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The applications of verifiable delay are also widespread in blockchain research, such as: computational timestamping, public random beacons, resource-efficient blockchains, and proofs of data replication. This paper introduces the concept of verifiable delay functions and systematically summarizes the types of verifiable delay functions. Firstly, the description and characteristics of verifiable delay functions are given, and weak verifiable delay functions, incremental verifiable delay functions, decodable verifiable delay functions, and trapdoor verifiable delay functions are introduced respectively. The construction of verifiable delay functions generally relies on two security assumptions: algebraic assumption or structural assumption. Then, the security assumptions of two different verifiable delay functions are described based on cryptography theory. Secondly, a post-quantum verifiable delay function based on super-singular isogeny is introduced. Finally, the paper summarizes the blockchain-related applications of verifiable delay functions.<\/jats:p>","DOI":"10.3390\/s22197524","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T05:12:21Z","timestamp":1665378741000},"page":"7524","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Verifiable Delay Function and Its Blockchain-Related Application: A Survey"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2467-5582","authenticated-orcid":false,"given":"Qiang","family":"Wu","sequence":"first","affiliation":[{"name":"Engineering Research Center of Digital Forensics, Ministry of Education, School of Computer Science, Nanjing University of Information Science & Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Xi","sequence":"additional","affiliation":[{"name":"Beijing Institute of Computer Technology & Application, Beijing 100082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiren","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Computer Technology & Application, Beijing 100082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2585-7978","authenticated-orcid":false,"given":"Shan","family":"Ji","sequence":"additional","affiliation":[{"name":"College of Computer Science & Technology, Nanjing University of Aeronautics & Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shenqing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science & Technology, Nanjing University of Aeronautics & Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6602-9576","authenticated-orcid":false,"given":"Yongjun","family":"Ren","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Digital Forensics, Ministry of Education, School of Computer Science, Nanjing University of Information Science & Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Boneh, D., Bonneau, J., B\u00fcnz, B., and Fisch, B. (2018, January 18\u201322). Verifiable delay functions. Proceedings of the Annual International Cryptology Conference, Santa Barbara, CA, USA.","DOI":"10.1007\/978-3-319-96884-1_25"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rotem, L. (2021, January 8\u201311). Simple and efficient batch verification techniques for verifiable delay functions. Proceedings of the Theory of Cryptography Conference, Raleigh, NC, USA.","DOI":"10.1007\/978-3-030-90456-2_13"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhou, M., Lin, X., Liu, A., and Che, Y. (2021, January 27\u201329). An improved blockchain consensus protocol with distributed verifiable delay function. Proceedings of the 2021 IEEE International Conference on Electronic Technology, Communication & Information, Changchun, China.","DOI":"10.1109\/ICETCI53161.2021.9563378"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1902","DOI":"10.1109\/TCSI.2020.2966755","article-title":"Design and implementation of a low-latency modular multiplication algorithm","volume":"67","year":"2020","journal-title":"IEEE Trans. Circuits Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lombardi, A., and Vaikuntanathan, V. (2020, January 17\u201321). Fiat-Shamir for repeated squaring with applications to PPAD-hardness and VDFs. Proceedings of the 40th Annual International Cryptology Conference, Santa Barbara, CA, USA.","DOI":"10.1007\/978-3-030-56877-1_22"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"D\u00f6ttling, N., Garg, S., Malavolta, G., and Vasudevan, P.N. (2020, January 14\u201316). Tight verifiable delay functions. Proceedings of the 12th International Conference on Security and Cryptography for Networks, Amalfi, Italy.","DOI":"10.1007\/978-3-030-57990-6_4"},{"key":"ref_7","unstructured":"Raghunandan, K.R., Aithal, G., and Shetty, S. (2019, January 26\u201328). Comparative analysis of encryption and decryption techniques using mersenne prime numbers and phony modulus to avoid factorization attack of RSA. Proceedings of the 2019 International Conference on Advanced Mechatronic Systems, Kusatsu, Japan."},{"key":"ref_8","unstructured":"Boneh, D., Benedikt, B., and Ben, F. (2018, January 2\u20136). A survey of two verifiable delay functions. Proceedings of the International Association for Cryptologic Research, Brisbane, QLD, Australia."