{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T15:58:25Z","timestamp":1790870305621,"version":"4.1.0"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>This paper presents a polynomial-time protocol for reaching Byzantine agreement in t + 1 rounds whenever n &gt; 3t, where n is the number of processors and t is an a priori upper bound on the number of failures. This resolves an open problem presented by Pease, Shostak, and Lamport in 1980. An early-stopping variant of this protocol is also presented, reaching agreement in a number of rounds that is proportional to the number of processors that actually fail.<\/jats:p>","DOI":"10.1137\/s0097539794265232","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"247-290","source":"Crossref","is-referenced-by-count":109,"title":["Fully Polynomial Byzantine Agreement for\n                    <i>n<\/i>\n                    &gt; 3\n                    <i>t<\/i>\n                    Processors in\n                    <i>t<\/i>\n                    + 1 Rounds"],"prefix":"10.1137","volume":"27","author":[{"given":"Juan A.","family":"Garay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yoram","family":"Moses","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01798957"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90035-E"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01187072"},{"key":"R4","unstructured":"P. Berman and J. A. Garay,\n                      Efficient distributed consensus with n=(3+\u03b5)t processors\n                      , in Proc. 5th Internat. Workshop on Distributed Algorithms, Lecture Notes in Comput. Sci. 579, Springer\u2010Verlag, New York, 1991, pp. 129\u2013142."},{"key":"R5","unstructured":"P. Berman and J. A. Garay, private communication, 1992."},{"key":"R6","unstructured":"P. Berman, J. A. Garay, and K. J. Perry,\n                      Towards optimal distributed consensus\n                      , in Proc. 30th IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 410\u2013415."},{"key":"R7","unstructured":"P. Berman, J. A. Garay, and K. J. Perry,\n                      Optimal early stopping in distributed consensus\n                      , in Proc. 6th Internat. Workshop on Distributed Algorithms, Lecture Notes in Comput. Sci. 647, Springer\u2010Verlag, New York, 1992, pp. 221\u2013237."},{"key":"R8","unstructured":"B. Coan,\n                      A communication\u2010efficient canonical form for fault\u2010tolerant distributed protocols\n                      , in Proc. 5th ACM Symposium on the Principles of Distributed Computing, ACM, New York, 1986, pp. 63\u201372."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02280838"},{"key":"R9","unstructured":"also in Proc. 26th Allerton Conference on Communication, Control and Computing, University of Illinois, Urbana, IL, 1988, pp. 663\u2013672."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01187076"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(82)90776-8"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(90)90014-9"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1145\/96559.96565"},{"key":"R14","unstructured":"D. Dolev and H. R. Strong,\n                      Polynomial algorithms for multiple processor agreement\n                      , in Proc. 14th Annual Symposium on Theory of Computing, ACM, New York, 1982, pp. 401\u2013407."},{"key":"R15","unstructured":"Michael Fischer, The consensus problem in unreliable distributed systems (a brief survey), Lecture Notes in Comput. Sci., Vol. 158, Springer, Berlin, 1983, 127\u201314085f:68008"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(82)90033-3"},{"key":"R17","unstructured":"P. Feldman and S. Micali,\n                      Optimal algorithms for Byzantine agreement\n                      , in Proc. of the 20th Annual Symposium on Theory of Computing, ACM, New York, 1988, pp. 148\u2013161."},{"key":"R18","unstructured":"J. A. Garay and Y. Moses,\n                      Fully polynomial Byzantine agreement in t+1 rounds\n                      , in Proc. of the 25th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 31\u201341."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(90)90185-Z"},{"key":"R20","unstructured":"R\u00fcdiger Reischuk, A new solution for the Byzantine generals problem, Lecture Notes in Comput. Sci., Vol. 158, Springer, Berlin, 1983, 382\u2013393734736"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1994.1029"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1145\/322186.322188"},{"key":"R23","unstructured":"M. Rabin,\n                      Randomized Byzantine generals\n                      , in Proc. 24th IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1983, pp. 403\u2013409."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/0216031"},{"key":"R25","unstructured":"O. Waarts,\n                      Coordinated traversal: Byzantine Agreement in Polynomial Time\n                      , M. Sc. thesis, Weizmann Institute of Science, Rehovot, Israel, 1988."},{"key":"R26","unstructured":"A. Zamsky,\n                      New Algorithms for Agreement in Synchronous Distributed Networks\n                      , M. Sc. thesis, Technion\u2014Israel Institute of Technology, Haifa, Israel, 1992."},{"key":"R27","unstructured":"A. Zamsky,\n                      A randomized Byzantine agreement protocol with constant expected time and guaranteed termination in optimal (deterministic) time\n                      , in Proc. 15th Annual ACM Symposium on Priniciples of Distributed Computing, ACM, New York, 1996, pp. 201\u2013208."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/s004460050012"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1145\/174644.174649"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539794265232","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:38Z","timestamp":1787336078000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539794265232"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0097539794265232"],"URL":"https:\/\/doi.org\/10.1137\/s0097539794265232","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}