The bipartite graph Gt constructed above is next
used to uniquely construct a symmetric key assignment
scheme used to establish secure communication in a
wireless network. Let Kt be a set of symmetric cryptographic keys [16], and let N = U [ B represent the
set of network nodes. For each kt 2 Kt, assign the key
kt to node n 2 N if and only if (n;kt) 2 Et. A pair of
nodes n1;n2 2 N can communicate securely if and only
if there exists at least one key kt 2 Kt such that both
(n1;kt) 2 Et and(n2;kt) 2 Et. If the key kt is held by any
compromised node w 2 C, the communication between
n1 and n2 is insecure against attacks by the adversary
(e.g. eavesdropping on encrypted messages). Hence, the
secure link is compromised if and only if there is one
such user w 2 C such that (w;kt) 2 Et.