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Medley, L., and Quaglia, E.A. (2021, January 12\u201314). Collaborative verifiable delay functions. Proceedings of the 17th International Conference on Information Security and Cryptology, Virtual Event.","DOI":"10.1007\/978-3-030-88323-2_27"},{"key":"ref_10","first-page":"12459","article-title":"Moduli spaces of quadratic rational maps with a marked periodic point of small order","volume":"2015","author":"Blanc","year":"2015","journal-title":"Int. Math. Res. Not."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7913","DOI":"10.1109\/TCOMM.2021.3111018","article-title":"On sequential decoding metric function of polarization-adjusted convolutional (PAC) codes","volume":"69","author":"Moradi","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Valiant, P. (2008). Incrementally verifiable computation or proofs of knowledge imply time\/space efficiency. Theory of Cryptography, Proceedings of the Fifth Theory of Cryptography Conference, New York, NY, USA, 19\u201321 March 2008, Springer.","DOI":"10.1007\/978-3-540-78524-8_1"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Canetti, R., Chiesa, A., and Tromer, E. (2013, January 2\u20134). Recursive composition and bootstrapping for SNARKs and proof-carrying data. Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, Palo Alto, CA, USA.","DOI":"10.1145\/2488608.2488623"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gritti, C. (2020, January 17\u201319). Publicly verifiable proofs of data replication and retrievability for cloud storage. Proceedings of the 2020 International Computer Symposium Conference, Tainan, Taiwan.","DOI":"10.1109\/ICS51289.2020.00091"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Abadi, A., and Kiayias, A. (2021, January 1\u20135). Multi-instance publicly verifiable time-lock puzzle and its applications. Proceedings of the 25th International Conference on Financial Cryptography and Data Security, Virtual Event.","DOI":"10.1007\/978-3-662-64331-0_28"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Burdges, J., and Feo, L.D. (2021, January 17\u201321). Delay encryption. Proceedings of the 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia.","DOI":"10.1007\/978-3-030-77870-5_11"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ren, Y.J., Zhu, F.J., Kumar, S.P., Wang, T., and Wang, J. (2020). Data query mechanism based on hash computing power of blockchain in Internet of Things. Sensors, 20.","DOI":"10.3390\/s20010207"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2113","DOI":"10.1007\/s00145-020-09364-x","article-title":"Efficient verifiable delay functions","volume":"33","author":"Wesolowski","year":"2020","journal-title":"J. Cryptol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1126\/science.abh0945","article-title":"Plastic ingestion as an evolutionary trap: Toward a holistic understanding","volume":"373","author":"Santos","year":"2021","journal-title":"Science"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"103044","DOI":"10.1016\/j.ijplas.2021.103044","article-title":"A mechanism-based multi-trap phase field model for hydrogen assisted fracture","volume":"144","author":"Isfandbod","year":"2021","journal-title":"Int. J. Plast."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Raikwar, M., and Gligoroski, D. (2021, January 27\u201330). R3V: Robust round robin VDF-based consensus. Proceedings of the 2021 3rd Conference on Blockchain Research & Applications for Innovative Networks and Services, Paris, France.","DOI":"10.1109\/BRAINS52497.2021.9569781"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11422","DOI":"10.1109\/JIOT.2021.3126340","article-title":"Toward reliable and confidential release for smart contract via ID-based TRE","volume":"9","author":"Jiang","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7856","DOI":"10.1109\/TIT.2020.3028439","article-title":"Inference under information constraints II: Communication constraints and shared randomness","volume":"66","author":"Acharya","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","unstructured":"Pietrzak, K. (2019, January 10\u201312). Simple verifiable delay functions. Proceedings of the 10th Innovations in Theoretical Computer Science Conference, San Diego, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s10623-021-00981-6","article-title":"Difference matrices with five rows over finite abelian groups","volume":"90","author":"Pan","year":"2022","journal-title":"Des. Codes Cryptogr."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.1109\/TIT.2019.2923758","article-title":"LCD and self-Orthogonal group codes in a finite abelian p -group algebra","volume":"66","author":"Li","year":"2020","journal-title":"IEEE Trans Inf. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3698","DOI":"10.1109\/TIT.2014.2314298","article-title":"Near-optimal partial hadamard codebook construction using binary sequences obtained from quadratic residue mapping","volume":"60","author":"Hong","year":"2014","journal-title":"IEEE Trans Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bettaieb, S., Bidoux, L., Blazy, O., and Gaborit, P. (2021, January 12\u201320). Zero-knowledge reparation of the v\u00e9ron and AGS code-based identification schemes. Proceedings of the 2021 IEEE International Symposium on Information Theory, Melbourne, VIC, Australia.","DOI":"10.1109\/ISIT45174.2021.9517937"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1109\/TIFS.2020.3045904","article-title":"On the security of lattice-based Fiat-Shamir signatures in the presence of