Communication Complexity Of Byzantine Agreement Revisited

If the protocol has the complexity of communication, there must be a node $p “leq f/2” that receives messages from `leq f/2`. In world 2, the opponent does everything like in world 1, except that (i) it does not damage $p, and (ii) it corrupts all the nodes in $U that have sent messages to $p (this may also contain the specified sender). These damaged nodes do not send messages to $p, but behave honestly with other nodes in $U. Since $p receives 1 “leq f/2” messages worldwide, the knots $f are not damaged in the world 2 .leq f/2- and V f/2). In 1980, PSL showed the first result of the feasibility of a consensus in contemporary Byzantine opponents. Their solution, however, had an exponential communication complexity (in $n, the number of parts). An obvious question then is to find the slightest communication complexity that can be achieved. Dolev and Resichuk have shown that the barrier of square communication complexity cannot be broken by deterministic protocols. The search for an evolutionary Byzantine arrangement has many challenges. In this article, we highlight the lower limit of Dolev and Reischuk in 1982. In our previous interventions with lower limits, we discussed the limit values for the conflicting threshold (i) DLS in partial synchronization and (ii) FLM in the absence of a confidence configuration.

In this article, we discuss another classic result of impossibility on the limits of the complexity of communication in the Byzantine broadcast. At a very high level, the Dolev and Resichuk says that if you send few messages < (f/2), then an honest party will receive no message! The party that does not receive any messages has no way of reaching an agreement with the rest. We use a trivial argument of indecision and create a world where a knot $p – no message at all. Therefore, the node of $p and $p cannot tell the difference between a world in which the specified sender sends 0 or a world in which it sends 1. Note: The border is for byzantine mailing (not the Byzantine arrangement). In terms of feasibility, the two problems are equivalent and each of them can be damaged by the other. However, the complexity of communication remains the same only if Byzantine shipments are carried out with a Byzantine arrangement; The sender can send the value to all nodes, and the nodes can execute a Byzantine agreement protocol.