Fully-Homomorphic Encryption from Lattice Isomorphism

Pedro Branco; Giulio Malavolta; Zayd Maradni

Paper 2025/993

Fully-Homomorphic Encryption from Lattice Isomorphism

Pedro Branco, Bocconi University

Giulio Malavolta, Bocconi University

Zayd Maradni, Max Planck Institute for Software Systems

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: A minor revision of an IACR publication in TCC 2025
Contact author(s): pedrodemelobranco @ gmail com
giulio malavolta @ hotmail it
zmaradni @ mpi-sws org
History: 2025-09-22: last of 2 revisions; 2025-05-29: received; See all versions
Short URL: https://ia.cr/2025/993
License: CC BY

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}
}