The Algorithmic Aspects of Creating and Using Wireless Sensor Network Key Spaces Based on Combinatorial Block Diagrams

Abstract

Algorithmic approach principles relating to development and use of wireless sensor network (WSS) key spaces are formulated based on an analysis of the keys management peculiarities. The formulated principles, which meet certain requirements for the WSS key spaces, have been elaborated proceeding from the assumption that their structure corresponds to one of the varieties of combinatorial block diagrams: cyclic or acyclic projective plane, linear or quadratic transversal block diagrams. Owing to the WSS having a distributed configuration, it becomes possible to avoid the need to construct a combinatorial block diagram in full scope, and the required blocks are computed, whenever necessary, in scaling the network (in adding new nodes) or when determining, in a decentralized manner, the switching parameters of specific nodes. To do so, it is necessary to have algorithms for computing the blocks of the combinatorial block diagram (as the sets of key numbers allocated to a given node) and dual blocks (as the sets of the numbers of nodes to which keys are assigned with the numbers coinciding with the numbers of dual blocks), as well as algorithms for solving derived problems: computing of the key numbers common to two nodes and the number of the node that has a common key with one of two nodes and, possibly, another key with the other one. These problems are solved by using the numbering of elements, blocks and dual blocks in accordance with the proposed duality rule: sets of elements and dual blocks are in one-to-one correspondence by numbering; the dual block with a specified number contains the numbers of blocks containing elements with this number. Distributed (independent) calculation of blocks is carried out on the basis of algebraic identifiers computed by block numbers. In addition to the possible absence of a physical connection between the nodes, the inadmissibility of using separate (compromised) keys is taken into account, and the incomplete furnishing of the network nodes with keys, as well as the incompleteness of the system implementation as a whole. Algorithms for computing the switching parameters of two nodes in designing the WSS and an algorithm for computer modeling of the calculation of such parameters during the WSS operation subject to the specified constraints and in using any of the above types of combinatorial block diagrams are presented.