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Byzantine Lattice Agreement in Synchronous Message Passing Systems

Authors Xiong Zheng, Vijay Garg



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Author Details

Xiong Zheng
  • Electrical and Computer Engineering, University of Texas at Austin, TX, USA
Vijay Garg
  • Electrical and Computer Engineering, University of Texas at Austin, TX, USA

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Xiong Zheng and Vijay Garg. Byzantine Lattice Agreement in Synchronous Message Passing Systems. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 32:1-32:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DISC.2020.32

Abstract

We propose three algorithms for the Byzantine lattice agreement problem in synchronous systems. The first algorithm runs in min {3h(X) + 6,6√{f_a} + 6}) rounds and takes O(n² min{h(X), √{f_a}}) messages, where h(X) is the height of the input lattice X, n is the total number of processes in the system, f is the maximum number of Byzantine processes such that n ≥ 3f + 1 and f_a ≤ f is the actual number of Byzantine processes in an execution. The second algorithm takes 3log n + 3 rounds and O(n² log n) messages. The third algorithm takes 4 log f + 3 rounds and O(n² log f) messages. All algorithms can tolerate f < n/3 Byzantine failures. This is the first work for the Byzantine lattice agreement problem in synchronous systems which achieves logarithmic rounds. In our algorithms, we apply a slightly modified version of the Gradecast algorithm given by Feldman et al [Feldman and Micali, 1988] as a building block. If we use the Gradecast algorithm for authenticated setting given by Katz et al [Katz and Koo, 2006], we obtain algorithms for the Byzantine lattice agreement problem in authenticated settings and tolerate f < n/2 failures.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Lattice agreement
  • Byzantine Failure
  • Gradecast

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References

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