  We study the secure and reliable connectivity of wireless sensor networks.
Security is assumed to be ensured by the random pairwise key predistribution
scheme of Chan, Perrig, and Song, and unreliable wireless links are represented
by independent on/off channels. Modeling the network by an intersection of a
random $K$-out graph and an Erd\H{o}s-R\'enyi graph, we present scaling
conditions (on the number of nodes, the scheme parameter $K$, and the
probability of a wireless channel being on) such that the resulting graph
contains no nodes with degree less than $k$ with high probability, when the
number of nodes gets large. Results are given in the form of zero-one laws and
are shown to improve the previous results by Ya\u{g}an and Makowski on the
absence of isolated nodes (i.e., absence of nodes with degree zero). Via
simulations, the established zero-one laws are shown to hold also for the
property of $k$-connectivity; i.e., the property that graph remains connected
despite the deletion of any $k-1$ nodes or edges.
