{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:30:37Z","timestamp":1778603437428,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T00:00:00Z","timestamp":1583798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Anhui Key Laboratory of Network and Information Security","award":["AHNIS2020003"],"award-info":[{"award-number":["AHNIS2020003"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972438"],"award-info":[{"award-number":["61972438"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61801004"],"award-info":[{"award-number":["61801004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Anhui Province","award":["1808085QF211"],"award-info":[{"award-number":["1808085QF211"]}]},{"name":"the Natural Science Foundation of Universities of Anhui Province","award":["KJ2019A0702"],"award-info":[{"award-number":["KJ2019A0702"]}]},{"name":"the Natural Science Foundation of Universities of Anhui Province","award":["KJ2019A0704"],"award-info":[{"award-number":["KJ2019A0704"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Different from the traditional healthcare field, Medical Cyber Physical Systems (MCPS) rely more on wireless wearable devices and medical applications to provide better medical services. The secure storage and sharing of medical data are facing great challenges. Blockchain technology with decentralization, security, credibility and tamper-proof is an effective way to solve this problem. However, capacity limitation is one of the main reasons affecting the improvement of blockchain performance. Certificateless aggregation signature schemes can greatly tackle the difficulty of blockchain expansion. In this paper, we describe a two-layer system model in which medical records are stored off-blockchain and shared on-blockchain. Furthermore, a multi-trapdoor hash function is proposed. Based on the proposed multi-trapdoor hash function, we present a certificateless aggregate signature scheme for blockchain-based MCPS. The purpose is to realize the authentication of related medical staffs, medical equipment, and medical apps, ensure the integrity of medical records, and support the secure storage and sharing of medical information. The proposed scheme is highly computationally efficient because it does not use bilinear maps and exponential operations. Many certificateless aggregate signature schemes without bilinear maps in Internet of things (IoT) have been proposed in recent years, but they are not applied to the medical field, and they do not consider the security requirements of medical data. The proposed scheme in this paper has high computing and storage efficiency, while meeting the security requirements in MCPS.<\/jats:p>","DOI":"10.3390\/s20051521","type":"journal-article","created":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T11:59:36Z","timestamp":1583841576000},"page":"1521","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["An Efficient Certificateless Aggregate Signature Scheme for Blockchain-Based Medical Cyber Physical Systems"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4626-6176","authenticated-orcid":false,"given":"Hong","family":"Shu","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer, Tongling University, Tongling 244061, China"},{"name":"Anhui Provincial Key Lab of Network and Information Security, Wuhu 241002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer, Tongling University, Tongling 244061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongqing","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer, Tongling University, Tongling 244061, China"},{"name":"Institute of Information Technology &amp; Engineering Management, Tongling University, Tongling 244061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0557-5084","authenticated-orcid":false,"given":"Fulong","family":"Chen","sequence":"additional","affiliation":[{"name":"Anhui Provincial Key Lab of Network and Information Security, Wuhu 241002, China"},{"name":"School of Computer and Information, Anhui Normal University, Wuhu 241002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Xie","sequence":"additional","affiliation":[{"name":"Anhui Provincial Key Lab of Network and Information Security, Wuhu 241002, China"},{"name":"School of Computer and Information, Anhui Normal University, Wuhu 241002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Sun","sequence":"additional","affiliation":[{"name":"Anhui Provincial Key Lab of Network and Information Security, Wuhu 241002, China"},{"name":"School of Computer and Information, Anhui Normal University, Wuhu 241002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.ins.2018.02.005","article-title":"Privacy-preserving Smart IoT-based Healthcare Big Data Storage and Self-adaptive Access Control System","volume":"479","author":"Yang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lee, I., and Sokolsky, O. (2010, January 17). Medical Cyber Physical Systems. Proceedings of the CPS Demystified Session, DAC 2010, Anaheim, CA, USA.","DOI":"10.1145\/1837274.1837463"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.pmcj.2019.03.004","article-title":"Identity-based Proxy-oriented Outsourcing with Public Auditing in Cloud-based Medical Cyber\u2013physical Systems","volume":"56","author":"Zhang","year":"2019","journal-title":"Pervasive Mob. