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.