Recursive constructions for perfect secret sharing schemes

A secret sharing scheme is a method which allows a secret to be shared amon g a set of participants in such a way that only qualified subsets of partic ipants can recover the secret. A secret sharing scheme is called perfect if unqualified subsets of participants obtain no information regarding the se cret. The information rate of a secret sharing scheme is defined to be the ratio between the size of secret and the maximum size of the shares. In thi s paper, we propose some recursive constructions for perfect secret sharing schemes with access structures of constant rank. Compared with the best pr evious constructions, our constructions have some improved lower bounds on the information rate. (C) 1999 Elsevier Science Ltd. All rights reserved.