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In this letter, we present a mixed binary linear programming framework to investigate the impact of one-time energy costs on the overall system lifetime in wireless sensor networks. We use public-key cryptography as our representative one-time initialization operation. We show that the effect of public-key cryptography on optimal routes selection depends on the ratio of electronics energy to amplifier energy. The simulation results also reveal that the impact of public key cryptography on the maximum achievable lifetime of a sensor network is not negligible and it does not steadily increase with the size of the network.