{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T07:34:41Z","timestamp":1778916881558,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Research Fund of Key Laboratory of Cryptography of Zhejiang Province","award":["ZCL21007"],"award-info":[{"award-number":["ZCL21007"]}]},{"name":"Open Research Fund of Key Laboratory of Cryptography of Zhejiang Province","award":["CCF-HuaweiBC2021009"],"award-info":[{"award-number":["CCF-HuaweiBC2021009"]}]},{"name":"Open Research Fund of Key Laboratory of Cryptography of Zhejiang Province","award":["JL71-20-017"],"award-info":[{"award-number":["JL71-20-017"]}]},{"name":"Populus Euphratica Found","award":["ZCL21007"],"award-info":[{"award-number":["ZCL21007"]}]},{"name":"Populus Euphratica Found","award":["CCF-HuaweiBC2021009"],"award-info":[{"award-number":["CCF-HuaweiBC2021009"]}]},{"name":"Populus Euphratica Found","award":["JL71-20-017"],"award-info":[{"award-number":["JL71-20-017"]}]},{"name":"2020 Industrial Internet Innovation and Development Project\u2014For the Power Industry Industrial Internet Network Trust Support Platform Project","award":["ZCL21007"],"award-info":[{"award-number":["ZCL21007"]}]},{"name":"2020 Industrial Internet Innovation and Development Project\u2014For the Power Industry Industrial Internet Network Trust Support Platform Project","award":["CCF-HuaweiBC2021009"],"award-info":[{"award-number":["CCF-HuaweiBC2021009"]}]},{"name":"2020 Industrial Internet Innovation and Development Project\u2014For the Power Industry Industrial Internet Network Trust Support Platform Project","award":["JL71-20-017"],"award-info":[{"award-number":["JL71-20-017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Consumers in electricity markets are becoming more proactive because of the rapid development of demand\u2013response management and distributed energy resources, which boost the transformation of peer-to-peer (P2P) energy-trading mechanisms. However, in the P2P negotiation process, it is a challenging task to prevent private information from being attacked by malicious agents. In this paper, we propose a privacy-preserving, two-party, secure computation mechanism for consensus-based P2P energy trading. First, a novel P2P negotiation mechanism for energy trading is proposed based on the consensus + innovation (C + I) method and the power transfer distribution factor (PTDF), and this mechanism can simultaneously maximize social welfare and maintain physical network constraints. In addition, the C + I method only requires a minimum set of information to be exchanged. Then, we analyze the strategy of malicious neighboring agents colluding to attack in order to steal private information. To defend against this attack, we propose a two-party, secure computation mechanism in order to realize safe negotiation between each pair of prosumers based on Paillier homomorphic encryption (HE), a smart contract (SC), and zero-knowledge proof (ZKP). The energy price is updated in a safe way without leaking any private information. Finally, we simulate the functionality of the privacy-preserving mechanism in terms of convergence performance, computational efficiency, scalability, and SC operations.<\/jats:p>","DOI":"10.3390\/s22229020","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T05:18:57Z","timestamp":1669094337000},"page":"9020","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Privacy-Preserving, Two-Party, Secure Computation Mechanism for Consensus-Based Peer-to-Peer Energy Trading in the Smart Grid"],"prefix":"10.3390","volume":"22","author":[{"given":"Zhihu","family":"Li","sequence":"first","affiliation":[{"name":"China Electric Power Research Institute, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiqing","family":"Xu","sequence":"additional","affiliation":[{"name":"State Grid Corporation of China, Beijing 100031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Zhai","sequence":"additional","affiliation":[{"name":"China Electric Power Research Institute, Beijing 100081, China"},{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Zhao","sequence":"additional","affiliation":[{"name":"China Electric Power Research Institute, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng","family":"Xu","sequence":"additional","affiliation":[{"name":"China Electric Power Research Institute, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5773-1491","authenticated-orcid":false,"given":"Zhenwei","family":"Guo","sequence":"additional","affiliation":[{"name":"Hangzhou Innovative Institute, Beihang University, Hangzhou 310051, China"},{"name":"Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hussain, S., and Kim, Y.C. (February, January 31). Fault resilient communication network architecture for monitoring and control of wind power farms. Proceedings of the 2016 18th International Conference on Advanced Communication Technology (ICACT), PyeongChang, Republic of Korea.","DOI":"10.1109\/ICACT.2016.7423598"},{"key":"ref_2","first-page":"7391","article-title":"A two-layer decentralized charging approach for residential electric vehicles based on fuzzy data fusion","volume":"34","author":"Hussain","year":"2022","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"ref_3","unstructured":"Hussain, S., Mohammad, F., and Kim, Y.C. (2017, January 18\u201320). Communication network architecture based on logical nodes for electric vehicles. Proceedings of the 2017 International Symposium on Information Technology Convergence, Shijiazhuang, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"15396","DOI":"10.1109\/TITS.2022.3140461","article-title":"Optimization of waiting time for electric vehicles using a fuzzy inference system","volume":"23","author":"Hussain","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3410","DOI":"10.1109\/JSYST.2018.2851140","article-title":"A decentralized deadline-driven electric vehicle charging recommendation","volume":"13","author":"Cao","year":"2018","journal-title":"IEEE Syst. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2763","DOI":"10.1007\/s11276-017-1502-5","article-title":"Multi-metric geographic routing for vehicular ad hoc networks","volume":"24","author":"Hassan","year":"2018","journal-title":"Wirel. Netw."},{"key":"ref_7","unstructured":"Schollmeier, R. (2001, January 27\u201329). A definition of peer-to-peer networking for the classification of peer-to-peer architectures and applications. Proceedings of the First International Conference on Peer-to-Peer Computing, Linkoping, Sweden."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.apenergy.2019.03.111","article-title":"A motivational game-theoretic approach for peer-to-peer energy trading in the smart grid","volume":"243","author":"Tushar","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1109\/TIE.2014.2341556","article-title":"Three-party energy management with distributed energy resources in smart grid","volume":"62","author":"Tushar","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kursawe, K., Danezis, G., and Kohlweiss, M. (2011). Privacy-friendly aggregation for the smart-grid. International Symposium on Privacy Enhancing Technologies Symposium, Springer.","DOI":"10.1007\/978-3-642-22263-4_10"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"\u00c1cs, G., and Castelluccia, C. (2011). I have a dream! (differentially private smart metering). International Workshop on Information Hiding, Springer.","DOI":"10.1007\/978-3-642-24178-9_9"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2227","DOI":"10.1109\/TIFS.2017.2704904","article-title":"Privacy preserving smart meter streaming against information leakage of appliance status","volume":"12","author":"Hong","year":"2017","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Shukla, S., Thakur, S., Hussain, S., and Breslin, J.G. (2021). A Blockchain-Enabled Fog Computing Model for Peer-To-Peer Energy Trading in Smart Grid. International Congress on Blockchain and Applications, Springer.","DOI":"10.1007\/978-3-030-86162-9_2"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6426","DOI":"10.1109\/TSG.2019.2904629","article-title":"Demand side load management for big industrial energy users under blockchain-based peer-to-peer electricity market","volume":"10","author":"Dang","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4097","DOI":"10.1109\/TPWRS.2018.2876612","article-title":"A distributed electricity trading system in active distribution networks based on multi-agent coalition and blockchain","volume":"34","author":"Luo","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3154","DOI":"10.1109\/TII.2017.2709784","article-title":"Enabling localized peer-to-peer electricity trading among plug-in hybrid electric vehicles using consortium blockchains","volume":"13","author":"Kang","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/TSMC.2019.2903485","article-title":"Automated demand response framework in ELNs: Decentralized scheduling and smart contract","volume":"50","author":"Yang","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1612","DOI":"10.1109\/TSMC.2019.2916565","article-title":"Energy crowdsourcing and peer-to-peer energy trading in blockchain-enabled smart grids","volume":"49","author":"Wang","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117417","DOI":"10.1016\/j.energy.2020.117417","article-title":"Smart contract architecture for decentralized energy trading and management based on blockchains","volume":"199","author":"Han","year":"2020","journal-title":"Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/TII.2021.3077008","article-title":"Blockchain-based fully peer-to-peer energy trading strategies for residential energy systems","volume":"18","author":"AlSkaif","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/TSMC.2021.3111135","article-title":"Demand\u2013Response