Paper 2026/465

Advanced cryptography from lattice isomorphism—new constructions of IBE and FHE

Zhengnan Lai, Cornell University

Noah Stephens-Davidowitz, Cornell University

Abstract

We show how to translate some of the more advanced techniques used in LWE-based cryptography to the setting of lattice-isomorphism-based cryptography, which was recently introduced by Ducas and van Woerden [Eurocrypt, 2022]. In particular, we show constructions of two powerful cryptographic primitives, identity-based encryption (IBE) and fully homomorphic encryption (FHE). We then prove their security under the assumption that a suitable version of the Lattice Isomorphism Problem is hard. Our constructions use quite general and modular techniques, and we expect them to have other applications. Specifically, we show that the now-ubiquitous techniques introduced by Gentry, Peikert, and Vaikuntanathan [STOC, 2008] to build IBE and Gentry, Sahai, and Waters [Crypto, 2013] to build FHE can be made to work in our setting using any sufficiently "nice" lattice.

@misc{cryptoeprint:2026/465,
      author = {Huck Bennett and Zhengnan Lai and Noah Stephens-Davidowitz},
      title = {Advanced cryptography from lattice isomorphism—new constructions of {IBE} and {FHE}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/465},
      year = {2026},
      url = {https://eprint.iacr.org/2026/465}
}