zbMATH — the first resource for mathematics

Verifiable homomorphic secret sharing. (English) Zbl 1421.94087
Baek, Joonsang (ed.) et al., Provable security. 12th international conference, ProvSec 2018, Jeju, South Korea, October 25–28, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11192, 40-55 (2018).
Summary: 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.
For the entire collection see [Zbl 1398.94007].
94A62 Authentication, digital signatures and secret sharing
Full Text: DOI