As Fully Homomorphic Encryption (FHE) enables computation over encrypted data, it is a natural question of how efficiently it handles standard integer computations like 64-bit arithmetic. It has long been believed that the CGGI/DM family or the BGV/BFV family are the best options, depending on the size of the parallelism. The discrete variant of CKKS, suggested by Drucker et al. J.Cryptol.’24, provides an interesting alternative for integer computations. Notably, the modular reduction framework proposed by Kim and Noh CiC’25 built on top of the CKKSstyle functional bootstrapping by Bae et al. Asiacrypt’24 gives an efficient arithmetic modulo small integers.In this work, we propose a novel homomorphic computer for unsigned integer computations. We represent a large integer (e.g. 64-bit) as a vector of smaller chunks (e.g. 4-bit) and construct arithmetic operations relying on discrete CKKS. The proposed scheme supports many of the operations supported in TFHE-rs while outperforming it in terms of amortized running time. Notably, our homomorphic 64-bit multiplication takes 8.85ms per slot, which is more than three orders of magnitude faster than TFHE-rs.
Jaehyung Kim (Fri,) studied this question.