Asynchronous Byzantine consensus with 2f+1 processes

  • Authors:
  • Miguel Correia;Giuliana S. Veronese;Lau Cheuk Lung

  • Affiliations:
  • Universidade de Lisboa, Lisboa, Portugal;Universidade de Lisboa, Lisboa, Portugal;Univ. Federal Santa Catarina, Florianopolis, Brazil

  • Venue:
  • Proceedings of the 2010 ACM Symposium on Applied Computing
  • Year:
  • 2010

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Abstract

Byzantine consensus in asynchronous message-passing systems has been shown to require at least 3f + 1 processes to be solvable in several system models (e.g., with failure detectors, partial synchrony or randomization). Recently a couple of solutions to implement Byzantine fault-tolerant state-machine replication using only 2f + 1 replicas have appeared. This reduction from 3f + 1 to 2f + 1 is possible with a hybrid system model, i.e., by extending the system model with trusted/trustworthy components that constrain the power of faulty processes to have certain behaviors. Despite these important results, the problem of solving Byzantine consensus with only 2f + 1 processes is still far from being well understood. In this paper we present a methodology to transform crash consensus algorithms into Byzantine consensus algorithms with different characteristics, with the assistance of a reliable broadcast primitive that requires trusted/trustworthy components to be implemented. We exemplify the methodology with two algorithms, one that uses failure detectors and one that is randomized. We also define a new flavor of consensus and use it to solve atomic broadcast, showing the practical interest of the transformations.