randomness leakage","volume":"16","author":"Liu","year":"2021","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"De-Feo, L., Masson, S., Petit, C., and Sanso, A. (2019, January 8\u201312). Verifiable delay functions from super-singular isogenies and pairings. Proceedings of the International Conference on the Theory & Application of Cryptology & Information Security, Kobe, Japan.","DOI":"10.1007\/978-3-030-34578-5_10"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5974","DOI":"10.1109\/TVT.2021.3078806","article-title":"Bilinear pairing-based hybrid signcryption for secure heterogeneous vehicular communications","volume":"70","author":"Ali","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.3934\/mbe.2019091","article-title":"Secure data storage based on blockchain and coding in edge computing","volume":"16","author":"Ren","year":"2019","journal-title":"Math. Biosci. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"101777","DOI":"10.1016\/j.ffa.2020.101777","article-title":"On oriented super-singular elliptic curves","volume":"69","author":"Onuki","year":"2021","journal-title":"Finite Fields Their Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2558","DOI":"10.1109\/LCOMM.2017.2750660","article-title":"Constructions of LDPCs from Elliptic Curves over finite fields","volume":"21","author":"Saouter","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/TIE.2012.2186104","article-title":"Efficient Elliptic Curve point multiplication using digit-serial binary field operations","volume":"60","author":"Sutter","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7750","DOI":"10.1109\/JSEN.2017.2720458","article-title":"Elliptic Curve-Based Secure Multidimensional Aggregation for Smart Grid Communications","volume":"17","author":"Senouci","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5892","DOI":"10.1109\/JIOT.2018.2869872","article-title":"Dynamic scalable Elliptic Curve cryptographic scheme and its application to in-vehicle security","volume":"6","author":"Wang","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1109\/TPDS.2014.2323062","article-title":"Parallel and high-speed computations of Elliptic Curve cryptography using hybrid-double multipliers","volume":"26","author":"Azarderakhsh","year":"2015","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1109\/TC.2020.3013266","article-title":"Elliptic Curve cryptography point multiplication core for hardware security module","volume":"69","author":"Mehrabi","year":"2020","journal-title":"IEEE Trans Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"6380","DOI":"10.1109\/TSP.2020.3036647","article-title":"Lattice reduction over imaginary quadratic fields","volume":"68","author":"Lyu","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1109\/JSYST.2018.2865216","article-title":"On decoupled decoding of quasi orthogonal STBCs using quaternion algebra","volume":"13","author":"Mushtaq","year":"2019","journal-title":"IEEE Syst. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1109\/TRO.2014.2341312","article-title":"Approaching dual quaternions from matrix algebra","volume":"30","author":"Thomas","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11786-022-00531-w","article-title":"Faster beta Weil pairing on BLS pairing friendly curves with odd embedding degree","volume":"16","author":"Laurian","year":"2022","journal-title":"Math. Comput. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2475","DOI":"10.1109\/TPDS.2015.2492962","article-title":"A comment on \u201cProcess placement in multicore clusters: Algorithmic issues and practical techniques\u201d","volume":"27","author":"Mann","year":"2016","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Nguyen, H., Nguyen, T.M.N.C., Nguyen, L., and Custovic, E. (2011, January 21\u201324). An FPGA-based implementation for repeated square-and-multiply polynomials. Proceedings of the 7th International Conference on Broadband Communications and Biomedical Applications, Melbourne, VIC, Australia.","DOI":"10.1109\/IB2Com.2011.6217915"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Ephraim, N., Freitag, C., Komargodski, I., and Pass, R. (2020, January 10\u201314). Continuous verifiable delay functions. Proceedings of the 39th Annual International Conference on the Theory & Applications of Cryptographic Techniques, Zagreb, Croatia.","DOI":"10.1007\/978-3-030-45727-3_5"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Ch\u00e1vez-Saab, J., Rodr\u00edguez-Henr\u00edquez, F., and Tibouchi, M. (2021, January 1\u20135). Verifiable isogeny walks: Towards an isogeny-based postquantum VDF. Proceedings of the International Conference on Selected Areas in Cryptography, Virtual Event.","DOI":"10.1007\/978-3-030-99277-4_21"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1145\/2856449","article-title":"Pinocchio: Nearly practical verifiable computation","volume":"59","author":"Parno","year":"2016","journal-title":"Commun. ACM"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6983","DOI":"10.1109\/JIOT.2020.3038388","article-title":"Novel Postquantum MQ-based signature scheme for Internet of things with parallel implementation","volume":"8","author":"Akleylek","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ipl.2005.11.015","article-title":"Improved generalized Atkin algorithm for computing square roots in finite fields","volume":"98","author":"Kong","year":"2006","journal-title":"Inform. Process. