Underwater Acoustic Sensor Networks (UASNs) have nowadays become an attractive topic in scientific studies and commercial applications. An important challenge in UASN's design is the limited network lifetime and low reliability caused by the limited battery energy of sensor nodes and harsh channel conditions in underwater environments. In addition, sensor nodes may generate sensitive data, which needs to be concealed. To this end, cryptographic encryption is a commonly used method to cipher a data before transmission to maintain security. However, encryption methods require additional computation and extra energy, which causes a decrease in the network lifetime. To this end, transmitting fragmented data through multiple paths can be used as a security countermeasure, in conjunction with encryption against silent listening attacks. To address these challenges, in this study, an optimization framework has been developed to analyze the effects of multi-path routing, packet duplication, encryption and data fragmentation on network lifetime. In addition to an optimal solution, Simulated Annealing, Golden Section Search and Genetic Algorithm-based heuristic methods have been developed. Performance results show that the proposed approach jointly solves the problem of UASN lifetime maximization, while providing network reliability and security.