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Highlighting that connectivity and communication are two separate concepts in a Wireless Sensor Network (WSN), we propose a novel model for connectivity of a WSN using first order Reed Muller codes. For communication, we choose to work with a model that utilizes Partially Balance Incomplete Block Designs (PBIBD). Two suitable cryptosystems can now be applied for the two different models. As a result, the resiliency of the WSN is appreciably improved without affecting the connectivity and scalability of the original communication model. Secure key establishment has been achieved by converting identifiers of nodes from pubic into private information.