Robust vector space secret sharing schemes

摘要

A secret sharing scheme makes it possible to distribute a secret value among a set of participants in such a way that only some qualified subsets can reconstruct the value of the secret. In such a scheme, some participants can lie about the value of their shares in order to obtain some illicit benefit. In a robust scheme, the probability that any non-qualified coalition of participants deceive an honest participant is bounded by some fixed value, even if they known the secret. A new robust secret sharing scheme is presented in this paper. This scheme improves the previous ones in two aspects. First, it presents a better relation between the information rate and the security against cheaters. Second, while the previous robust schemes were designed only for threshold structures, the present one can realize access structures in a more general family.