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10916-018-1121-4","article-title":"Blockchain-based Medical Records Secure Storage and Medical Service Framework","volume":"43","author":"Yi","year":"2019","journal-title":"J. Med. Syst."},{"key":"ref_5","first-page":"270","article-title":"Research Progress of Blockchain Technology and Its Application in Information Security","volume":"29","author":"Liu","year":"2018","journal-title":"J. Softw."},{"key":"ref_6","first-page":"1474","article-title":"Blockchain Application Development Techniques","volume":"28","author":"Tsai","year":"2017","journal-title":"J. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102481","DOI":"10.1016\/j.jnca.2019.102481","article-title":"A Comprehensive Survey on Attacks, Security Issues and Blockchain Solutions for IoT and IIoT","volume":"149","author":"Sengupta","year":"2020","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.ins.2012.07.004","article-title":"An Efficient Certificateless Aggregate Signature with Constant Pairing Computations","volume":"219","author":"Xiong","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gong, Z., Long, Y., Hong, X., and Chen, K. (August, January 30). Two Certificateless Aggregate Signatures from Bilinear Maps. Proceedings of the 8th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel\/Distributed Computing (SNPD 2007), Qingdao, China.","DOI":"10.1109\/SNPD.2007.132"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.ins.2014.07.019","article-title":"Notes on the Security of Certificateless Aggregate Signature Schemes","volume":"287","author":"Zhang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2681","DOI":"10.1109\/TIFS.2015.2473820","article-title":"An Efficient Identity-Based Conditional Privacy-Preserving Authentication Scheme for Vehicular Ad Hoc Networks","volume":"10","author":"He","year":"2015","journal-title":"IEEE Trans. Inf. Forensic Secur."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Suciu, G., N\u0103drag, C., Istrate, C., Vulpe, A., Ditu, M.C., and Subea, O. (2018, January 25\u201328). Comparative Analysis of Distributed Ledger Technologies. Proceedings of the 6th Global Wireless Summit (GWS 2018), Chiang Rai, Thailand.","DOI":"10.1109\/GWS.2018.8686563"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/s10916-018-0993-7","article-title":"Medblock: Efficient and Secure Medical Data Sharing via Blockchain","volume":"42","author":"Fan","year":"2018","journal-title":"J. Med Syst."},{"key":"ref_14","first-page":"1555","article-title":"A Medical Data Sharing Model via Blockchain","volume":"43","author":"Xue","year":"2017","journal-title":"Acta Autom. Sin."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"14757","DOI":"10.1109\/ACCESS.2017.2730843","article-title":"MeDShare: Trust-less Medical Data Sharing among Cloud Service Providers via Blockchain","volume":"5","author":"Xia","year":"2017","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1109\/TDSC.2016.2616861","article-title":"Security and Privacy in Decentralized Energy Trading through Multi-signatures, Blockchain and Anonymous Messaging Streams","volume":"15","author":"Aitzhan","year":"2016","journal-title":"IEEE Trans. Dependable Secur. Comput."},{"key":"ref_17","first-page":"414","article-title":"Aggregation of Gamma-Signatures and Applications to Bitcoin","volume":"2018","author":"Zhao","year":"2018","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"ref_18","first-page":"556","article-title":"Efficient Multi-party Fair Contract Signing Protocol based on Blockchains","volume":"5","author":"Gao","year":"2018","journal-title":"J. Cryptologic Res."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, Y., Li, R., Liu, X., Wang, J., Tang, C., and Kang, H. (2017, January 15\u201318). Enhancing Anonymity of Bitcoin Based on Ring Signature Algorithm. Proceedings of the 13th International Conference on Computational Intelligence and Security (CIS 2017), HongKong, China.","DOI":"10.1109\/CIS.2017.00075"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20632","DOI":"10.1109\/ACCESS.2018.2809426","article-title":"An ID-based Linearly Homomorphic Signature Scheme and Its Application in Blockchain","volume":"6","author":"Lin","year":"2018","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"27205","DOI":"10.1109\/ACCESS.2018.2827203","article-title":"A Secure Cryptocurrency Scheme Based on Post-quantum Blockchain","volume":"6","author":"Gao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_22","unstructured":"Shamir, A. (1984, January 9\u201311). Identity-based Cryptosystems and Signature Schemes. Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques, Paris, France."