Multi-party dynamic quantum homomorphic encryption scheme based on rotation operators

TL;DR

This paper addresses secure delegated quantum computation in distributed networks by proposing a multi-party dynamic quantum homomorphic encryption scheme based on rotation operators. The approach uses GHZ-based secret splitting, QOTP encryption, and a trusted key center to enable non-interactive evaluation of arbitrary quantum circuits while dynamically accommodating server churn. Core contributions include a rotation-operator based $T$-gate replacement that eliminates non-interactive phase errors, a scalable $(M+N)$-party architecture with MDI-QKD key distribution and circuit substitution, and formal proofs of information-theoretic security and full homomorphism, corroborated by IBM Quantum Experience simulations. The work demonstrates enhanced practicality for quantum distributed networks with high qubit efficiency and dynamic server management.

Abstract

Quantum homomorphic encryption is the corresponding technology of classical homomorphic encryption in the quantum field. Due to its ability to ensure the correctness of computation and the security of data, it is particularly suitable for delegated computation in quantum cloud networks. However, previous schemes were unable to simultaneously handle the volatility problem of servers dynamically and eliminate the error caused by homomorphic evaluation of T-gate non-interactively. Therefore, a novel multi-party dynamic quantum homomorphic encryption scheme based on rotation operators is proposed in this paper. Firstly, the proposed scheme uses the rotation operators to solve the phase gate error that occurs during the homomorphic evaluation of T-gate non-interactively. Secondly, the scheme can dynamically deal with instability of servers, such as adding a server or removing a server. Then, the trusted key center is introduced, which is responsible for key updating and circuit replacement, which lowers the requirements for quantum capabilities on the client. Finally, this scheme extends the single-client multi-server model to the multi-client multi-server model, making it more suitable for quantum distributed networks and enhancing its practicality. In addition, we theoretically prove the correctness and fully homomorphic property of the proposed scheme, and verify it through the simulation conducted on the IBM Quantum Experience. Security analysis and efficiency analysis further demonstrate that the proposed scheme is information-theoretically secure and possesses high qubit efficiency.

Figures (4)

• Figure 1: Flow chart of quantum homomorphic encryption scheme
• Figure 2: The example of secret splitting with one client, three servers and five-bit data
• Figure 3: The diagram of the quantum circuit
• Figure 4: The result of the quantum circuit

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof