Reusable Multi-Stage Multi-Secret Sharing Scheme Based on Asmuth-Bloom Sequence

Two secret sharing schemes that use Asmuth-Bloom sequence and are based on Chinese Reminder Theorem (CRT) are proposed in this paper. The first scheme is designed for the case of a single se-cret 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 applica-ble even with a new secret. Also only one share needs to be kept by each participant even for the multi-secret sharing scheme. Further, the schemes are capable of verifying the honesty of the participants including the dealer. Correctness of the schemes is also discussed. Keywords: Multi-Secret, Mignotte’s sequence, Asmuth-Bloom sequence