Abstract
Many key pre-distribution (KPD) schemes based on combinatorial design were proposed for secure communication of wireless sensor networks (WSNs). Due to complexity of constructing the combinatorial design, it is infeasible to generate key rings using the corresponding combinatorial design in large scale deployment of WSNs. In this paper, we present a definition of new combinatorial design, termed “µ-partially balanced incomplete block design (µ-PBIBD)”, which is a refinement of partially balanced incomplete block design (PBIBD), and then describe a 2-D construction of µ-PBIBD which is mapped to KPD in WSNs. Our approach is of simple construction which provides a strong key connectivity and a poor network resilience. To improve the network resilience of KPD based on 2-D µ-PBIBD, we propose a KPD scheme based on 3-D Ex-µ-PBIBD which is a construction of µ-PBIBD from 2-D space to 3-D space. Ex-µ-PBIBD KPD scheme improves network scalability and resilience while has better key connectivity. Theoretical analysis and comparison with the related schemes show that key pre-distribution scheme based on Ex-µ-PBIBD provides high network resilience and better key scalability, while it achieves a trade-off between network resilience and network connectivity.