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2018 | OriginalPaper | Chapter

Verifiable Homomorphic Secret Sharing

Authors : Georgia Tsaloli, Bei Liang, Aikaterini Mitrokotsa

Published in: Provable Security

Publisher: Springer International Publishing

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Abstract

In this paper, we explore the multi-server (i.e., multiple servers are employed to perform computations) and multi-client (i.e., multiple clients outsource joint computations on their joint inputs) scenario that avoids single points of failure and provides higher security and privacy guarantees. More precisely, we introduce the notion of verifiable homomorphic secret sharing (VHSS) for multi-input, that allows n clients to outsource joint computations on their joint inputs to m servers without requiring any communication between the clients or the servers; while providing the verifiable capability to any user to confirm that the final output (rather than each share) is correct. Our contributions are two-fold: (i) we provide a detailed example for casting Shamir’s secret sharing scheme over a finite field \(\mathbb {F}\) as an n-client, m-server, t-secure perfectly secure, additive HSS scheme for the function f that sums n field elements, and (ii) we propose an instantiation of an n-client, m-server, t-secure computationally secure, multiplicative VHSS scheme for the function f that multiplies n elements under the hardness assumption of the fixed inversion problem in bilinear maps.

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previous chapter Location-Proof System Based on Secure Multi-party Computations

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Title: Verifiable Homomorphic Secret Sharing
Authors: Georgia Tsaloli
Bei Liang
Aikaterini Mitrokotsa
Publisher: Springer International Publishing
Book: Provable Security
Print ISBN: 978-3-030-01445-2

Electronic ISBN: 978-3-030-01446-9

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-030-01446-9_3

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