{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T01:51:29Z","timestamp":1781747489996,"version":"3.54.5"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T00:00:00Z","timestamp":1781740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T00:00:00Z","timestamp":1781740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Supported by Hebei Natural Science Foundation","award":["F2025201052"],"award-info":[{"award-number":["F2025201052"]}]},{"name":"Funded by Science Research project of Hebei Education Department","award":["QN2025014"],"award-info":[{"award-number":["QN2025014"]}]},{"name":"Foundation of President of Hebei University","award":["XZJJ202303"],"award-info":[{"award-number":["XZJJ202303"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Smart grid systems use communication infrastructure and embedded devices to achieve data communication between devices and control centers. Ensuring the secure transmission and privacy protection of user electricity consumption data is a core challenge facing smart grids. However, existing authentication schemes often suffer from centralized bottlenecks, limited scalability, and insufficient privacy protection. This paper proposes a Multi-Authority Privacy-Preserving Aggregate Signature scheme (MAPS-G) specifically for smart grid environments. A distributed multi-authorization architecture is used to eliminate single points of failure, and the identity of devices is protected by an anonymous mechanism. To further reduce communication and computational overheads, an aggregator is introduced to batch verify messages using the aggregate signature technique. At the same time, a pseudonym update strategy is designed to ensure the unlinkability between different sessions. Security analysis shows that the proposed scheme is robust in terms of privacy protection and resistance to common attacks. Performance analysis experiments show that the proposed scheme significantly outperforms existing models in terms of computation, communication, and energy efficiency, and is suitable for resource-constrained devices such as smart meters.<\/jats:p>","DOI":"10.1186\/s42400-025-00534-7","type":"journal-article","created":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T01:01:31Z","timestamp":1781744491000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A multi-authority aggregate signature scheme for privacy-preserving and efficient message authentication in the smart grid"],"prefix":"10.1186","volume":"9","author":[{"given":"Shuo","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7380-7993","authenticated-orcid":false,"given":"Yifan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenlei","family":"Chai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenpeng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,18]]},"reference":[{"key":"534_CR1","doi-asserted-by":"publisher","first-page":"9182","DOI":"10.1109\/ACCESS.2023.3237643","volume":"11","author":"M Akg\u00fcn","year":"2023","unstructured":"Akg\u00fcn M, Soykan EU, Soykan G (2023) A privacy-preserving scheme for smart grid using trusted execution environment. IEEE Access 11:9182\u20139196","journal-title":"IEEE Access"},{"key":"534_CR2","doi-asserted-by":"crossref","unstructured":"Boneh D, Gentry C, Lynn B, Shacham H (2003) \u201cAggregate and verifiably encrypted signatures from bilinear maps,\u201d in Proc. Int. Conf. Theory and Applications of Cryptographic Techniques (EUROCRYPT), Warsaw, Poland, 416\u2013432","DOI":"10.1007\/3-540-39200-9_26"},{"key":"534_CR3","unstructured":"Cygwin, \u201cCygwin: Linux environment emulator for Windows,\u201d (2022) [Online]. Available: http:\/\/www.cygwin.com\/"},{"key":"534_CR4","unstructured":"Cygwin, \u201cLinux environment emulator for Windows,\u201d (2022) [Online]. Available: http:\/\/www.cygwin.com\/"},{"issue":"1","key":"534_CR5","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1109\/JIOT.2022.3199480","volume":"10","author":"L Deng","year":"2022","unstructured":"Deng L et al (2022) Secure identity-based designated verifier anonymous aggregate signature scheme suitable for smart grids. IEEE Internet Things J 10(1):57\u201365","journal-title":"IEEE Internet Things J"},{"issue":"3","key":"534_CR6","doi-asserted-by":"publisher","first-page":"4242","DOI":"10.1109\/JSYST.2020.2970427","volume":"14","author":"L Deng","year":"2020","unstructured":"Deng L, Ning B, Jiang Y (2020) A lightweight certificateless aggregation signature scheme with provably security in the standard model. IEEE Syst J 14(3):4242\u20134251","journal-title":"IEEE Syst