Paper 2025/1440 Original: eprint.iacr.org/2025/1440 ↗

Faster Homomorphic Integer Computer

Abstract

We design a fully homomorphic encryption for moduli of the form $b^k$ with small $b$. Our construction asymptotically improves upon Kim [TCHES'25]: for fixed $b$, the multiplication latency decreases from $O(k \log k)$ to $O(\log k)$ while preserving amortized latency. Our experiments show that our $64$-bit multiplication achieves $\approx 6 \times$ lower latency than Kim and slightly lower latency than TFHE-rs, while improving amortized latency by three orders of magnitude over TFHE-rs. The performance gap widens for larger precision. For instance, our $512$-bit multiplication achieves $\approx 49 \times$ lower latency and four orders of magnitude lower amortized latency than TFHE-rs. We also outperform Boneh and Kim [Crypto'25] with $4.70 \times$ lower latency and $75.3 \times$ lower amortized latency for $256$-bit multiplication.