Multi-stage multi-secret sharing schemes based on Chinese Remainder Theorem

Abstract

One secret sharing scheme that uses the Mignotte's sequence and another secret sharing scheme that uses the Asmuth-Bloom sequence are proposed in this paper. Both the secret sharing schemes are based on the Chinese Remainder Theorem (CRT). Novelty of the two proposed schemes is that the shares of the participants are reusable i.e. same shares are applicable even with a new secret. Also only one share needs to be kept by each participant even for the muslti-secret sharing scheme. Further, the schemes are capable of verifying the honesty of the participants including the dealer. Correctness of the proposed schemes is discussed and show that the proposed schemes are computationally secure.