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A distributed Wireless Sensor Network (WSN) is a collection of n sensors with limited hardware resources. Sensors can exchange messages via Radio Frequency (RF), whose range usually covers only a limited number of other sensors. An interesting problem is how to implement secure pair-wise communications among any pair of sensors in a WSN. A WSN requires completely distributed solutions which are particularly challenging due to the limited resources and the size of the network. Moreover, WSNs can be subject to several security threats, including the physical compromising of a sensor. Hence, any solution for secure pairwise communications should tolerate the collusion of a set of corrupted sensors. This paper describes a probabilistic model and two protocols to establish a secure pair-wise communication channel between any pair of sensors in the WSN, by assigning a small set of random keys to each …