In the context of wireless sensor networks, computation/communication tradeoffs may appear in many aspects of the system design. In this paper, we present a linear programming framework to guide designers in effectively using these tradeoffs for prolonging network lifetime. To investigate the tradeoff in more concrete terms, as our representative problem we choose a security service; non-repudiation which can be supported with different types of digital signature algorithms. Since these algorithms have high computation and/or communication overheads, supporting non-repudiation of sensor data has been traditionally considered to be infeasible in wireless sensor networks. Using our framework, we compare three signature algorithms with respect to their effect on network lifetime in different topologies and operating conditions. We have shown that with proper algorithm selection the lifetime reduction due to the utilization of digital signatures can be as low as 10%; however, non-optimal algorithm selection can result in more than 90% lifetime reduction compared to a network not supporting non-repudiation.