How to construct a verifiable multi‐secret sharing scheme based on graded encoding schemes

Abstract

In a verifiable multi-secret sharing scheme, a dealer distributes multiple secrets between a group of participants and also additional information is given that allows each participant to check whether his share is valid. In this study, the authors present a novel verifiable multi-secret sharing (VMSS) scheme with general access structure using monotone span programs, which its security is based on graded encoding schemes. More precisely, they reduce the hardness of graded decision-Diffie–Hellman problem to the computational security of the authors’ scheme in the standard model. To the best of the authors’ knowledge, this is the first study to present a VMSS scheme based on graded encoding schemes.