A wide range of important cloud applications, e.g., database analytics, graph analytics, and genome analysis, spend a considerable amount of time performing bulk bitwise operations (e.g., AND, OR, XOR). These applications often operate on highly sensitive data, making data privacy a critical concern. Homomorphic encryption (HE) enables secure computation on encrypted data without requiring decryption, ensuring privacy in untrusted and shared environments. We analyze 13 end-to-end applications across three domains (healthcare, graph, and database analytics) and observe that bulk bitwise operations take 62-100% of the execution time of the healthcare and graph workloads. The key problem is that existing HE approaches perform them with high-latency homomorphic operations (e.g., multiplication or lookup tables) and significantly increase the data size. Our goal is to enable fast bulk bitwise operations on homomorphically encrypted data by designing an efficient HE algorithm that reduces the use of these costly operations. To this end, we propose HULK, which performs two key steps: (1) it constructs bulk bitwise operations using low-cost homomorphic additions, which compute the Hamming weight of the encrypted operand bits in every slot of a packed ciphertext without any homomorphic multiplication, and (2) it decodes the result of an AND, OR, or XOR from the Hamming weight with a single indicator polynomial, keeping the result in the standard encoding. Across 13 end-to-end applications in healthcare, graph, and database analytics, HULK improves performance over the arithmetic approach used by prior works by up to 7.26x (CPU) and 6.65x (GPU), and on average by 2.32x/1.78x/1.45x (CPU) and 2.08x/1.70x/1.51x (GPU) for healthcare/graph/database analytics. When we increase the reduction depth in a representative application, HULK's speedup grows to 10.10x over the state-of-the-art GPU baseline.

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