Games for Peer-to-Peer Energy Trading With the Hyperledger Blockchain","volume":"52","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1109\/TSG.2020.3022601","article-title":"A blockchain-enabled multi-settlement quasi-ideal peer-to-peer trading framework","volume":"12","author":"AlAshery","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.apenergy.2019.04.132","article-title":"Design and management of a distributed hybrid energy system through smart contract and blockchain","volume":"248","author":"Li","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3214303","article-title":"A survey on homomorphic encryption schemes: Theory and implementation","volume":"51","author":"Acar","year":"2018","journal-title":"ACM Comput. Surv. (CSUR)"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5233","DOI":"10.1109\/TSG.2021.3091624","article-title":"A homomorphic encryption-based private collaborative distributed energy management system","volume":"12","author":"Cheng","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100891","DOI":"10.1016\/j.swevo.2021.100891","article-title":"Energy trading IoT system based on blockchain","volume":"64","author":"Yi","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Liu, N., Wang, C., Cheng, M., and Wang, J. (2016). A privacy-preserving distributed optimal scheduling for interconnected microgrids. Energies, 9.","DOI":"10.3390\/en9121031"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.automatica.2018.07.005","article-title":"Privacy preserving distributed optimization using homomorphic encryption","volume":"96","author":"Lu","year":"2018","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lu, Y., Lian, J., and Zhu, M. (2020, January 1\u20133). Privacy-preserving transactive energy system. Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA.","DOI":"10.23919\/ACC45564.2020.9147486"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF00139569","article-title":"Rational choice and economic behavior","volume":"1","author":"Day","year":"1971","journal-title":"Theory Decis."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1109\/TSG.2020.3019603","article-title":"Chance-constrained peer-to-peer joint energy and reserve market considering renewable generation uncertainty","volume":"12","author":"Guo","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4151","DOI":"10.1109\/TSG.2021.3075707","article-title":"Online optimization for real-time peer-to-peer electricity market mechanisms","volume":"12","author":"Guo","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4646","DOI":"10.1109\/TIE.2019.2931229","article-title":"A decentralized bilateral energy trading system for peer-to-peer electricity markets","volume":"67","author":"Khorasany","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TPWRS.2004.826708","article-title":"Role of distribution factors in congestion revenue rights applications","volume":"19","author":"Liu","year":"2004","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1109\/TPWRS.2018.2872880","article-title":"Consensus-based approach to peer-to-peer electricity markets with product differentiation","volume":"34","author":"Sorin","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2553","DOI":"10.1109\/TPWRS.2019.2896654","article-title":"Exogenous cost allocation in peer-to-peer electricity markets","volume":"34","author":"Baroche","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3994","DOI":"10.1109\/TPWRS.2018.2808961","article-title":"Energy collectives: A community and fairness based approach to future electricity markets","volume":"34","author":"Moret","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_38","unstructured":"Paillier, P. (1999, January 2\u20136). Public-key cryptosystems based on composite degree residuosity classes. Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques, Prague, Czech Republic."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1109\/TSG.2021.3139618","article-title":"A Multi-Stage Information Protection Scheme for CDA-Based Energy Trading Market in Smart Grids","volume":"13","author":"Ma","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s10207-010-0119-9","article-title":"A generalization of Paillier\u2019s public-key system with applications to electronic voting","volume":"9","author":"Jurik","year":"2010","journal-title":"Int. J. Inf. Secur."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/9020\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:23:00Z","timestamp":1760145780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/9020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,21]]},"references-count":40,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22229020"],"URL":"https:\/\/doi.org\/10.3390\/s22229020","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,21]]}}}