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kumar, P., Sharma, V., and Sharma, G. (2016, January 29\u201330). Certificateless Aggregate Signature Schemes: A Review. Proceedings of the 2016 International Conference on Computing, Communication and Automation (ICCCA), Greater Noida, India.","DOI":"10.1109\/CCAA.2016.7813777"},{"key":"ref_24","unstructured":"Al-Riyami, S.S., and Paterson, K.G. (December, January 30). Certificateless Public Key Cryptography. Proceedings of the Advances in Cryptology\u2014ASIACRYPT 2003, 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, Z.F., Wong, D.S., Xu, J., and Feng, D. (2006, January 6\u20139). Certificateless Public-key Signature: Security Model and Efficient Construction. Proceedings of the International Conference on Applied Cryptography and Network Security, Singapore.","DOI":"10.1007\/11767480_20"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Boneh, D., Gentry, C., Lynn, B., and Shacham, H. (2003, January 4\u20138). Aggregate and Verifiably Encrypted Signatures from Bilinear Maps. Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2003), Warsaw, Poland.","DOI":"10.1007\/3-540-39200-9_26"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1016\/j.ins.2013.09.032","article-title":"Insecurity of an Efficient Certificateless Aggregate Signature with Constant Pairing Computations","volume":"268","author":"He","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_28","first-page":"3204","article-title":"Efficient and Provide Security Certificateless Aggregate Signature Scheme","volume":"26","author":"Zhou","year":"2015","journal-title":"J. Softw."},{"key":"ref_29","first-page":"1","article-title":"An Efficient Certificateless Aggregate Signature without Pairings for Vehicular Ad Hoc Networks","volume":"451","author":"Cui","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_30","first-page":"2185","article-title":"Fully Anonymous Blockchain based on Aggregate Signature and Confidential Transaction","volume":"55","author":"Wang","year":"2018","journal-title":"J. Comput. Res. Dev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TIFS.2012.2232653","article-title":"Online\/offline Signatures for Low-power Devices","volume":"8","author":"Yao","year":"2012","journal-title":"IEEE Trans. Inf. Forensic Secur."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Danzi, P., Kal\u00f8r, A.E., Stefanovi\u0107, \u010c., and Popovski, P. (2019). Repeat-Authenticate Scheme for Multicasting of Blockchain Information in IoT Systems. arXiv.","DOI":"10.1109\/GCWkshps45667.2019.9024468"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kaga, Y., Fujio, M., Naganuma, K., Takahashi, K., Murakami, T., Ohki, T., and Nishigaki, M. (2017, January 13\u201315). A Secure and Practical Signature Scheme for Blockchain Based on Biometrics. Proceedings of the Information Security Practice and Experience (ISPEC 2017), Melbourne, VIC, Australia.","DOI":"10.1007\/978-3-319-72359-4_55"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s102070100002","article-title":"The Elliptic Curve Digital Signature Algorithm (ECDSA)","volume":"1","author":"Johnson","year":"2001","journal-title":"Int. J. Inf. Secur."},{"key":"ref_35","unstructured":"Krawczyk, H.M., and Rabin, T.D. (2000, January 2\u20134). Chameleon Signatures. Proceedings of the Network and Distributed System Security Symposium (NDSS 2000), San Diego, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Shamir, A., and Tauman, Y. (2001, January 19\u201323). Improved Online\/Offline Signature Schemes. Proceedings of the 21th Annual International Cryptology Conference (CRYPTO 2001), Santa Barbara, CA, USA.","DOI":"10.1007\/3-540-44647-8_21"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Shu, H., Chen, F.L., Xie, D., Sun, L.P., Qi, P., and Huang, Y.Q. (2019). An Aggregate Signature Scheme Based on a Trapdoor Hash Function for the Internet of Things. Sensors, 19.","DOI":"10.3390\/s19194239"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chandrasekhar, S., and Singhal, M. (2015, January 28\u201330). Efficient and Scalable Aggregate Signcryption Scheme based on Multi-trapdoor Hash Functions. Proceedings of the 1st Workshop on Security and Privacy in the Cloud, Florence, Italy.","DOI":"10.1109\/CNS.2015.7346875"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.cose.2017.02.008","article-title":"A Novel Access Control Protocol Using Proxy Signatures for Cloud-based Health Information Exchange","volume":"67","author":"Chandrasekhar","year":"2017","journal-title":"Comput. Secur."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.ins.2014.09.065","article-title":"Cryptanalysis and Improvement of a Certificateless Aggregate Signature Scheme","volume":"295","author":"Cheng","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_41","unstructured":"Maji, H.K., Prabhakaran, M., and Rosulek, M. (2011, January 14\u201318). Attribute-based Signatures. Proceedings of Cryptographers\u2019 Track at the RSA conference, San Francisco, CA, USA."},{"key":"ref_42","unstructured":"(2020, January 07). Health informatics-Pseudonymization, ISO 25237. Available online: https:\/\/www.iso.org\/standard\/63553.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/5\/1521\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:05:43Z","timestamp":1760173543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/5\/1521"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,10]]},"references-count":42,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["s20051521"],"URL":"https:\/\/doi.org\/10.3390\/s20051521","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,10]]}}}