C. Padró, G. Sáez

Secret sharing schemes with bipartite access structure

IEEE Transactions on Information Theory 46 (2000) 2596-2605. A previous version of this paper appeared in Advances in Cryptology - EUROCRYPT'98, Lecture Notes in Computer Science 1403 (1998) 500-511. Espoo, Finland, 1998. A short note with some corrections to this paper appeared in IEEE Transactions on Information Theory 50 (2004) 1373.


Abstract

We study the information rate of secret sharing schemes whose access structure is bipartite. In a bipartite access structure there are two classes of participants and all participants in the same class play an equivalent role in the structure. We characterize completely the bipartite access structures that can be realized by an ideal secret sharing scheme. Both upper and lower bounds on the optimal information rate of bipartite access structures are given. These results are applied to the particular case of weighted threshold access structure with two weights.