{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T23:01:11Z","timestamp":1777676471549,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,25]],"date-time":"2021-09-25T00:00:00Z","timestamp":1632528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Ukraine","award":["2020.01\/0351"],"award-info":[{"award-number":["2020.01\/0351"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Two double-spend attack strategies on a proof-of-stake consensus are considered. For each strategy, the probability of its success is obtained, which depends on the network parameters and the number of confirmation blocks. These results can be used to define how many confirmation blocks a vendor should wait after a correspondent transaction before sending goods or services.<\/jats:p>","DOI":"10.3390\/s21196408","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T22:16:38Z","timestamp":1632780998000},"page":"6408","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Blockchain Technologies: Probability of Double-Spend Attack on a Proof-of-Stake Consensus"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8846-332X","authenticated-orcid":false,"given":"Mikolaj","family":"Karpinski","sequence":"first","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lyudmila","family":"Kovalchuk","sequence":"additional","affiliation":[{"name":"IOHK, Singapore 049908, Singapore"},{"name":"Institute of Physics and Technology, National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d, 03056 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Kochan","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3494-0493","authenticated-orcid":false,"given":"Roman","family":"Oliynykov","sequence":"additional","affiliation":[{"name":"IOHK, Singapore 049908, Singapore"},{"name":"Department of Computer Science, V.N. 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(2021). Computing resource allocation scheme for DAG-based IOTA nodes. Sensors, 21.","DOI":"10.3390\/s21144703"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Oswald, E., and Fischlin, M. (2015). The bitcoin backbone protocol: Analysis and applications. Advances in Cryptology\u2014EUROCRYPT 2015, Springer.","DOI":"10.1007\/978-3-662-46803-6"},{"key":"ref_3","unstructured":"Nakamoto, S. (2021, July 18). Bitcoin: A Peer-to-Peer Electronic Cash System. Available online: https:\/\/bitcoin.org\/bitcoin.pdf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1156","DOI":"10.1093\/rfs\/hhaa075","article-title":"Blockchain without waste: Proof-of-Stake","volume":"Volume 34","author":"Jiang","year":"2021","journal-title":"The Review of Financial Studies"},{"key":"ref_5","unstructured":"(2021, July 19). Number Of Orphaned Blocks. Available online: https:\/\/www.blockchain.com\/charts\/n-orphaned-blocks."},{"key":"ref_6","unstructured":"Rosenfeld, M. (2014). Analysis of Hashrate-Based Double Spending, Cornell University. Available online: https:\/\/arxiv.org\/abs\/1402.2009."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.entcs.2016.12.006","article-title":"Double-Spend attack models with time advantange for bitcoin","volume":"329","author":"Rocha","year":"2016","journal-title":"Electron. Notes Theor. Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Grunspan, C., and P\u00e9rez-Marco, R. (2018). Double spend races. Int. J. Theor. Appl. Financ., 21.","DOI":"10.1142\/S021902491850053X"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.comcom.2020.01.079","article-title":"Decreasing security threshold against double spend attack in networks with slow synchronization","volume":"154","author":"Kovalchuk","year":"2020","journal-title":"Comput. Commun."},{"key":"ref_10","unstructured":"(2021, July 19). Proof of Stake Instead of Proof of Work. Available online: https:\/\/bitcointalk.org\/index.php?topic=27787."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117134","DOI":"10.1109\/ACCESS.2019.2936094","article-title":"Survey of blockchain from the perspectives of applications, challenges and opportunities","volume":"7","author":"Monrat","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","unstructured":"King, S., Nadal, S., and PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake (2021, July 19). Self-Published Paper, 19 August 2012. Available online: https:\/\/decred.org\/research\/king2012.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Katz, J., and Shacham, S. (2017). Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol. LNCS Advances in Cryptology, Proceedings of the CRYPTO 2017: 37th Annual International Cryptology Conference, Santa Barbara, CA, USA, 20\u201324 August 2017, Part I, Springer.","DOI":"10.1007\/978-3-319-63697-9"},{"key":"ref_14","unstructured":"David, B., Gazi, P., Kiayias, A., and Russell, A. (2021, July 19). Ouroboros Praos: An Adaptively-Secure, Semi-Synchronous Proof-of-Stake Protocol. Cryptology ePrint Archive: Report 2017\/573. Available online: https:\/\/eprint.iacr.org\/2017\/573."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Badertscher, C., Gazi, P., Kiayias, A., Russell, A., and Zikas, V. (2021, July 19). Ouroboros Genesis: Composable Proof-of-Stake Blockchains with Dynamic Availability. Cryptology ePrint Archive: Report 2018\/378. Available online: https:\/\/eprint.iacr.org\/2018\/378.","DOI":"10.1145\/3243734.3243848"},{"key":"ref_16","unstructured":"Badertscher, C., Gazi, P., Kiayias, A., Russell, A., and Zikas, V. (2021, July 19). Ouroboros Chronos: Permissionless Clock Synchronization via Proof-of-Stake. Cryptology ePrint Archive: Report 2019\/838. Available online: https:\/\/eprint.iacr.org\/2019\/838."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, W., Li, Z., and Li, H. (2020). Hybrid consensus algorithm based on modified proof-of-probability and DPoS. Future Internet, 12.","DOI":"10.3390\/fi12080122"},{"key":"ref_18","unstructured":"Gilad, Y., Hemo, R., Micali, S., Vlachos, G., and Zeldovich, N. (2021, July 19). (MIT Computer Science and Artificial Intelligence Laboratory (MIT SCAIL), Cambridge, MA, USA). Algorand: Scaling Byzantine Agreements for Cryptocurrencies. Cryptology ePrint Archive: Report 2017\/454. Available online: https:\/\/eprint.iacr.org\/2017\/454."},{"key":"ref_19","unstructured":"Daian, P., Pass, R., and Shi, E. (2021, July 19). (Cornell University, Cornell Tech, Ithaca, NY, USA). Snow White: Robustly Reconfigurable Consensus and Applications to Provably Secure Proof of Stake. Cryptology ePrint Archive: Report 2016\/919. Available online: https:\/\/eprint.iacr.org\/2016\/919."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Longo, R., Podda, A.S., and Saia, R. (2020). Analysis of a consensus protocol for extending consistent subchains on the bitcoin blockchain. Computation, 8.","DOI":"10.3390\/computation8030067"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ga\u017ei, P., Kiayias, A., and Zindros, D. (2019, January 19\u201323). Proof-of-Stake sidechains. Proceedings of the 2019 IEEE Symposium on Security and Privacy (SP), San Francisco, CA, USA.","DOI":"10.1109\/SP.2019.00040"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/978-3-319-67816-0_17","article-title":"Securing Proof-of-Stake Blockchain Protocols","volume":"Volume 10436","author":"Hartenstein","year":"2017","journal-title":"Data Privacy Management, Cryptocurrencies and Blockchain Technology"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"253","DOI":"10.3233\/AIS-210601","article-title":"Smart Contracts for Automated Control System in Blockchain Based Smart Cities","volume":"13","author":"Pradhan","year":"2021","journal-title":"J. Ambient. Intell. Smart Environ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18901","DOI":"10.1007\/s11042-021-10715-4","article-title":"Ethereum for Internet of Things security","volume":"80","author":"Raj","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_25","unstructured":"Feller, W. (1970). An Introduction to Probability Theory and its Applications, Wiley."},{"key":"ref_26","unstructured":"Paris, R.B. (2021, July 19). Chapter 8 Incomplete Gamma and Related Functions. Digital Library of Mathematical Functions, Available online: https:\/\/dlmf.nist.gov\/8."},{"key":"ref_27","unstructured":"Kovalchuk, L., Rodinko, M., Oliynykov, R., Kaidalov, D., and Nastenko, A. (2021, January 23\u201325). Probability of double spend attack for network with non-zero synchronization time. Proceedings of the 21st Central European Conference on Cryptology (CECC \u20192021), Debrecen, Hungary."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6408\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:05:03Z","timestamp":1760166303000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,25]]},"references-count":27,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["s21196408"],"URL":"https:\/\/doi.org\/10.3390\/s21196408","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,25]]}}}