Almost-Surely Terminating Asynchronous Byzantine Agreement Revisited

All You Need is DAG

“…To interpret the DAG, each process divides its local into waves, where each wave consists of 4 consecutive rounds. For example, 's first wave consists of [1], [2], [3], and [4]. Formally, the ℎ round of wave , where ∈ [1..4], ∈ N, is defined as round( , ) ≜ 4( − 1) + .…”

“…To this end, we use standard quorum intersection. Process commits the wave vertex leader if: 4)] : strong_path( ′ , ) ≥ 2 + 1 (Line 36).…”

“…[ 1 ] with a strong path from 3 are in the [ 1 ] as well). To complete the mapping, when completes 3 and broadcasts 4 in round 4 , then 4 has in its causal history the same values that would have been in in the equivalent common-core algorithm.…”

“…Note that since Byzantine processes cannot equivocate, and since every round in the DAG has at least 2 + 1 vertices, any vertex that adds to [ 4 ] has to reference at least + 1 vertices that 4 also references, even vertices sent from Byzantine processes. Thus, based on the common-core guarantee, there is a set ⊂ [ 1 ] s.t.…”

“…Their communication and time complexity was exponential and a significant amount of work has been done since then in attempt to achieve optimal complexity under different assumptions. Some works consider the information theoretical settings and present protocols with polylogarithmic complexity that tolerate adversaries with unbounded computational power [4,26,38]. Others follow a more practical approach and consider a computationally bounded adversary to be able to use cryptographic primitives to improve complexity [1,12,13,35].…”