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Graphics processing units (GPUs) are becoming default accelerators in many domains such as high-performance computing (HPC), deep learning, and virtual/augmented reality. Recently, GPUs have also shown significant speedups for a variety of security-sensitive applications such as encryptions. These speedups have largely benefited from the high memory bandwidth and compute throughput of GPUs. One of the key features to optimize the memory bandwidth consumption in GPUs is intra-warp memory access coalescing, which merges memory requests originating from different threads of a single warp into as few cache lines as possible. However, this coalescing feature is also shown to make the GPUs prone to the correlation timing attacks as it exposes the relationship between the execution time and the number of coalesced accesses. Consequently, an attacker is able to correctly reveal an AES private key via repeatedly gathering encrypted data and execution time on a GPU. In this work, we propose a series of defense mechanisms to alleviate such timing attacks by carefully trading off performance for improved security. Specifically, we propose to randomize the coalescing logic such that the attacker finds it hard to guess the correct number of coalesced accesses generated. To this end, we propose to randomize: a) the granularity (called as subwarp) at which warp threads are grouped together for coalescing, and b) the threads selected by each subwarp for coalescing. Such randomization techniques result in three mechanisms: fixed-sized subwarp (FSS), random-sized subwarp (RSS), and random-threaded subwarp (RTS). We find that the combination of these security mechanisms offers 24- to 961-times improvement in the security against the correlation timing attacks with 5 to 28% performance degradation. Online copy: http://adwaitjog.github.io/docs/pdf/rcoal-hpca18.pdf