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/TITS.2021.3100103","article-title":"Novel vote scheme for decision-making feedback based on blockchain in internet of vehicles","volume":"23","author":"Ren","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_52","first-page":"1","article-title":"Regulatable and hardware-based proof of stake to approach nothing at stake and long range attacks","volume":"1","author":"Feng","year":"2022","journal-title":"IEEE Trans. Serv. Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1109\/JBHI.2014.2343632","article-title":"Designing robust and reliable timestamps for remote patient monitoring","volume":"19","author":"Clarke","year":"2015","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Landerreche, E., Stevens, M., and Schaffner, C. (2020, January 10\u201314). Non-interactive cryptographic timestamping based on verifiable delay functions. Proceedings of the 24th International Conference on Financial Cryptography & Data Security, Kota Kinabalu, Malaysia.","DOI":"10.1007\/978-3-030-51280-4_29"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.32604\/csse.2023.030646","article-title":"Distributed timestamp mechanism based on verifiable delay functions","volume":"44","author":"Wu","year":"2023","journal-title":"Comput. Syst. Sci. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Schindler, P., Judmayer, A., Hittmeir, M., Stifter, N., and Weippl, E. (2020, January 23\u201326). RandRunner: Distributed randomness from trapdoor VDFs with strong uniqueness. Proceedings of the 2020 Network & Distributed System Security Symposium Conference, San Diego, CA, USA.","DOI":"10.14722\/ndss.2021.24116"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.future.2020.09.019","article-title":"Multiple cloud storage mechanism based on blockchain in smart homes","volume":"115","author":"Ren","year":"2021","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s12095-017-0264-3","article-title":"Malleability of the blockchain\u2019s entropy","volume":"10","author":"Pierrot","year":"2018","journal-title":"Cryptogr. Commun."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3390\/cryptography6010005","article-title":"Designing a practical code-based signature scheme from zero-knowledge proofs with trusted setup","volume":"6","author":"Gueron","year":"2022","journal-title":"Cryptography"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"15596","DOI":"10.1109\/JIOT.2021.3073500","article-title":"Blockchain-aided privacy-preserving outsourcing algorithm of bilinear pairings for Internet of things devices","volume":"8","author":"Zhang","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Toyoda, K., and Zhang, A.N. (2019, January 9\u201312). Mechanism design for an incentive-aware blockchain-enabled federated learning platform. Proceedings of the 2019 IEEE International Conference on Big Data (Big Data), Los Angeles, CA, USA.","DOI":"10.1109\/BigData47090.2019.9006344"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2824","DOI":"10.3390\/su12072824","article-title":"Robust proof of stake: A new consensus protocol for sustainable blockchain systems","volume":"12","author":"Li","year":"2020","journal-title":"Sustainability"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"3143","DOI":"10.1109\/TWC.2015.2402680","article-title":"Strategy-proof resource allocation mechanism for multi-flow wireless multicast","volume":"14","author":"Ko","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_64","first-page":"3271","article-title":"Long-term preservation of electronic record based on digital continuity in smart cities","volume":"66","author":"Ren","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_65","first-page":"62","article-title":"Blockchain-based decentralized user authentication scheme for letter of guarantee in financial contract management","volume":"1","author":"Sasikumar","year":"2022","journal-title":"Malays. J. Comput. Sci."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"6835","DOI":"10.1109\/JIOT.2019.2911969","article-title":"Proof-of-Work consensus approach in blockchain technology for cloud and fog computing using maximization-factorization statistics","volume":"6","author":"Kumar","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/TPDS.2020.3030063","article-title":"BOSSA: A decentralized system for proofs of data retrievability and replication","volume":"32","author":"Chen","year":"2021","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TSC.2018.2813368","article-title":"Replication schemes for highly available workflow engines","volume":"14","author":"Rothermel","year":"2021","journal-title":"IEEE Trans. Serv. Comput."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"6715","DOI":"10.1109\/JIOT.2019.2911010","article-title":"Replication of smart-city Internet of Things assets in a municipal deployment","volume":"6","author":"Nelson","year":"2019","journal-title":"IEEE Internet Things J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7524\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:18Z","timestamp":1760143578000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,4]]},"references-count":69,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22197524"],"URL":"https:\/\/doi.org\/10.3390\/s22197524","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,4]]}}}