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How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, the authors solve an open problem proposed by Spiez et al. recently, namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, they show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.'s scheme and Pang et al.'s scheme. Finally, based on the algorithm mentioned above, they devise an ideal multi-secret sharing scheme for families of access structures, which possesses more vivid authorized sets than that of the threshold scheme.
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