Graph-theoretic design and analysis of key predistribution schemes

Abstract

Key predistribution schemes for resource-constrained networks are methods for allocating symmetric keys to devices in such a way as to provide an efficient trade-off between key storage, connectivity and resilience. While there have been many suggested constructions for key predistribution schemes, a general understanding of the design principles on which to base such constructions is somewhat lacking. Indeed even the tools from which to develop such an understanding are currently limited, which results in many relatively ad hoc proposals in the research literature.It has been suggested that a large edge-expansion coefficient in the key graph is desirable for efficient key predistribution schemes. However, attempts to create key predistribution schemes from known expander graph constructions have only provided an extreme in the trade-off between connectivity and resilience: namely, they provide perfect resilience at the expense of substantially lower connectivity than can be achieved with the same key storage.Our contribution is two-fold. First, we prove that many existing key predistribution schemes produce key graphs with good expansion. This provides further support and justification for their use, and confirms the validity of expansion as a sound design principle. Second, we propose the use of incidence graphs and concurrence graphs as tools to represent, design and analyse key predistribution schemes. We show that these tools can lead to helpful insights and new constructions.

Bidirectional hash chains generically enhances resilience of key predistribution schemes

“…Constructions of appropriate designs that form the foundations of combinatorial KPS are well briefed in [5,6,18,20,23,25,26]. Stinson's book [27] elaborately presents the construction of several combinatorial designs with concrete analyses.…”

“…Several works [5, 7, 18] demonstrate that deterministic schemes have provable desirable properties over their random counterparts. This leads to proposals of numerous efficient DKPSs [5, 6, 8, 9, 23] using combinatorial tricks. Bag et al [24] and Kendall and Martin [23] laid down the necessary criteria for DKPS in a distributed environment; while Sarkar [19] hints at desirable features of combinatorial hierarchical subset construction.…”

“…This leads to proposals of numerous efficient DKPSs [5, 6, 8, 9, 23] using combinatorial tricks. Bag et al [24] and Kendall and Martin [23] laid down the necessary criteria for DKPS in a distributed environment; while Sarkar [19] hints at desirable features of combinatorial hierarchical subset construction. Constructions of appropriate designs that form the foundations of combinatorial KPS are well briefed in [5, 6, 18, 20, 23, 25, 26].…”

“…Bag et al [24] and Kendall and Martin [23] laid down the necessary criteria for DKPS in a distributed environment; while Sarkar [19] hints at desirable features of combinatorial hierarchical subset construction. Constructions of appropriate designs that form the foundations of combinatorial KPS are well briefed in [5, 6, 18, 20, 23, 25, 26]. Stinson's book [27] elaborately presents the construction of several combinatorial designs with concrete analyses.…”

Isoperimetric Numbers of Randomly Perturbed Intersection Graphs

“…We then define the random intersection graph G(n, m, p) with vertex set V and vertices v i , v j ∈ V adjacent if and only if there exists some w ∈ W such that both v i and v j are adjacent to w in B(n, m, p). Several variant models of random intersection graphs have been proposed, and many graph-theoretic properties of G(n, m, p), such as degree distribution, connected components, fixed subgraphs, independence number, clique number, diameter, Hamiltonicity and clustering, have been extensively studied [8,9,[11][12][13][14]. We refer the reader to References [15,16] for an updated review of recent results in this prolific field.…”