{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T20:16:12Z","timestamp":1783973772336,"version":"3.55.0"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T00:00:00Z","timestamp":1595548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>As the core of blockchain technology, the consensus algorithm plays an important role in determining the security, data consistency, and efficiency of blockchain systems. The existing mainstream consensus algorithm is experiencing difficulties satisfying the needs of efficiency, security, and decentralization in real-world scenarios. This paper proposes a hybrid consensus algorithm based on modified Proof-of-Probability and Delegated Proof-of-Stake. In this method, the work of block generation and validation is, respectively, completed by the nodes using the modified Proof-of-Probability consensus algorithm and Delegated Proof-of-Stake consensus algorithm. When a transaction occurs, the system sends several target hash values to the whole network. Each modified Proof-of-Probability node has a different sorting algorithm, so they have different mining priorities. Every time a hash is decrypted by a modified Proof-of-Probability node, the modulo operation is done to the value of nonce, which is then compared with the expected value given by the supernode selected by the Delegated Proof-of-Stake nodes. If they are not the same, the Proof-of-Probability node enters the waiting time and the other Proof-of-Probability nodes continue to mine. By adopting two consensus algorithms, the malicious nodes must control more than 51% of the nodes that adopt the two consensus algorithms, at the same time, to effectively attack the system, that is, they must have more than 51% of the computing power and more than 51% of the tokens. This not only increases the cost of malicious attacks, but also reduces waste of computing power. In addition, the efficiency of the DPoS algorithm makes up for the deficiency of the PoP algorithm in system efficiency, and the mining behavior based on probability in the PoP algorithm also significantly weakens the ability of supernodes in the DPoS algorithm to conduct monopoly behavior or other malicious behaviors. In a word, the combination of the two algorithms makes the system perform better in terms of security, system efficiency, and decentralization.<\/jats:p>","DOI":"10.3390\/fi12080122","type":"journal-article","created":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T09:06:09Z","timestamp":1595581569000},"page":"122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Hybrid Consensus Algorithm Based on Modified Proof-of-Probability and DPoS"],"prefix":"10.3390","volume":"12","author":[{"given":"Baocheng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, North China University of Technology, Beijing 100144, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9775-5335","authenticated-orcid":false,"given":"Zetao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, North China University of Technology, Beijing 100144, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haibin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Computer and Software Engineering, Shandong College of Electronic Technology, Jinan 250200, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,24]]},"reference":[{"key":"ref_1","first-page":"11","article-title":"Survey of block chain","volume":"2","author":"Shen","year":"2016","journal-title":"J. Netw. Inf. Secur."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117266","DOI":"10.1109\/ACCESS.2020.3004486","article-title":"ABlockchain-Based Transaction Validation Protocol for a Secure Distributed IoT Network","volume":"8","author":"Hosen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Malik, A.A., Tosh, D.K., and Ghosh, U. (2019, January 10\u201313). Non-Intrusive Deployment of Blockchain in Establishing Cyber-Infrastructure for Smart City. Proceedings of the 2019 16th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), Boston, MA, USA.","DOI":"10.1109\/SAHCN.2019.8824921"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Singh, P., Nayyar, A., Kaur, A., and Ghosh, U. (2020). Blockchain and Fog Based Architecture for Internet of Everything in Smart Cities. Future Internet, 12.","DOI":"10.3390\/fi12040061"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1145\/357172.357176","article-title":"The Byzantine generals. Problem","volume":"4","author":"Lamport","year":"1982","journal-title":"ACM Trans. Program. Lang. