In this paper, we present the model of threshold schemes with weights as a natural generalization of Shamir's threshold scheme and show how to apply the model to construct secret sharing schemes by two examples.
In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.
In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access structures by using linear multi-secret sharing schemes is shown. Furthermore, the concept of optimal linear multi-secret sharing scheme is presented and the several schemes are proved to be optimal.
