{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T15:59:49Z","timestamp":1783007989007,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T00:00:00Z","timestamp":1746662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFB2701600"],"award-info":[{"award-number":["2022YFB2701600"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The consensus protocol is a fundamental building block in distributed computing and has been widely used in blockchain systems in recent years. Paxos, introduced by Lamport, stands out as one of the most widely adopted consensus protocols and has found application in renowned distributed systems, including Google\u2019s Spanner system. Abraham et al. analyzed the FaB Paxos protocol, a Byzantine version of Paxos. They abstracted the single-shot FaB Paxos into a Byzantine broadcast protocol and further gave an enhanced protocol known as Abraham et al.\u2019s BB. Abraham et al.\u2019s BB protocol achieved optimal two-round message interaction under good conditions, satisfying the optimal fault tolerance threshold of n=5t\u22121 where n represents total number of nodes in the system and t denotes the tolerable number of Byzantine nodes. This paper delves into scenarios wherein the actual number of Byzantine nodes surpasses the fault tolerance threshold during the operation of Abraham et al.\u2019s BB protocol. To address this, we propose a forensic protocol designed to offer forensic support in cases of agreement violations. The forensic protocol aims to label Byzantine nodes through irrefutable evidence. We analyze the forensic protocol, elucidating the number of Byzantine nodes that the forensic protocol can label under different circumstances, along with the corresponding number of required messages. Additionally, we present an impossibility result, indicating that forensic support for Abraham et al.\u2019s BB is impossible when the number of Byzantine nodes exceeds 2t\u22122.<\/jats:p>","DOI":"10.3390\/e27050504","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T04:06:21Z","timestamp":1746677181000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Forensic Support for Abraham et al.\u2019s BB Protocol"],"prefix":"10.3390","volume":"27","author":[{"given":"Qidi","family":"You","sequence":"first","affiliation":[{"name":"Beijing Institute of Satellite Information Engineering, Beijing 100086, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongjian","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Software, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiyong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Satellite Information Engineering, Beijing 100086, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaotong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Satellite Information Engineering, Beijing 100086, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaiwen","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Software, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kexin","family":"Hu","sequence":"additional","affiliation":[{"name":"Institute of Software, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Zhongguancun Laboratory, Beijing 100086, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,8]]},"reference":[{"key":"ref_1","unstructured":"Lamport, L., Shostak, R., and Pease, M. 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