  The security of wireless sensor networks is an active topic of research where
both symmetric and asymmetric key cryptography issues have been studied. Due to
their computational feasibility on typical sensor nodes, symmetric key
algorithms that use the same key to encrypt and decrypt messages have been
intensively studied and perfectly deployed in such environment. Because of the
wireless sensor's limited infrastructure, the bottleneck challenge for
deploying these algorithms is the key distribution. For the same reason of
resources restriction, key distribution mechanisms which are used in
traditional wireless networks are not efficient for sensor networks.
  To overcome the key distribution problem, several key pre-distribution
algorithms and techniques that assign keys or keying material for the networks
nodes in an offline phase have been introduced recently. In this paper, we
introduce a supplemental distribution technique based on the communication
pattern and deployment knowledge modeling. Our technique is based on the
hierarchical grid deployment. For granting a proportional security level with
number of dependent sensors, we use different polynomials in different orders
with different weights. In seek of our proposed work's value, we provide a
detailed analysis on the used resources, resulting security, resiliency, and
connectivity compared with other related works.
