  Key predistribution is a well-known technique for ensuring secure
communication via encryption among sensors deployed in an ad-hoc manner to form
a sensor network. In this paper, we propose a novel 2-Phase technique for key
predistribution based on a combination of inherited and random key assignments
from the given key pool to individual sensor nodes. We also develop an
analytical framework for measuring security-performance tradeoffs of different
key distribution schemes by providing metrics for measuring sensornet
connectivity and resiliency to enemy attacks. In particular, we show
analytically that the 2-Phase scheme provides better average connectivity and
superior $q$-composite connectivity than the random scheme. We then prove that
the invulnerability of a communication link under arbitrary number of node
captures by an adversary is higher under the 2-Phase scheme. The probability of
a communicating node pair having an exclusive key also scales better with
network size under the 2-Phase scheme. We also show analytically that the
vulnerability of an arbitrary communication link in the sensornet to single
node capture is lower under 2-Phase assuming both network-wide as well as
localized capture. Simulation results also show that the number of exclusive
keys shared between any two nodes is higher while the number of $q$-composite
links compromised when a given number of nodes are captured by the enemy is
smaller under the 2-Phase scheme as compared to the random one.
