Data confidentiality implies that data access is limited to authorized entities only, thus measured data and transmitted data by wireless sensors require optimum security and privacy. Various techniques have been employed to implement effective security mechanisms for a wireless sensor network. However, the arsenal of these potential solutions is useless, considering the constrained nature of the Wireless Sensor Network (WSN) resources in terms of memory, processing and computational capacity. While considering an effective solution for this situation, care must be taken not to trade the desired solution for other factors. This paper considers the implementation of a probabilistic approach for key management in WSN. In the implementation, all kinds of communication within the wireless sensor nodes are presented by forwarding encrypted keys for mutual authentication. A successful authentication opens a communication channel for the communicating nodes. The encrypted keys are computed by generating a polynomial which constitutes the hashed ID concatenated with the master key and Message Authentication Code (MAC) address of the node. The results presented from the simulation of this model are benchmarked with the Dynamically Generated Polynomial (DGP). The proposed model was simulated using MATLAB tools and the comparison of the results obtained shows that the proposed model outperforms the DGP model by 87%, based on the key metrics which are energy consumption, storage and communication overhead.