The use of combinatorics in key management

We consider the key management problem in a large network wherecommunicating nodes use symmetric-key cryptography to provideend-to-end encryption. A number of interesting mathematicalapplications arise, and we concentrate on the use of combinatoricsto facilitate a number of important key management issues. Motivatedby a recent PhD thesis (Quinn 1991), we describe a combinatorialstructure, known as a key distribution pattern. This structureuses subkeys both to reduce storage requirements at the nodesand to allow direct secure communication between nodes withoutfurther recourse to the key distribution centre. The competinginterests of reduced storage and good security pose problemswhich find solutions in the use of certain combinatorial incidencestructures, geometrical configurations, and orthogonal arrays.