Revocable Cryptography from Learning with Errors

Quantum cryptography leverages unique properties of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics and design cryptographic schemes with key revocation capabilities. We consider schemes where secret keys are represented as quantum states with the guarantee that, once the secret key is successfully revoked from a user, they no longer have the ability to perform the same functionality as before. We define and construct several fundamental cryptographic primitives with key-revocation capabilities, namely pseudorandom functions, secret-key and public-key encryption, and even fully homomorphic encryption, assuming the quantum sub-exponential hardness of the learning with errors problem. Central to all our constructions is our method of making the Dual-Regev encryption (Gentry, Peikert and Vaikuntanathan, STOC 2008) scheme revocable.