CRT based multi-secret sharing schemes: revisited

Abstract

Secret sharing is a cryptographic primitive, which is used to distribute a secret among a set of participants in such a way that an authorised subset of participants can uniquely reconstruct the secret and an unauthorised subset can get no information about the secret. In this paper, we propose multi-stage multi-secret sharing scheme based on Mignotte's sequence and multi-level multi-secret sharing scheme based on Asmuth's Bloom sequence. The advantage of the proposed schemes is that the secret space is larger than that of the existing schemes. There is no leakage of information through public values. Novelty of these schemes is that the participants can reuse their shares for each new set of secrets without refreshing their shares. Moreover, the first scheme can verify the honesty of both the dealer and participants. The correctness of the proposed schemes is discussed and shows that the proposed schemes are computationally secure.