{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:27:38Z","timestamp":1776990458093,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T00:00:00Z","timestamp":1731542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020","award":["101007820\u2014TRUST"],"award-info":[{"award-number":["101007820\u2014TRUST"]}]},{"name":"European Union\u2019s Horizon 2020","award":["ECS00000041-VITALITY-CUP D83C22000710005"],"award-info":[{"award-number":["ECS00000041-VITALITY-CUP D83C22000710005"]}]},{"name":"European Union\u2014NextGenerationEU under the Italian Ministry of University and Research (MIUR), National Innovation Ecosystem","award":["101007820\u2014TRUST"],"award-info":[{"award-number":["101007820\u2014TRUST"]}]},{"name":"European Union\u2014NextGenerationEU under the Italian Ministry of University and Research (MIUR), National Innovation Ecosystem","award":["ECS00000041-VITALITY-CUP D83C22000710005"],"award-info":[{"award-number":["ECS00000041-VITALITY-CUP D83C22000710005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JSAN"],"abstract":"<jats:p>Blockchain-based sensor networks offer promising solutions for secure and transparent data management in IoT ecosystems. However, efficient set membership proofs remain a critical challenge, particularly in resource-constrained environments. This paper introduces a novel OR-aggregation approach (where \u201cOR\u201d refers to proving that an element equals at least one member of a set without revealing which one) for zero-knowledge set membership proofs, tailored specifically for blockchain-based sensor networks. We provide a comprehensive theoretical foundation, detailed protocol specification, and rigorous security analysis. Our implementation incorporates optimization techniques for resource-constrained devices and strategies for integration with prominent blockchain platforms. Extensive experimental evaluation demonstrates the superiority of our approach over existing methods, particularly for large-scale deployments. Results show significant improvements in proof size, generation time, and verification efficiency. The proposed OR-aggregation technique offers a scalable and privacy-preserving solution for set membership verification in blockchain-based IoT applications, addressing key limitations of current approaches. Our work contributes to the advancement of efficient and secure data management in large-scale sensor networks, paving the way for wider adoption of blockchain technology in IoT ecosystems.<\/jats:p>","DOI":"10.3390\/jsan13060078","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T09:14:31Z","timestamp":1731575671000},"page":"78","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficient Zero-Knowledge Proofs for Set Membership in Blockchain-Based Sensor Networks: A Novel OR-Aggregation Approach"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2331-6326","authenticated-orcid":false,"given":"Oleksandr","family":"Kuznetsov","sequence":"first","affiliation":[{"name":"Department of Theoretical and Applied Sciences, eCampus University, Via Isimbardi 10, 22060 Novedrate, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8893-9244","authenticated-orcid":false,"given":"Emanuele","family":"Frontoni","sequence":"additional","affiliation":[{"name":"Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30\/32, 62100 Macerata, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1700-3075","authenticated-orcid":false,"given":"Marco","family":"Arnesano","sequence":"additional","affiliation":[{"name":"Department of Theoretical and Applied Sciences, eCampus University, Via Isimbardi 10, 22060 Novedrate, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kateryna","family":"Kuznetsova","sequence":"additional","affiliation":[{"name":"Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30\/32, 62100 Macerata, Italy"},{"name":"Vision, Robotics and Artificial Intelligence Lab (VRAI), Via Brecce Bianche 12, 60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120443","DOI":"10.1016\/j.apenergy.2022.120443","article-title":"Blockchain + IoT Sensor Network to Measure, Evaluate and Incentivize Personal Environmental Accounting and Efficient Energy Use in Indoor Spaces","volume":"332","author":"Ma","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.dcan.2022.04.007","article-title":"A Blockchain-Empowered Authentication Scheme for Worm Detection in Wireless Sensor Network","volume":"10","author":"Chen","year":"2024","journal-title":"Digit. Commun. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.comcom.2022.10.016","article-title":"Design of Secured Blockchain Based Decentralized Authentication Protocol for Sensor Networks with Auditing and Accountability","volume":"197","author":"Dwivedi","year":"2023","journal-title":"Comput. