Imagine that several divisions of the Byzantine army are stored outside an enemy city, each division is commanded by its own general. Generals can only communicate with each other by messenger. After observing the enemy, they must opt for a common action plan. However, some generals may be traitors who try to prevent loyal generals from reaching an agreement. The generals must decide when they attack the city, but they need a large majority of their army to attack at the same time. Generals must have an algorithm to ensure that (a) all loyal generals decide on the same plan of action, and (b) a small number of traitors cannot lead loyal generals to adopt a bad plan. The general faithful will do everything the algorithm says, but traitors can do whatever they want. The algorithm must guarantee the condition (a) regardless of what the traitors do. Not only should loyal generals agree, but they should agree on a reasonable plan. A Byzantine error (also an interactive consistency, a congruence of sources, an avalanche of errors, a Byzantine agreement problem, a Byzantine genetic problem and a Byzantine failure) is a condition of a computer system, especially distributed computer systems, where components can fail and contain imperfect information about component failure. The term has its name from an allegory, the “Bizantin General`s problem”, designed to describe a situation in which the players in the system must agree on a concerted strategy to avoid a catastrophic failure of the system, but some of these actors are unreliable.
The concept of the Byzantine margin of error in a cryptocurrency is the characteristic of reaching agreement or consensus on certain blocks based on proof of work, even if some nodes do not react or emit malicious values to control the evil network. BFT`s main objective is to protect the system even in the event of defective nodules. This will also help reduce the influence of defective nodes. At the beginning of the project, it was not known how many computers were needed to ensure that a conspiracy of defective computers could not “counteract” the efforts of computers that function properly to reach consensus. Shostak has shown that it takes at least 3n-1 and has developed a two-round 3n-1 messaging protocol that would work for No. 1. His colleague Marshall Pease generalized the algorithm for each > 0 and proved that the 3n-1 is both necessary and sufficient. These results, along with Leslie Lamport`s subsequent evidence on 3n sufficiency with digital signatures, were published in the groundbreaking Document, Reaching Agreement in the Presence of Faults.  The authors were awarded the 2005 W. Dijkstra Edsger Prize for this work. Byzantine errors are considered the most common and difficult class of errors among error modes. The Fail-Stop-Fail mode takes the simplest end of the spectrum.
While fail-stop error mode simply means that the only way to reach the defect is a node crash detected by other nodes, Byzantine errors do not involve constraints, meaning that the undone node can generate any data, including data that make it appear as a functional node.
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