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Abstract: In this study, we introduce Coala, a novel framework designed to enhance the performance of finite field transformations for GPU environments. We have developed a GPU-optimized version of the Discrete Galois Transformation (DGT), a variant of the Number Theoretic Transform (NTT). We introduce a novel data access pattern scheme specifically engineered to enable coalesced accesses, significantly enhancing the efficiency of data transfers between global and shared memory. This enhancement not only boosts execution efficiency but also optimizes the interaction with the GPU's memory architecture. Additionally, Coala presents a comprehensive framework that optimizes the allocation of computational tasks across the GPU's architecture and execution kernels, thereby maximizing the use of GPU resources. Lastly, we provide a flexible method to adjust security levels and polynomial sizes through the incorporation of an in-kernel RNS method, and a flexible parameter generation approach. Comparative analysis against current state-of-the-art techniques reveals significant improvements. We observe performance gains of 2.82′ − 17.18′ against other DGT works on GPUs for different parameters, achieved concurrently with equal or lesser memory utilization.