Kendall, Michelle

To secure a network of small devices using symmetric key cryptography is a non-trivial task. Nevertheless, it is important because public key cryptography is computationally expensive and therefore infeasible to implement on some small, battery-powered devices with limited memory. We study methods for allocating symmetric keys to devices before deployment, known as key predistribution schemes. Using combinatorial techniques, we analyse and design a variety of key predistribution schemes. We provide a correction to the previously stated formula for calculating the resilience of certain random key predistribution schemes, presenting instead a rigorously proved and widely applicable formula. We also present a simplified formula for calculating the connectivity. Next, we examine the role of expander graphs in key predistribution schemes. We demonstrate that good expansion is desirable for robust schemes, and discuss how this can be achieved. In particular, we examine the expansion of key predistribution schemes built from expander graph constructions, which provide perfect resilience. We show that if perfect resilience is not required, key predistribution schemes with higher connectivity and expansion can be created from hypergraphs and designs, and we explore the relationships between these constructions. We argue for the use of hypergraphs to represent and analyse key predistribution schemes, and identify open problems which, if solved, could lead to further suitable and robust constructions for key predistribution schemes. Finally, we study a class of schemes which we call 'broadcast-enhanced key predistribution schemes'. These are schemes which make use of a trusted base station and a broadcast channel to update and revoke keys in a network whilst it is operational. We explore the range of benefits which such schemes can provide, and present and analyse two constructions for particular scenarios: a scheme which allows efficient revocation of devices, and a scheme which creates hierarchy amongst the devices for efficient routing and battery consumption. We demonstrate that our schemes provide effective and flexible trade-offs between the conflicting parameters of connectivity, resilience, key storage and broadcast load.</p

Combinatorial Aspects of Key Predistribution for Resource-Constrained Networks

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Royal Holloway - Pure