Key predistribution schemes (KPSs) have played an important role in security of wireless sensor networks (WSNs). Due to comprehensive and simple structures, various types of combinatorial designs are used to construct KPSs. In general, compared to random KPSs, combinatorial KPSs have higher local connectivity but lower resilience against a node capture attack. In this paper, we apply two methods based on hash chains on KPSs based on transversal designs (TDs) to improve the resilience and the expressions for the metrics of the resulting schemes are derived.

This paper presents a combinatiorial characterization of broadcast authentication in which a transmitter broadcasts v messages e1(s), , ev(s) to authenticate a source state s to all n receivers so that any k receivers cannot cheat any other receivers, where ei is a key. Suppose that each receiver has l keys. First, we prove that k < l if v < n. Then we show an upper bound of n such that n v(v - 1)/l(l - 1) for k = l - 1 and n /+ for k < l - 1. Further, a scheme for k = 1 - 1 which meets the upper bound is presented by using a BIBD and a scheme for k < l - 1 such than n = / is presented by using a Steiner system. Some other efficient schemes are also presented.