The use of combinatorics in key management

We consider the key management problem in a large network where communicating nodes use symmetric-key cryptography to provide end-to-end encryption. A number of interesting mathematical applications arise, and we concentrate on the use of combinatorics to facilitate a number of important key management issues. Motivated by a recent PhD thesis, we describe a combinatorial structure, known as a key distribution pattern. This structure uses subkeys both to reduce storage requirements at the nodes and to allow direct secure communication between nodes without further recourse to the key distribution centre. The competing interests of reduced storage and good security pose problems which find solutions in the use of certain combinatorial incidence structures, geometrical configurations, and orthogonal arrays.