{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T08:19:09Z","timestamp":1772612349512,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T00:00:00Z","timestamp":1772064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U22B2026, 62572121"],"award-info":[{"award-number":["U22B2026, 62572121"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Xizang","award":["XZ202501ZY0094"],"award-info":[{"award-number":["XZ202501ZY0094"]}]},{"name":"Frontier Technology R&amp;D Program of Jiangsu","award":["BF2025067"],"award-info":[{"award-number":["BF2025067"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Aiming at the challenge that traditional signature schemes struggle to simultaneously achieve efficiency, resistance to quantum attacks, and privacy protection, this paper proposes a lattice-based conditional privacy-preserving certificateless aggregate signature method (LCP-CAS). The scheme adopts an unordered aggregation algorithm to compress multiple signatures, in arbitrary order, into a single fixed-length aggregate signature, thereby achieving linear scalability in verification complexity. Its security is based on the hardness of the Ring Short Integer Solution (RSIS) problem, ensuring post-quantum resistance. By incorporating a conditional privacy-preserving mechanism, the scheme realizes device anonymity while supporting identity traceability, thus balancing privacy protection with regulatory requirements. Security analysis shows that the scheme meets the security requirements, including integrity, non-repudiation, conditional privacy preservation, and resistance to collusion attacks. Compared with existing related schemes, LCP-CAS achieves reduces aggregation and verification overhead while maintaining practicality in large-scale settings such as industrial IoT and device monitoring.<\/jats:p>","DOI":"10.3390\/e28030258","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T13:58:03Z","timestamp":1772114283000},"page":"258","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["LCP-CAS: Lattice-Based Conditional Privacy-Preserving Certificateless Aggregation Signature Scheme for Industrial IoT"],"prefix":"10.3390","volume":"28","author":[{"given":"Lin","family":"Shi","sequence":"first","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziyi","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziyan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7202-4939","authenticated-orcid":false,"given":"Liquan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ushkov, A.N., Strelkov, N.O., Krutskikh, V.V., and Chernikov, A.I. (2023, January 27\u201331). Industrial Internet of Things Platform for Water Resource Monitoring. Proceedings of the 2023 International Russian Smart Industry Conference (SmartIndustryCon), Sochi, Russia.","DOI":"10.1109\/SmartIndustryCon57312.2023.10110776"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1007\/978-3-031-62273-1_25","article-title":"An Anomaly Detection Framework for IIoT-Based Smart Farming Systems","volume":"Volume 1019","author":"Arai","year":"2024","journal-title":"Intelligent Computing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"25568","DOI":"10.1109\/JIOT.2024.3361801","article-title":"TrustNextGen: Security aspects of trustworthy next generation industrial Internet of Things (IIoT)","volume":"11","author":"Rathee","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.comcom.2021.10.010","article-title":"Certificateless signature schemes in industrial Internet of Things: A comparative survey","volume":"181","author":"Hussain","year":"2022","journal-title":"Comput. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7059","DOI":"10.1109\/TII.2021.3084753","article-title":"Blockchain-based reliable and efficient certificateless signature for IIoT devices","volume":"18","author":"Wang","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.future.2024.04.042","article-title":"CABC: A cross-domain authentication method combining blockchain with certificateless signature for IIoT","volume":"158","author":"Feng","year":"2024","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1884","DOI":"10.1109\/TII.2023.3282317","article-title":"Cryptanalysis and improvement of a blockchain-based certificateless signature for IIoT devices","volume":"20","author":"Yang","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/3-540-39200-9_26","article-title":"Aggregate and Verifiably Encrypted Signatures from Bilinear Maps","volume":"Volume 2656","author":"Biham","year":"2003","journal-title":"Advances in Cryptology\u2014EUROCRYPT 2003"},{"key":"ref_9","unstructured":"Shor, P.W. (1994, January 20\u201322). Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS), Santa Fe, NM, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1103\/PhysRevLett.79.325","article-title":"Quantum Mechanics Helps in Searching for a Needle in a Haystack","volume":"79","author":"Grover","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"132472","DOI":"10.1109\/ACCESS.2022.3227394","article-title":"Improving Bitcoin\u2019s post-quantum transaction efficiency with a novel lattice-based aggregate signature scheme based on CRYSTALS-Dilithium and a STARK protocol","volume":"10","author":"Quan","year":"2022","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kniep, Q., and Wattenhofer, R. (2024, January 1\u20135). Byzantine fault-tolerant aggregate signatures. Proceedings of the 19th ACM Asia Conference on Computer and Communications Security (AsiaCCS 2024), Singapore.","DOI":"10.1145\/3634737.3657020"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"33986","DOI":"10.1109\/ACCESS.2018.2847411","article-title":"A lattice-based unordered aggregate signature scheme based on the intersection method","volume":"6","author":"Lu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_14","unstructured":"Boneh, D., and Kim, S. (2026, January 05). One-Time and Interactive Aggregate Signatures from Lattices. Preprint, 2020. Available online: https:\/\/crypto.stanford.edu\/~skim13\/agg_ots.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wu, W., and Ye, F. (IEEE Internet Things J., 2025). A secure and efficient certificateless aggregate signature authentication scheme with pseudonyms for VANETs, IEEE Internet Things J., in press.","DOI":"10.1109\/JIOT.2024.3459033"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1007\/s11401-023-0053-6","article-title":"Lattice-based cryptography: A survey","volume":"44","author":"Wang","year":"2023","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s00145-023-09485-z","article-title":"Masking the GLP lattice-based signature scheme at any order","volume":"37","author":"Barthe","year":"2024","journal-title":"J. Cryptol."},{"key":"ref_18","first-page":"87","article-title":"A survey on discrete Gaussian samplers in lattice based cryptography","volume":"Volume 13964","author":"Zhou","year":"2023","journal-title":"Emerging Information Security and Applications"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1007\/978-3-642-29011-4_43","article-title":"Lattice signatures without trapdoors","volume":"Volume 7237","author":"Pointcheval","year":"2012","journal-title":"Advances in Cryptology\u2014EUROCRYPT 2012"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/978-3-642-40041-4_3","article-title":"Lattice signatures and bimodal Gaussians","volume":"Volume 8042","author":"Canetti","year":"2013","journal-title":"Advances in Cryptology\u2014CRYPTO 2013"},{"key":"ref_21","first-page":"1662","article-title":"Certificateless aggregate signatures: A comprehensive survey and comparative analysis","volume":"30","author":"Verma","year":"2024","journal-title":"J. Univ. Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1007\/978-3-540-40061-5_29","article-title":"Certificateless Public Key Cryptography","volume":"Volume 2894","author":"Laih","year":"2003","journal-title":"Advances in Cryptology\u2014ASIACRYPT 2003"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s001450010003","article-title":"Security Arguments for Digital Signatures and Blind Signatures","volume":"13","author":"Pointcheval","year":"2000","journal-title":"J. Cryptol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Debris-Alazard, T., Fallahpour, P., and Stehl\u00e9, D. (2024, January 24\u201328). Quantum oblivious LWE sampling and insecurity of standard model lattice-based SNARKs. Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC 2024), Vancouver, BC, Canada.","DOI":"10.1145\/3618260.3649766"},{"key":"ref_25","first-page":"100843","article-title":"LB-CLAS: Lattice-based conditional privacy-preserving certificateless aggregate signature scheme for VANET","volume":"50","author":"Xu","year":"2024","journal-title":"Veh. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10031","DOI":"10.1109\/JIOT.2023.3324744","article-title":"An NTRU-based certificateless aggregate signature scheme for underwater acoustic communication","volume":"11","author":"Xu","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"10393","DOI":"10.1109\/TVT.2023.3260579","article-title":"Public blockchain-envisioned security scheme using post quantum lattice-based aggregate signature for Internet of drones applications","volume":"72","author":"Bagchi","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1007\/s12083-023-01588-5","article-title":"A lattice-based unordered certificateless aggregate signature scheme for cloud medical health monitoring system","volume":"17","author":"Dong","year":"2024","journal-title":"Peer-to-Peer Netw. 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