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Multiplicative and Verifiably Multiplicative Secret Sharing for Multipartite Adversary Structures by Reo Eriguchi; Noboru Kunihiro; Koji Nuida is a Computer Science article available to read on EtoBox.

What is Multiplicative and Verifiably Multiplicative Secret Sharing for Multipartite Adversary Structures about?

d-Multiplicative secret sharing enables n players to locally compute additive shares of the product of d secrets from their shares. Barkol et al. (Journal of Cryptology, 2010) show that it is possible to construct a d-multiplicative scheme for any adversary structure satisfying the Q d property, in which no d sets cover the whole set of players. In this paper, we focus on multipartite adversary structures and propose efficient multiplicative and verifiably multiplicative secret sharing schemes tailored to them. First, our multiplicative scheme is applicable to any multipartite Q d -adversary structure. If the number of parts is constant, our scheme achieves a share size polynomial in the number n of players while the general construction by Barkol et al. results in exponentially large share size in the worst case. We also propose its variant defined over smaller fields. As a result, for a special class of bipartite adversary structures with two maximal points, it achieves a constant share size for arbitrary n while the share size of the first scheme necessarily incurs a logarithmic factor of n. Secondly, we devise a more efficient scheme for a special class of multipartite ones suc

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Author

Reo Eriguchi; Noboru Kunihiro; Koji Nuida

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Computer Science (Physical Sciences)