Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks

Area of Science:

• Quantum Computing
• Cryptography
• Network Security

Background:

• Current quantum homomorphic encryption (QHE) schemes typically involve a single evaluator with limited quantum computational capabilities.
• This limitation restricts the flexibility and applicability of QHE in complex quantum network environments.

Purpose of the Study:

• To propose a novel (t,n)-threshold quantum homomorphic encryption (TQHE) network scheme.
• To enable collaborative computation on encrypted quantum data by multiple evaluators.
• To enhance the flexibility and security of quantum computations in network settings.

Main Methods:

• The proposed scheme is based on the Shamir secret sharing protocol.
• It allows k (t≤k≤n) evaluators to collaboratively perform computations on encrypted quantum data.
• Each evaluator can execute arbitrary single-qubit gate operations assigned by the data owner.

Main Results:

• A specific (3,5)-threshold TQHE network scheme example is presented.
• The scheme's correctness and feasibility were demonstrated through simulations on the IBM quantum computing cloud platform.
• Security analysis confirms the scheme's robustness against various potential attacks.

Conclusions:

• The developed (t,n)-threshold QHE scheme significantly improves upon existing QHE limitations.
• The collaborative computation model enhances the flexibility and power of quantum network environments.
• The scheme offers a secure and practical solution for distributed quantum computations on encrypted data.