Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks
Currently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform ar...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/7 |
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| author | Yongli Tang Menghao Guo Binyong Li Kaixin Geng Jinxia Yu Baodong Qin |
| author_facet | Yongli Tang Menghao Guo Binyong Li Kaixin Geng Jinxia Yu Baodong Qin |
| author_sort | Yongli Tang |
| collection | DOAJ |
| description | Currently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform are usually somewhat limited, which significantly reduces the flexibility of the scheme in quantum network environments. In this paper, we propose a novel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mspace width="4.pt"></mspace><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula>-threshold QHE (TQHE) network scheme based on the Shamir secret sharing protocol, which allows <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mspace width="4.pt"></mspace><mo>(</mo><mi>t</mi><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> evaluators to collaboratively perform evaluation computation operations on each qubit within the shared encrypted sequence. Moreover, each evaluator, while possessing the ability to perform all single-qubit unitary operations, is able to perform arbitrary single-qubit gate computation task assigned by the data owner. We give a specific (3, 5)-threshold example, illustrating the scheme’s correctness and feasibility, and simulate it on IBM quantum computing cloud platform. Finally, it is shown that the scheme is secure by analyzing encryption/decryption private keys, ciphertext quantum state sequences during transmission, plaintext quantum state sequence, and the result after computations on the plaintext quantum state sequence. |
| format | Article |
| id | doaj-art-5564d360a1004d0b9c198cb092c6743a |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-5564d360a1004d0b9c198cb092c6743a2025-01-24T13:31:38ZengMDPI AGEntropy1099-43002024-12-01271710.3390/e27010007Flexible Threshold Quantum Homomorphic Encryption on Quantum NetworksYongli Tang0Menghao Guo1Binyong Li2Kaixin Geng3Jinxia Yu4Baodong Qin5School of Software, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, ChinaAdvanced Cryptography and System Security Key Laboratory of Sichuan, Chengdu 610225, ChinaSchool of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, ChinaSchool of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, ChinaShaanxi Key Laboratory of Information Communication Network and Security, Xi’an University of Posts & Telecommunications, Xi’an 710121, ChinaCurrently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform are usually somewhat limited, which significantly reduces the flexibility of the scheme in quantum network environments. In this paper, we propose a novel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mspace width="4.pt"></mspace><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula>-threshold QHE (TQHE) network scheme based on the Shamir secret sharing protocol, which allows <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mspace width="4.pt"></mspace><mo>(</mo><mi>t</mi><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> evaluators to collaboratively perform evaluation computation operations on each qubit within the shared encrypted sequence. Moreover, each evaluator, while possessing the ability to perform all single-qubit unitary operations, is able to perform arbitrary single-qubit gate computation task assigned by the data owner. We give a specific (3, 5)-threshold example, illustrating the scheme’s correctness and feasibility, and simulate it on IBM quantum computing cloud platform. Finally, it is shown that the scheme is secure by analyzing encryption/decryption private keys, ciphertext quantum state sequences during transmission, plaintext quantum state sequence, and the result after computations on the plaintext quantum state sequence.https://www.mdpi.com/1099-4300/27/1/7threshold quantum homomorphic encryptionShamir secret sharingquantum computationquantum computing cloud platform |
| spellingShingle | Yongli Tang Menghao Guo Binyong Li Kaixin Geng Jinxia Yu Baodong Qin Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks Entropy threshold quantum homomorphic encryption Shamir secret sharing quantum computation quantum computing cloud platform |
| title | Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks |
| title_full | Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks |
| title_fullStr | Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks |
| title_full_unstemmed | Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks |
| title_short | Flexible Threshold Quantum Homomorphic Encryption on Quantum Networks |
| title_sort | flexible threshold quantum homomorphic encryption on quantum networks |
| topic | threshold quantum homomorphic encryption Shamir secret sharing quantum computation quantum computing cloud platform |
| url | https://www.mdpi.com/1099-4300/27/1/7 |
| work_keys_str_mv | AT yonglitang flexiblethresholdquantumhomomorphicencryptiononquantumnetworks AT menghaoguo flexiblethresholdquantumhomomorphicencryptiononquantumnetworks AT binyongli flexiblethresholdquantumhomomorphicencryptiononquantumnetworks AT kaixingeng flexiblethresholdquantumhomomorphicencryptiononquantumnetworks AT jinxiayu flexiblethresholdquantumhomomorphicencryptiononquantumnetworks AT baodongqin flexiblethresholdquantumhomomorphicencryptiononquantumnetworks |