Scaling of Networks and their Key Systems Based on Combined Combinatorial Block Designs

Abstract

A new method of scaling wireless sensor networks, as well as key distribution schemes and key spaces in them based on a combined combinatorial block design formed on the set of all pairs composed of blocks and corresponding to their elements dual blocks of a given combinatorial block design is presented. Estimates are given for the cardinalities of scaled circuits based on the combined projective plane, the combined modified residual block design, and the combined residual combinatorial transversal block design. It is shown that the size of the key memory of the nodes of such networks does not depend on the parameters of the combinatorial block design and is two key units, but in schemes based on the combined projective plane, the length of the shortest route between the vertices of the key matching graph increases to three. The consequences of node capture are evaluated and ways to limit them with a guaranteed security parameter are proposed. For schemes based on a combined cyclic projective plane, as applied to the w-safe WSN of a "smart home", communication schemes between nodes along routes of length from one to three and an example of a protocol are presented. An example of such a WSN containing 910 nodes that are child nodes from 31 to 91 routers is given.