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Fully-Homomorphic Encryption from Lattice Isomorphism

Authors:
Pedro Branco , Bocconi University
Giulio Malavolta , Bocconi University
Zayd Maradni , Max Planck Institute for Software Systems
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Conference: TCC 2025
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.
BibTeX
@inproceedings{tcc-2025-36197,
  title={Fully-Homomorphic Encryption from Lattice Isomorphism},
  publisher={Springer-Verlag},
  author={Pedro Branco and Giulio Malavolta and Zayd Maradni},
  year=2025
}