Reusable Multi-Stage Multi-Secret Sharing Schemes Based on CRT

Abstract

Three secret sharing schemes that use the Mignotte’s sequence and two secret sharing schemes that use the Asmuth-Bloom sequence are proposed in this paper. All these five secret sharing schemes are based on Chinese Remainder Theorem (CRT) [8]. The first scheme that uses the Mignotte’s sequence is a single secret scheme; the second one is an extension of the first one to Multi-secret sharing scheme. The third scheme is again for the case of multi-secrets but it is an improvement over the second scheme in the sense that it reduces the number of public values. The first scheme that uses the Asmuth-Bloom sequence is designed for the case of a single secret and the second one is an extension of the first scheme to the case of multi-secrets. Novelty of the 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.

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