Unconditionally secure multi-secret sharing scheme

Abstract

In Shamir's (t, n) secret sharing (SS) scheme, a master secrets is divided into n shares by a dealer and is shared among n shareholders in such a way that any t or more than t shares can reconstruct this master secret; but fewer than t shares cannot obtain any information about the master secret s. Although Shamir's scheme is unconditionally secure, it unfortunately requires a large data expansion (i.e., t shares are needed to reclaim one secret). Therefore, Shamir's scheme is inefficient as a conveyor of information. Multi-secret sharing (MSS) scheme, which allows multiple master secrets to be shared among shareholders, has been proposed to improve the efficiency of Shamir's scheme. However, all existing MSS schemes are computationally secure. In this paper, we propose an unconditionally secure MSS scheme based on Shamir's scheme. Our proposed MSS scheme allows each shareholder to keep only one private share and uses it to share t master secrets.