Question

In a Byzantine Fault Tolerant consensus system, what is the maximum number of malicious nodes (f) allowed in a network of (n) nodes to ensure the system remains functional?

Accepted Answer

In a Byzantine Fault Tolerant system, the network must contain at least 3f + 1 total nodes to tolerate f malicious nodes. This formula is derived from the requirement to maintain consensus despite nodes that may fail silently, provide incorrect information, or act maliciously to disrupt the system. A node is considered Byzantine if it exhibits arbitrary behavior, such as sending conflicting messages to different parts of the network. To ensure safety and liveness, the system must receive consistent information from a quorum of nodes. A quorum is a minimum number of nodes required to agree on a decision before it is considered valid. In this system, you must have enough honest nodes to reach a majority while still accounting for the possibility that f nodes are malicious and f nodes are slow or unresponsive. If you have n nodes, you must be able to verify the state of the system using a set of nodes that excludes the f malicious ones. The requirement n is greater than or equal to 3f + 1 ensures that the honest nodes always outnumber the malicious ones, even when accounting for the worst-case scenario where f nodes are both malicious and non-responsive. For example, if you have 4 total nodes, you can tolerate 1 malicious node because 3 nodes remain honest, which is enough to form a quorum and verify the truth. If you had 3 nodes, 1 malicious node would represent one-third of the total, making it impossible to distinguish between a faulty node and an honest one, thereby preventing a reliable consensus.

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In a Byzantine Fault Tolerant consensus system, what is the maximum number of malicious nodes (f) allowed in a network of (n) nodes to ensure the system remains functional?