Paper 2025/346 Original: eprint.iacr.org/2025/346 ↗
Homomorphic Encryption for Large Integers from Nested Residue Number Systems
Abstract
Existing fully homomorphic encryption (FHE) schemes primarily support a plaintext space defined over a relatively small prime. However, in some important applications of FHE one needs arithmetic over a large prescribed prime. In this paper we construct a new FHE system that is specifically designed for this purpose. Our system composes three layers of residue systems to enable much better performance than was previously possible. Our experiments show that for arithmetic modulo a 256-bit integer, when compared to the TFHE-rs implementation of 256-bit arithmetic, our new system achieves a factor of two thousand better multiplication throughput and a factor of twenty better latency. Moreover, for a 2048-bit prime modulus we achieve far better performance than was previously possible.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2025-06-10: last updated
- 2025-02-25: published
- Short URL
- https://ia.cr/2025/346
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/346,
author = {Dan Boneh and Jaehyung Kim},
title = {Homomorphic Encryption for Large Integers from Nested Residue Number Systems},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/346},
year = {2025},
url = {https://eprint.iacr.org/2025/346}
}