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3416","DOI":"10.1109\/COMST.2018.2842460","article-title":"A survey on security and privacy issues of bitcoin","volume":"20","author":"Conti","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_7","unstructured":"Dwork, C., and Naor, M. (1992, January 16\u201320). Pricing via Processing, Or, Combatting Junk Mail. Proceedings of the Annual International Cryptology Conference, Santa Barbara, CA, USA."},{"key":"ref_8","unstructured":"King, S., and Nadal, S. (2018, May 15). PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake [EB\/OL]. Available online: https:\/\/peercoin.net\/assets\/paper\/peercoin-paper.pdf."},{"key":"ref_9","unstructured":"Dantheman (2019, November 15). DPOS Consensus Algorithm\u2014The Missing White Paper [EB\/OL]. Available online: https:\/\/steemit.com\/bitshares\/@.testz\/bitshares-history-delegated-proof-of-stake-dpos."},{"key":"ref_10","unstructured":"Sungmin, K., and Joongheon, K. (2018, January 4\u20138). POSTER: Mining with Proof-of-Probability in Blockchain. Proceedings of the 2018 on Asia Conference on Computer and Communications Security (ASIACCS\u2019 18), Incheon, Korea."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tromp, J. (2015). Cuckoo Cycle: A memory bound graph-theoretic proof-of-work. Financial Cryptography and Data Security, Springer. BITCOIN 2015.","DOI":"10.1007\/978-3-662-48051-9_4"},{"key":"ref_12","unstructured":"Nakamoto, S. (2019, October 21). Bitcoin: A Peer-to-Peer Electronic Cash System. Technical Report. Available online: http:\/\/bitcoin.org\/bitcoin.pdf."},{"key":"ref_13","unstructured":"Antonopoulos, A.M. (2014). Mastering Bitcoin: Unlocking Digital Crypto-Currencies, O\u2019 Reilly."},{"key":"ref_14","unstructured":"BTC.com (2018, May 13). Mineral Pool Statistics [EB\/OL]. Available online: https:\/\/btc.com\/stats\/pool?pool_mode=day."},{"key":"ref_15","first-page":"1038","article-title":"It will cost you nothing to \u2018kill\u2019 a proof-of-stake","volume":"34","author":"Houy","year":"2014","journal-title":"Cryptocurrency"},{"key":"ref_16","first-page":"1","article-title":"Review for consensus mechanism of. cryptocurrency system","volume":"26","author":"Xia","year":"2017","journal-title":"Comput. Syst. Appl."},{"key":"ref_17","unstructured":"Castro, M., and Liskov, B. (1999, January 22\u201325). Practical Byzantine fault tolerance. Proceedings of the OSDI, New Orleans, LA, USA."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Nayak, K., Kumar, S., Miller, A., and Shi, E. (2016, January 21\u201324). Stubborn Mining: Generalizing Selfish Mining and Combining with an Eclipse Attack. Proceedings of the IEEE European Symposium on Security & Privacy, Saarbr\u00fccken, Germany.","DOI":"10.1109\/EuroSP.2016.32"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Eyal, I., and Sirer, E.G. (2014, January 3\u20137). Majority is not enough: Bitcoin Mining is Vulnerable. Proceedings of the International Conference on Financial Cryptography and Data Security, Christ Church, Barbados.","DOI":"10.1007\/978-3-662-45472-5_28"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Karame, G., Androulaki, E., and Capkun, S. (2012, January 16\u201318). Two bitcoins at the price of one? Double-spending attacks on fast payments in bitcoin. Proceedings of the Conference on Computer & Communications Security, Raleigh, NC, USA.","DOI":"10.1145\/2382196.2382292"},{"key":"ref_21","unstructured":"Mirkovic, J., Robinson, M., Reiher, P., and Oikonomou, G. (2005). Distributed Defense against DDOS Attacks, University of Delaware. University of Delaware CIS Department Technical Report CIS-TR-2005-02."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Douceur, J.R. (2002, January 7\u20138). The Sybil Attack. Proceedings of the Peer-to-Peer Systems, First International Workshop (IPTPS), Cambridge, MA, USA.","DOI":"10.1007\/3-540-45748-8_24"}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/12\/8\/122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:51:18Z","timestamp":1760176278000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/12\/8\/122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":22,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["fi12080122"],"URL":"https:\/\/doi.org\/10.3390\/fi12080122","relation":{},"ISSN":["1999-5903"],"issn-type":[{"value":"1999-5903","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,24]]}}}