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.procs.2022.10.128","article-title":"Use of Blockchain in Health Sensor Networks to Secure Information Integrity and Accountability","volume":"210","author":"Godawatte","year":"2022","journal-title":"Procedia Comput. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100211","DOI":"10.1016\/j.bcra.2024.100211","article-title":"Energy-Aware Proof-of-Authority: Blockchain Consensus for Clustered Wireless Sensor Network","volume":"5","author":"Hanggoro","year":"2024","journal-title":"Blockchain Res. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101233","DOI":"10.1016\/j.measen.2024.101233","article-title":"Evaluating Simulation Tools for Securing Sensor Data with Blockchain: A Comprehensive Analysis","volume":"33","author":"Patel","year":"2024","journal-title":"Meas. Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"110212","DOI":"10.1016\/j.dib.2024.110212","article-title":"Cyberattack Patterns in Blockchain-Based Communication Networks for Distributed Renewable Energy Systems: A Study on Big Datasets","volume":"53","author":"Faheem","year":"2024","journal-title":"Data Brief"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102325","DOI":"10.1016\/j.jsc.2024.102325","article-title":"Short Proofs of Ideal Membership","volume":"125","author":"Hofstadler","year":"2024","journal-title":"J. Symb. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liu, H., Luo, X., Liu, H., and Xia, X. (2021, January 23\u201326). Merkle Tree: A Fundamental Component of Blockchains. Proceedings of the 2021 International Conference on Electronic Information Engineering and Computer Science (EIECS), Changchun, China.","DOI":"10.1109\/EIECS53707.2021.9588047"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/LCA.2023.3289515","article-title":"Hardware Accelerated Reusable Merkle Tree Generation for Bitcoin Blockchain Headers","volume":"22","author":"Jeon","year":"2023","journal-title":"IEEE Comput. Archit. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ozcelik, I., Medury, S., Broaddus, J., and Skjellum, A. (2021, January 11\u201313). An Overview of Cryptographic Accumulators. Proceedings of the 7th International Conference on Information Systems Security and Privacy ICISSP\u2014Volume 1, 2021, Virtual.","DOI":"10.5220\/0010337806610669"},{"key":"ref_12","unstructured":"ZK Whiteboard Sessions (2024, October 05). ZK Whiteboard Sessions. Available online: https:\/\/zkhack.dev\/whiteboard."},{"key":"ref_13","first-page":"102184","article-title":"A Sharding Blockchain Protocol for Enhanced Scalability and Performance Optimization through Account Transaction Reconfiguration","volume":"36","author":"Wu","year":"2024","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jung, S., Yoo, Y., Yang, G., and Yoo, C. (2024). Prediction of Permissioned Blockchain Performance for Resource Scaling Configurations. ICT Express, in press.","DOI":"10.1016\/j.icte.2024.09.003"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110544","DOI":"10.1016\/j.comnet.2024.110544","article-title":"Enhancing Privacy and Security in 5G Networks with an Anonymous Handover Protocol Based on Blockchain and Zero Knowledge Proof","volume":"250","author":"Haddad","year":"2024","journal-title":"Comput. Netw."},{"key":"ref_16","first-page":"103678","article-title":"Leveraging Zero Knowledge Proofs for Blockchain-Based Identity Sharing: A Survey of Advancements, Challenges and Opportunities","volume":"80","author":"Zhou","year":"2024","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103686","DOI":"10.1016\/j.jnca.2023.103686","article-title":"A Survey of State-of-the-Art Sharding Blockchains: Models, Components, and Attack Surfaces","volume":"217","author":"Li","year":"2023","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.future.2021.07.035","article-title":"Scalable Blockchains\u2014A Systematic Review","volume":"126","author":"Nasir","year":"2022","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_19","first-page":"61","article-title":"Distributed Computations for Large-Scale Networked Systems Using Belief Propagation","volume":"2","author":"Cai","year":"2023","journal-title":"J. Autom. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100820","DOI":"10.1016\/j.ejcon.2023.100820","article-title":"A Novel Distributed Algorithm for Estimation and Control of Large-Scale Systems","volume":"72","author":"Farina","year":"2023","journal-title":"Eur. J. