In this paper we study anonymous secret sharing schemes. Informally, in an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In such schemes the computation of the secret can be carried out by giving the shares to a black box that does not know the identities of the participants holding those shares. Phillips and Phillips gave necessary and sufficient conditions for the existence of an anonymous secret sharing scheme where the size of the shares given to each participant is equal to the size of the secret. In this paper, we provide lower bounds on the size of the share sets in any (t, w) threshold scheme, and for an infinite class of non-threshold access structures. We also discuss constructions for anonymous secret sharing schemes, and apply them to access structures obtained from complete multipartite graphs.
Blundo, C., & Stinson, D. R. (1997). Anonymous secret sharing schemes. Discrete Applied Mathematics, 77(1), 13–28. https://doi.org/10.1016/S0166-218X(97)89208-6