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

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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 leveled fully homomorphic encryption (FHE). We then prove their security under the assumption that a suitable version of the Lattice Isomorphism Problem is hard