International Association
for Cryptologic Research

We design a fast and efficient fully homomorphic encryption for radix power modulus. We mainly rely on the CKKS modular reduction by Kim and Noh [CiC'25] and the intermediate CKKS encoding from NeuJeans [Ju et al.;CCS'24]. Our construction is a direct improvement of the homomorphic integer computer by Kim [TCHES'25]: The asymptotic latency reduces from $O(k)$ to $O(\log k)$ for a given plaintext modulus $b^k$ for a fixed radix base $b$, while keeping the throughput. Our experiments show that the latency of our $64$ bit multiplication is $\approx 6$ times faster than Kim and slightly faster than TFHE-rs, while being three orders of magnitude better in terms of throughput than TFHE-rs. The performance gap widens for larger precision. Our work also concretely outperforms the work by Boneh and Kim [Crypto'25], by a factor of $4.70$ better latency and $75.3$ times better throughput for $256$ bit multiplication.