Toward a formal proof for multi-secret sharing in the random oracle model

Abstract

ABSTRACT A general multi-secret sharing (GMS) scheme allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets simultaneously, while any unauthorized subset of participants cannot get any information about the secrets. The first formal security model of multi-stage secret sharing (MSS) schemes with a computational security proof in the random oracle model (ROM) had been introduced recently by Herranz et al. To the best of our knowledge, so far, there exists no computational secure GMS with a formal proof in ROM in the literature. This is what we will do in this paper. After describing formally the computational security of a GMS, we propose a GMS with adding a formal proof of computational security in ROM.