Optimal key pre‐distribution schemes from affine resolvable and partially affine resolvable designs

Abstract

AbstractVarious key pre‐distribution schemes (KPSs) for distributed sensor networks (DSNs) were obtained from different combinatorial designs. A block design may be mapped to a KPS where is the number of nodes or network size and is the number of keys (points) per node. A KPS is corresponding to a symmetric balanced incomplete block design has full connectivity where all nodes are connected to each other. But it is desirable that all nodes do not share common keys as the compromise of any node will destroy the whole network (see Lee & Stinson, 2005; Martin, 2009). To meet the situation, Lee and Stinson (2005) introduced μ—common intersection design which has disjoint blocks and these disjoint blocks can establish a secure communication through certain common intersecting blocks. Here we have proposed optimal KPSs from affine resolvable and partially affine resolvable balanced incomplete block designs, group divisible designs and L2—type designs. It is shown that these designs are important classes of μ—common intersection designs. The KPSs obtained here are optimal in the sense of local connectivity. Mathematics Subject Classification (2010): 94C30; 68R05; 05B05; 62K10.