.g., researchers, companies, hospitals) need to outsource joint computations based on joint inputs to external cloud servers in order to provide useful results. Often clients want to guarantee that the results are correct and thus, an output that can be publicly verified is required. However, important security and privacy challenges are raised, since clients may hold sensitive information and the cloud servers can be untrusted. Our goal is to allow the clients to protect their secret data, while providing public verifiability i.e., everyone should be able to verify the correctness of the computed result.

In this paper, we propose three concrete constructions of verifiable additive homomorphic secret sharing (VAHSS) to solve this problem. Our instantiations combine an additive homomorphic secret sharing (HSS) scheme, which relies on Shamir’s secret sharing scheme over a finite field \(\mathbb {F}\), for computing the sum of the clients’ secret inputs, and three different methods for achieving public verifiability. More precisely, we employ: (i) homomorphic collision-resistant hash functions; (ii) linear homomorphic signatures; as well as (iii) a threshold RSA signature scheme. In all three cases we provide a detailed correctness, security and verifiability analysis and discuss their efficiency.

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Notes

  1. 1.

    \(\tau _i\), when computed, can be included in the list of public parameters pp.

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Acknowledgement

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. We would also like to thank Daniel Slamanig and Bei Liang for the helpful comments and discussions.

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Georgia Tsaloli & Aikaterini Mitrokotsa

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  1. Georgia Tsaloli
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  2. Aikaterini Mitrokotsa
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Correspondence to Georgia Tsaloli .

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Editors and Affiliations

  1. Hanyang University, Seoul, Korea (Republic of)

    Jae Hong Seo

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Tsaloli, G., Mitrokotsa, A. (2020). Sum It Up: Verifiable Additive Homomorphic Secret Sharing. In: Seo, J. (eds) Information Security and Cryptology – ICISC 2019. ICISC 2019. Lecture Notes in Computer Science(), vol 11975. Springer, Cham. https://doi.org/10.1007/978-3-030-40921-0_7

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  • DOI: https://doi.org/10.1007/978-3-030-40921-0_7

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  • Print ISBN: 978-3-030-40920-3

  • Online ISBN: 978-3-030-40921-0

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