Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.

Intelligent Automation & Soft ComputingJan 1, 202217 citations

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

Zhenzhen Li, Ming-Kui Liu, Wen-Ling Yang +2 more

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 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.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 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.

arXiv:2505.06955Physica ScriptaJan 22, 20260 citations

Reverse Delegated Training and Private Inference via Perfectly-Secure Quantum Homomorphic Encryption

Sergio A. Ortega, Miguel A. Martin-Delgado

Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+ $T$ decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+$T$ decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.

quant-pharXiv:2602.12712Feb 16, 20260 citations

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decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.