Multi-party quantum homomorphic encryption scheme based on quantum teleportation

The quantum homomorphic encryption involves performing homomorphic operations directly on the quantum ciphertext state without the need to convert the ciphertext to plaintext before performing homomorphic operations. In this paper, we propose an n-party quantum homomorphic encryption scheme based on quantum teleportation, which can be used to achieve non-interactivity, eliminate errors caused by T-gate evaluation, and allow clients’ private data to undergo arbitrary quantum computations across multiple servers without the need for the server to decrypt the data. In this scheme, the client prepares and encrypts GHZ states and single-particle states. Subsequently, the client transmits the single-particle states and particles of the GHZ state to the server. The server performs joint measurements on the received particles, performs homomorphic operations on the single-particle states, and simultaneously updates the key. Finally, the result of the homomorphic operation is decrypted using the first particle in the GHZ state. This scheme is non-interactive, information-theoretically secure, and utilizes a one-time quantum channel. Furthermore, we apply the Quantum Homomorphic Encryption (QHE) scheme to quantum private comparison and successfully perform private comparison operations on the origin quantum.