Traffic Decorrelation Techniques for Countering Colluding Eavesdroppers in WSNs

Proof: Consider a source v with a hop-count η = |p(v, u)| to the destination u. Nodes in p(v, u) randomly select their transmission times within an interval T . Let the randomly selected transmission times be denoted by t1, t2, . . . , tη. We compute the average number of hops (H) traversed over T by a packet m originating at v1, using a combinatorial approach. The value of H depends on the arrangement order of t1, t2, . . . , tη. All possible arrangements nη! occur with equal probability, as the transmission times of each sensor are randomly and independently selected within T.. A packet traverses η hops during T , only if t1 < t2 < . . . < tη . This events occurs with probability,