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As High-Performance Computing (HPC) applications with data security requirements are increasingly moving to execute in the public cloud, there is a demand that the cloud infrastructure for HPC should support privacy and integrity. Incorporating privacy and integrity mechanisms in the communication infrastructure of today's public cloud is challenging because recent advances in the networking infrastructure in data centers have shifted the communication bottleneck from the network links to the network endpoints and because encryption is computationally intensive. In my Ph.D. research, I consider incorporating encryption to support privacy and integrity in the Message Passing Interface (MPI) library, which is widely used in HPC applications. In this dissertation, first I will present the baseline encrypted MPI library. I have used this baseline library to measure the performance overhead for both point-to-point and collective communication. Then I will discuss the optimization techniques I have used to optimize point-to-point communication for both small and large messages. After that, I will discuss the techniques used to design novel encrypted algorithms for the Scatter collective operation. I have performed evaluation on three platforms and also using Docker containers. The results show that my techniques achieve significantly higher performance than the data encryption method of the Docker swarm. The evaluation on three platforms indicates that the proposed techniques are more effective when the network speed is significantly higher than single-core encryption performance, a likely scenario in the future.