Qiwu: Exploiting Ciphertext-Level SIMD Parallelism in Homomorphic Encryption Programs

Fully Homomorphic Encryption (FHE), particularly the CKKS scheme, enables computation on encrypted data, facilitating secure task offloading to untrusted servers. CKKS allows packing multiple complex values into a single ciphertext, crucial for fixed-point arithmetic in machine learning, while leveraging SIMD parallelism at the plaintext level. However, operations such as reductions can degrade performance by creating a large number of bubbles (or gaps) in intermediate ciphertexts, leading to wasted computational resources. We introduce Qiwu, a ciphertext-level vectorization approach that enhances performance by fusing multiple ciphertexts containing bubbles. Qiwu uses a DSL to specify zero bubbles in input ciphertexts and nonzero bubbles in output ciphertexts, employs data-flow analysis to track them, and formulates a fusion plan guided by a cost-benefit assessment. Implemented in an existing FHE compiler, Qiwu was evaluated on four applications (including three machine learning tasks) and three kernels. It achieves speedups of up to 18.0× on CPUs, averaging 3.4× (geometric mean), compared to the state-of-the-art compiler that exploit only plaintext-level parallelism.