Unconditionally secure multi-secret sharing scheme

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.