J"},{"key":"534_CR7","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1109\/TIFS.2024.3515812","volume":"20","author":"P Duan","year":"2025","unstructured":"Duan P, Ma Z, Gao H, Tian T, Zhang Y (2025) Multi-authority attribute-based encryption scheme with access delegation for cross blockchain data sharing. IEEE Trans Inf Forensics Security 20:323\u2013337","journal-title":"IEEE Trans Inf Forensics Security"},{"issue":"1","key":"534_CR8","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1109\/TII.2021.3074915","volume":"18","author":"MB Gough","year":"2022","unstructured":"Gough MB, Santos SF, AlSkaif T, Javadi MS, Castro R, Catal\u00e3o JPS (2022) Preserving privacy of smart meter data in a smart grid environment. IEEE Trans Ind Informat 18(1):707\u2013718","journal-title":"IEEE Trans Ind Informat"},{"key":"534_CR9","doi-asserted-by":"publisher","first-page":"114025","DOI":"10.1016\/j.enbuild.2024.114025","volume":"308","author":"J Gumz","year":"2024","unstructured":"Gumz J, Fettermann DC (2024) User\u2019s perspective in smart meter research: State-of-the-art and future trends. Energy and Buildings 308:114025","journal-title":"Energy and Buildings"},{"issue":"11","key":"534_CR10","doi-asserted-by":"publisher","first-page":"8935","DOI":"10.1109\/JIOT.2021.3056477","volume":"8","author":"Y Hou","year":"2021","unstructured":"Hou Y et al (2021) Certificate-based parallel key-insulated aggregate signature against fully chosen key attacks for industrial Internet of Things. IEEE Internet Things J 8(11):8935\u20138948","journal-title":"IEEE Internet Things J"},{"issue":"12","key":"534_CR11","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1109\/MCOM.2016.1600321CM","volume":"54","author":"J Jiang","year":"2016","unstructured":"Jiang J, Qian Y (2016) Distributed communication architecture for smart grid applications. IEEE Commun Mag 54(12):60\u201367","journal-title":"IEEE Commun Mag"},{"issue":"3","key":"534_CR12","doi-asserted-by":"publisher","first-page":"3808","DOI":"10.1109\/JSYST.2020.3015424","volume":"15","author":"K Kar","year":"2020","unstructured":"Kar K, Jayaprakash J, Naik K, Abdelkader T (2020) A secure and lightweight protocol for message authentication in wireless sensor networks. IEEE Syst J 15(3):3808\u20133819","journal-title":"IEEE Syst J"},{"issue":"8","key":"534_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/dac.5467","volume":"36","author":"A Kavitha","year":"2023","unstructured":"Kavitha A, Guravaiah RK, Velusamy SL, Suseela S, Kumar D (2023) DR-NAP: Data reduction strategy using neural adaptation phenomenon in wireless sensor networks. Int J Commun Syst 36(8):e5467","journal-title":"Int J Commun Syst"},{"key":"534_CR14","doi-asserted-by":"publisher","first-page":"3076","DOI":"10.1007\/s11227-018-2312-y","volume":"75","author":"P Kumar","year":"2019","unstructured":"Kumar P et al (2019) Secure CLS and CL-AS schemes designed for VANETs. J Supercomput 75:3076\u20133098","journal-title":"J Supercomput"},{"issue":"1","key":"534_CR15","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1109\/JSYST.2022.3180221","volume":"17","author":"Y Liang","year":"2023","unstructured":"Liang Y, Liu Y (2023) Analysis and improvement of an efficient certificateless aggregate signature with conditional privacy preservation in VANETs. IEEE Syst J 17(1):664\u2013672","journal-title":"IEEE Syst J"},{"issue":"4","key":"534_CR16","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1109\/TCSS.2022.3232173","volume":"10","author":"H Liu","year":"2023","unstructured":"Liu H, Han D, Cui M, Li K-C, Souri A, Shojafar M (2023) IdenMultiSig: Identity-based decentralized multi-signature in Internet of Things. IEEE Trans Comput Social Syst 10(4):1711\u20131721","journal-title":"IEEE Trans Comput Social Syst"},{"key":"534_CR17","doi-asserted-by":"crossref","unstructured":"Liu K, Wang C, Zhou X (2023) \u201cDecentralizing access control system for data sharing in smart grid,\u201d High-Confidence Computing, 100113","DOI":"10.1016\/j.hcc.2023.100113"},{"key":"534_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.seta.2023.103414","volume":"60","author":"A Mahmood","year":"2023","unstructured":"Mahmood A, Khan A, Anjum A, Maple C, Jeon G (2023) An efficient and privacy-preserving blockchain-based secure data aggregation in smart grids. Sustainable Energy Technologies and Assessments 60:103414","journal-title":"Sustainable Energy Technologies and Assessments"},{"issue":"1","key":"534_CR19","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1109\/JSYST.2020.2966526","volume":"15","author":"Q Mei","year":"2020","unstructured":"Mei Q et al (2020) Efficient certificateless aggregate signature with conditional privacy preservation in IoV. IEEE Syst J 15(1):245\u2013256","journal-title":"IEEE Syst J"},{"issue":"3","key":"534_CR20","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s001450010003","volume":"13","author":"D Pointcheval","year":"2000","unstructured":"Pointcheval D, Stern J (2000) Security arguments for digital signatures and blind signatures. J Cryptol 13(3):361\u2013396","journal-title":"J Cryptol"},{"issue":"9","key":"534_CR21","doi-asserted-by":"publisher","first-page":"12370","DOI":"10.1109\/TVT.2024.3383967","volume":"73","author":"S Prajapat","year":"2024","unstructured":"Prajapat S et al (2024) Secure lattice-based aggregate signature scheme for vehicular ad hoc networks. IEEE Trans Veh Technol 73(9):12370\u201312384","journal-title":"IEEE Trans Veh Technol"},{"issue":"1","key":"534_CR22","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1109\/JSYST.2022.3188012","volume":"17","author":"Z Qiao","year":"2023","unstructured":"Qiao Z et al (2023) An efficient certificate-based aggregate signature scheme with provable security for Industrial Internet of Things. IEEE Syst J 17(1):72\u201382","journal-title":"IEEE Syst J"},{"issue":"5","key":"534_CR23","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1109\/MCOM.001.2000679","volume":"59","author":"Z Rahman","year":"2021","unstructured":"Rahman Z, Khalil I, Yi X, Atiquzzaman M (2021) Blockchain-based security framework for a critical industry 4.0 cyber-physical system. IEEE Commun Mag 59(5):128\u2013134","journal-title":"IEEE Commun Mag"},{"key":"534_CR24","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1007\/s42979-023-01955-2","volume":"4","author":"P Rani","year":"2023","unstructured":"Rani P, Singh AK (2023) An efficient and privacy-preserving data aggregation scheme for smart grids in cloud environment. SN Computer Science 4:540","journal-title":"SN Computer Science"},{"key":"534_CR25","doi-asserted-by":"publisher","DOI":"10.1002\/2050-7038.12411","volume":"30","author":"BK Sethi","year":"2020","unstructured":"Sethi BK, Mukherjee D, Singh D, Misra RK, Mohanty SR (2020) Smart home energy management system under false data injection attack. Int. Trans. Electr. Energy Syst. 30:e12411","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"534_CR26","first-page":"47","volume":"196","author":"A Shamir","year":"1984","unstructured":"Shamir A (1984) Identity-based cryptosystem and signature scheme. Proc Adv Cryptol Crypto 196:47\u201353","journal-title":"Proc Adv Cryptol Crypto"},{"key":"534_CR27","doi-asserted-by":"crossref","unstructured":"Sikeridis D, Bidram A, Devetsikiotis M, Reno MJ (2020) \u201cA blockchain-based mechanism for secure data exchange in smart grid protection systems,\u201d in Proc. IEEE 17th Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA, 1\u20136","DOI":"10.1109\/CCNC46108.2020.9045368"},{"key":"534_CR28","doi-asserted-by":"crossref","unstructured":"Su Y, Zhang X, Qin J, Ma J (2023) \u201cEfficient and flexible multiauthority attribute-based authentication for IoT devices,\u201d IEEE Internet Things J., 10, 15, 13945\u201313958, Aug. 1,","DOI":"10.1109\/JIOT.2023.3263497"},{"key":"534_CR29","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10586-021-03420-2","volume":"25","author":"A Tomar","year":"2022","unstructured":"Tomar A, Tripathi S (2022) Blockchain-assisted authentication and key agreement scheme for fog-based smart grid. Clust Comput 25:451\u2013468","journal-title":"Clust Comput"},{"key":"534_CR30","doi-asserted-by":"crossref","unstructured":"Verma GK, Gope P, Saxena N, Kumar N (2022) \u201cCB-DA: Lightweight and escrow-free certificate-based data aggregation for smart grid,\u201d IEEE Transactions on Dependable and Secure Computing, vol. 20, no. 3, pp. 2011\u20132024, May\u2013Jun. 2023","DOI":"10.1109\/TDSC.2022.3169952"},{"issue":"7","key":"534_CR31","doi-asserted-by":"publisher","first-page":"5254","DOI":"10.1109\/JIOT.2021.3109153","volume":"9","author":"L Wu","year":"2022","unstructured":"Wu L, Xu M, Fu S, Luo Y, Wei Y (2022) FPDA: Fault-tolerant and privacy-enhanced data aggregation scheme in fog-assisted smart grid. IEEE Internet Things J 9(7):5254\u20135265","journal-title":"IEEE Internet Things J"},{"issue":"1","key":"534_CR32","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1109\/TDSC.2023.3252593","volume":"21","author":"L Wu","year":"2024","unstructured":"Wu L, Fu S, Luo Y, Yan H, Shi H, Xu M (2024) A robust and lightweight privacy-preserving data aggregation scheme for smart grid. IEEE Transactions on Dependable and Secure Computing 21(1):270\u2013283","journal-title":"IEEE Transactions on Dependable and Secure Computing"},{"key":"534_CR33","doi-asserted-by":"publisher","first-page":"5276813","DOI":"10.1155\/2020\/5276813","volume":"2020","author":"Z Xu","year":"2020","unstructured":"Xu Z, He D, Kumar N, Choo K-KR (2020) Efficient certificateless aggregate signature scheme for performing secure routing in VANETs. Secur. Commun. Netw. 2020:5276813","journal-title":"Secur. Commun. Netw."