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e00325","DOI":"10.1016\/j.jbvi.2022.e00325","article-title":"Scaling, Blockchain Technology, and Entrepreneurial Opportunities in Developing Countries","volume":"18","author":"Rawhouser","year":"2022","journal-title":"J. Bus. Ventur. Insights"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"110336","DOI":"10.1016\/j.comnet.2024.110336","article-title":"Blockchain Solutions for Trustworthy Decentralization in Social Networks","volume":"244","author":"Mlika","year":"2024","journal-title":"Comput. Netw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"103927","DOI":"10.1016\/j.agsy.2024.103927","article-title":"Supporting a Systems Approach to Scaling for All; Insights from Using the Scaling Scan Tool","volume":"217","author":"Woltering","year":"2024","journal-title":"Agric. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"104880","DOI":"10.1016\/j.jpdc.2024.104880","article-title":"Learning-Driven Hybrid Scaling for Multi-Type Services in Cloud","volume":"189","author":"Zhang","year":"2024","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.aej.2024.02.031","article-title":"Blockchain Technology Meets 6 G Wireless Networks: A Systematic Survey","volume":"92","author":"Sajid","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_26","first-page":"103898","article-title":"High-Speed Batch Verification for Discrete-Logarithm-Based Signatures via Multi-Scalar Multiplication Algorithm","volume":"87","author":"Li","year":"2024","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"114799","DOI":"10.1016\/j.tcs.2024.114799","article-title":"Towards Zero Knowledge Argument for Double Discrete Logarithm with Constant Cost","volume":"1018","author":"Krishnan","year":"2024","journal-title":"Theor. Comput. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"100530","DOI":"10.1016\/j.cosrev.2022.100530","article-title":"Elliptic Curve Cryptography; Applications, Challenges, Recent Advances, and Future Trends: A Comprehensive Survey","volume":"47","author":"Ullah","year":"2023","journal-title":"Comput. Sci. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"109330","DOI":"10.1016\/j.compeleceng.2024.109330","article-title":"A Systematic Review on Elliptic Curve Cryptography Algorithm for Internet of Things: Categorization, Application Areas, and Security","volume":"118","author":"Adeniyi","year":"2024","journal-title":"Comput. Electr. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/bs.adcom.2020.08.004","article-title":"Digital Signatures\u2606","volume":"Volume 121","author":"Aggarwal","year":"2021","journal-title":"Advances in Computers"},{"key":"ref_31","unstructured":"Pandey, R., Goundar, S., and Fatima, S. (2023). Chapter 14\u2014Cryptography in Blockchain. Distributed Computing to Blockchain, Academic Press."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bartoli, C., and Cascudo, I. (2023). On Sigma-Protocols and (Packed) Black-Box Secret Sharing Schemes. IACR International Conference on Public-Key Cryptography, Springer Nature.","DOI":"10.1007\/978-3-031-57722-2_14"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kushilevitz, E., and Malkin, T. (2016). Improved OR-Composition of Sigma-Protocols. Proceedings of the Theory of Cryptography, Springer.","DOI":"10.1007\/978-3-662-49099-0"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, M., Chen, Y., Yao, C., and Wang, Z. (2023). Sigma Protocols from Verifiable Secret Sharing and Their Applications. International Conference on the Theory and Application of Cryptology and Information Security, Springer Nature.","DOI":"10.1007\/978-981-99-8724-5_7"},{"key":"ref_35","unstructured":"Deng, S., and Du, B. (2024, October 05). zkTree: A Zero-Knowledge Recursion Tree with ZKP Membership Proofs. Cryptol. ePrint Arch., Available online: https:\/\/eprint.iacr.org\/2023\/208."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kuznetsov, O., Rusnak, A., Yezhov, A., Kanonik, D., Kuznetsova, K., and Domin, O. (2024). Efficient and Universal Merkle Tree Inclusion Proofs via OR Aggregation. Cryptography, 8.","DOI":"10.3390\/cryptography8030028"},{"key":"ref_37","first-page":"49228","article-title":"Enhanced Security and Efficiency in Blockchain With Aggregated Zero-Knowledge Proof Mechanisms","volume":"12","author":"Kuznetsov","year":"2024","journal-title":"IEEE Access"},{"key":"ref_38","unstructured":"Kuznetsov, O. (2024, November 06). Google Colab: Ed25519SetMembership for IoT. Available online: https:\/\/colab.research.google.com\/drive\/1wX6HoJk3MDWCkRnv7ee2sBOiyznRfYU1?usp=sharing."}],"container-title":["Journal of Sensor and Actuator Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2224-2708\/13\/6\/78\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:32:17Z","timestamp":1760113937000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2224-2708\/13\/6\/78"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,14]]},"references-count":38,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["jsan13060078"],"URL":"https:\/\/doi.org\/10.3390\/jsan13060078","relation":{},"ISSN":["2224-2708"],"issn-type":[{"value":"2224-2708","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,14]]}}}