Hierarchies of keys in secure multicast communications

This work considers the key management for secure multicast in the Logical Key Hierarchy (LKH) model and proposes a methodology to establish the minimal key bit length that guarantees a specified degree of confidentiality for the multicast communications managed within this model. We also introduce the concepts of information lifetime and of information dependence to formalize the intuition that keys should be longer, and thus stronger, when used to encrypt “important” information, that is information (including other keys) that need to be kept confidential for a longer period. Then, these concepts are used to build a formal theory that is applied to set the correct bit length of every key in the system in such a way to guarantee the prescribed degree of confidentiality of the multicast messages. Quite surprisingly, we formally show that not all the keys in the LKH hierarchy should have the same length; this observation, besides being of theoretical interest, also leads to substantial savings in terms of memory, computation, and bandwidth. The theory we develop to obtain these results can be useful in other contexts as well.