Paper 2025/993 Original: eprint.iacr.org/2025/993 ↗
Fully-Homomorphic Encryption from Lattice Isomorphism
Abstract
The lattice isomorphism problem (LIP) asks, given two lattices $\Lambda_0$ and $\Lambda_1$, to decide whether there exists an orthogonal linear map from $\Lambda_0$ to $\Lambda_1$. In this work, we show that the hardness of (a circular variant of) LIP implies the existence of a fully-homomorphic encryption scheme for all classical and quantum circuits. Prior to our work, LIP was only known to imply the existence of basic cryptographic primitives, such as public-key encryption or digital signatures.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2025-09-22: last updated
- 2025-05-29: published
- Short URL
- https://ia.cr/2025/993
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/993,
author = {Pedro Branco and Giulio Malavolta and Zayd Maradni},
title = {Fully-Homomorphic Encryption from Lattice Isomorphism},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/993},
year = {2025},
url = {https://eprint.iacr.org/2025/993}
}