},{"key":"534_CR34","doi-asserted-by":"publisher","first-page":"102698","DOI":"10.1016\/j.sysarc.2022.102698","volume":"131","author":"S Yu","year":"2022","unstructured":"Yu S, Park K (2022) ISG-SLAS: Secure and lightweight authentication and key agreement scheme for industrial smart grid using fuzzy extractor. Journal of Systems Architecture 131:102698","journal-title":"Journal of Systems Architecture"},{"issue":"12","key":"534_CR35","doi-asserted-by":"publisher","first-page":"3430","DOI":"10.1109\/TPDS.2022.3153930","volume":"33","author":"Y Zhan","year":"2022","unstructured":"Zhan Y, Zhou L, Wang B et al (2022) Efficient function queryable and privacy-preserving data aggregation scheme in smart grid. IEEE Trans Parallel Distrib Syst 33(12):3430\u20133441","journal-title":"IEEE Trans Parallel Distrib Syst"},{"key":"534_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.csi.2024.103894","volume":"92","author":"Q Zhang","year":"2025","unstructured":"Zhang Q et al (2025) Revocable identity-based designated verifier proxy re-signature with signature evolution. Comput. Stand. Interfaces 92:103894","journal-title":"Comput. Stand. Interfaces"},{"issue":"3","key":"534_CR37","doi-asserted-by":"publisher","first-page":"1242","DOI":"10.1109\/TDSC.2023.3275972","volume":"21","author":"J Zhang","year":"2024","unstructured":"Zhang J, Dong C (2024) On the security of lightweight and escrow-free certificate-based data aggregation for smart grid. IEEE Transactions on Dependable and Secure Computing 21(3):1242\u20131243","journal-title":"IEEE Transactions on Dependable and Secure Computing"},{"issue":"6","key":"534_CR38","doi-asserted-by":"publisher","first-page":"4225","DOI":"10.1109\/TDSC.2021.3124546","volume":"19","author":"X Zhang","year":"2022","unstructured":"Zhang X, Huang C, Zhang Y, Cao S (2022) Enabling verifiable privacy-preserving multi-type data aggregation in smart grids. IEEE Trans Dependable Secure Comput 19(6):4225\u20134239","journal-title":"IEEE Trans Dependable Secure Comput"},{"key":"534_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jisa.2022.103118","volume":"66","author":"W Zhang","year":"2022","unstructured":"Zhang W, Liu S, Xia Z (2022) A distributed privacy-preserving data aggregation scheme for smart grid with fine-grained access control. Journal of Information Security and Applications 66:103118","journal-title":"Journal of Information Security and Applications"},{"key":"534_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.csi.2023.103741","volume":"86","author":"Z Zhao","year":"2023","unstructured":"Zhao Z et al (2023) Full black-box retrievable and accountable identity-based encryption. Computer Standards & Interfaces 86:103741","journal-title":"Computer Standards & Interfaces"},{"issue":"9","key":"534_CR41","doi-asserted-by":"publisher","first-page":"11664","DOI":"10.1109\/JIOT.2024.3521370","volume":"12","author":"C Zhao","year":"2025","unstructured":"Zhao C et al (2025) BPRM: Blockchain-based privacy preserving and robust data aggregation supporting multifunctionality for fog-assisted smart grid. IEEE Internet Things J 12(9):11664\u201311675","journal-title":"IEEE Internet Things J"}],"container-title":["Cybersecurity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-025-00534-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s42400-025-00534-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-025-00534-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T01:01:36Z","timestamp":1781744496000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s42400-025-00534-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,18]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["534"],"URL":"https:\/\/doi.org\/10.1186\/s42400-025-00534-7","relation":{},"ISSN":["2523-3246"],"issn-type":[{"value":"2523-3246","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,18]]},"assertion":[{"value":"17 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors approval and consent to participate.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Consent.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interest"}}],"article-number":"90"}}