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

TL;DR

This paper enhances permutational-key quantum homomorphic encryption by integrating quantum error correction that operates as a homomorphism, enabling secure, error-resilient quantum computations without revealing the encryption key.

Contribution

It introduces a method to combine permutational-key quantum homomorphic encryption with homomorphic quantum error correction, improving security and error management.

Findings

Successful integration of quantum error correction with homomorphic encryption

Enabling encoding and decoding without revealing the permutation key

Maintaining information-theoretic security in quantum protocols

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.