Permutational-key quantum homomorphic encryption with homomorphic quantum error-correction

Abstract: The gold-standard for security in quantum cryptographic protocols is information-theoretic security. Information-theoretic security is surely future-proof, because it makes no assumptions on the hardness of any computational problems and relies only on the fundamental laws of quantum mechanics. Here, we revisit a permutational-key quantum homomorphic encryption protocol with information-theoretic security. We explain how to integrate this protocol with quantum error correction that has the error correction encoding as a homomorphism. This feature enables both client and server to apply the encoding and decoding step for the quantum error correction, without use of the encrypting permutation-key.