The current application is directed to computationally efficient attribute-based access control that can be used to secure access to stored information in a variety of different types of computational systems. Many of the currently disclosed computationally efficient implementations of attribute-based access control employ hybrid encryption methodologies in which both an attribute-based encryption or a similar, newly-disclosed policy-encryption method as well as a hierarchical-key-derivation method are used to encrypt payload keys that are employed, in turn, to encrypt data that is stored into, and retrieved from, various different types of computational data-storage systems.