A Proactive Multi Stage Secret Sharing Scheme for Any Given Access Structure

Abstract

In proactive secret sharing schemes, the secret shares are periodically renewed without modifying the secret such that an adversary is unable to get any information about the secret shares unless he is able to obtain a certain number of secret shares in a short time interval. In this paper, using monotone span programs (MSP) we devise a new linear multi-secret sharing (LMSS) scheme which is also multi-stage. We also give a new general method to construct proactive and multi-use linear multi-secret sharing schemes based on MSP. An important advantage of our method compared to the others is that it does not need private channels between each pair of participants or an encryption scheme between them. Finally, we prove that our new scheme satisfies the definition of a perfect LMSS scheme.