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In this paper we present the  Multidimensional Byzantine Agreement (MBA) Protocol , a  leaderless  Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value    $$\bot $$  ⊥ that signals irreconcilable disagreement. The MBA Protocol is probabilistic and its execution halts with probability 1, and the number of steps necessary to halt follows a Bernoulli-like distribution. The design combines a  Multidimensional Graded Consensus  and a  Multidimensional Binary Byzantine Agreement , the generalization to the multidimensional case of two protocols presented by Micali et al. (SIAM J Comput 26(4):873–933, 1997; Byzantine agreement, made trivial, 2016). We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious.

Multidimensional Byzantine agreement in a synchronous setting