Methods of encrypting monotonic access structures

We will present some ideas about sharing a secret in a monotonic access structure. We show the relations which occur between the method of encrypting a monotonic access structure with the use of basis sets or maximal unprivileged sets, and that based on a logical formula (used by Benaloh and Leichter in [1]). We will also give some facts connected with the problem of security, including the aspects of a hierarchy security in the structure. The method of encrypting a monotonic access structure using a family of basis sets or a family of maximal sets that cannot reconstruct the secret will be described in a general way. Some aspects of using the latter based on a logical formula will be also given. Any (general) access structure can be encrypted by each of them but the way of sharing a secret is quite different and usually a specified method has to be chosen to achieve a desirable level of security and time complexity.