Advanced Cryptography from Lattice Isomorphism - New Constructions of IBE and FHE

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. BIOGRAPHICAL SKETCH Zhengnan Lai received his Bachelor of Arts degree in Mathematics and Computer Science from Cornell University in 2024. In 2026, he completed his Master of Science degree in Computer Science at Cornell University, specializing in theoretical computer science. During his graduate studies, Zhengnan worked under the supervision of Dr Noah Stephens-Davidowitz, focusing on theoretical cryptography. Zhengnan plans to continue his research in theoretical cryptography as he pursues a Ph.D. in Computer Science at Northeastern University.