Fully homomorphic encryption (FHE) frees cloud computing from privacy concerns by enabling secure computation on encrypted data. However, its substantial computational and memory overhead results in significantly slower performance compared to unencrypted processing. To mitigate this overhead, we present Cheddar, a high-performance FHE library for GPUs, achieving substantial speedups over previous GPU implementations. We systematically enable 32-bit FHE execution, leveraging the 32-bit integer datapath within GPUs. We optimize GPU kernels using efficient low-level primitives and algorithms tailored to specific GPU architectures. Further, we alleviate the memory bandwidth burden by adjusting common FHE operational sequences and extensively applying kernel fusion. Cheddar delivers performance improvements of 2.18--4.45$\times$ for representative FHE workloads compared to state-of-the-art GPU implementations.
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