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Multi-secret sharing scheme has been well studied in recent years. In most multi-secret sharing schemes, all secrets must be recovered synchronously; the shares cannot be reused any more. In 2017, Harn and Hsu proposed a novel and reasonable feature in multiple secret sharing, such that the multiple secrets should be reconstructed asynchronously and the recovering of previous secrets do not leak any information on unrecovered secrets. Harn and Hsu also proposed a (t,n) multi-secret sharing scheme that satisfies this feature. However, the analysis on Harn-Hsu’s scheme is wrong, and their scheme fails to satisfy this feature. If one secret is reconstructed, all the other unrecovered secrets can be computed by any t − 1 shareholders illegitimately. Another problem in Harn-Hsu’s work is that the parameters are unreasonable which will be shown as follows. In this paper, we prove the incorrectness of Harn-Hsu’s scheme and propose a new (t,n) multi-secret sharing scheme which is extended from Harn-Hsu’s scheme; our proposed scheme satisfies the feature introduced by Harn and Hsu.

(t,n) multi-secret sharing scheme extended from Harn-Hsu’s scheme