The evaluation of both arithmetic and logic operations on machine words (e.g., 64-bit registers) in homomorphic settings is an attractive problem due to its close alignment with real-world programming models. Classical FHE schemes, such as BGV/BFV/TFHE/CKKS, typically excel at only one class of operations. Recent FHE schemes, such as REFHE and CPL (both appearing at Eurocrypt'26), support such operations but require iterative bootstrapping, with the number of iterations scaling with the machine word bitwidth, either linearly or logarithmically.

​We propose an FHE scheme that supports both arithmetic and logic operations on vectors of machine words. The scheme operates in two modes: arithmetic triangle mode and boolean flattened mode. Bootstrapping is used either to refresh noise within a mode, or to convert from arithmetic mode to boolean mode. Both refreshing and conversion require only two to three CKKS bootstrapping operations.

​This talk mainly covers recent work by Gao and Zheng (Crypto'26) and also includes some new results in preparation.​

Hongren Zheng is a Ph.D. student at Tsinghua University, advised by Prof. Mingyu Gao. He graduated from the Yao Class at Tsinghua University in 2022. His Ph.D. research spans a broad range of topics in the FHE ecosystem, including hardware acceleration, compilers, and new FHE schemes.​