Byzantine Generals’ Problem

When communication within a group or party cannot be trusted or verified, it is a situation where consensus on a single strategy is required from all members.

A situation where communication that requires consensus on a single strategy from all members within a group or party cannot be trusted or verified.

What Is the Byzantine Generals’ Problem?

The Byzantine Generals’ Problem is a thought experiment that deals with a key question of computer science: is it possible to form a consensus in a computer network composed of independent, geographically distributed nodes?

The problem was proposed in 1982 by researchers from the SRI International Research Institute. 

It goes as follows: there are a number of Byzantine generals besieging a city. They can only communicate via sending messengers to each other. The generals must agree on a common plan of action: whether to attack the city or retreat. However, some of the generals are traitorous and actively working against the forming of a consensus; their number and identities are unknown.

The question posed by the problem is what decision-making algorithm the generals should use to devise a common plan — regardless of the traitors’ interference — and whether such an algorithm exists at all.

According to the researchers’ own analysis, such a system is indeed feasible, but the number of loyal generals must strictly exceed two-thirds. For example, in a situation with three generals, one of which is traitorous, the loyal ones can never guarantee that they will be able to reach a consensus.

This problem is highly relevant for cryptocurrencies as they are, in essence, distributed computer systems: they are composed of transaction-processing nodes that are independent of each other and any central authority and can only communicate remotely. They are the “generals” that need to reach a consensus about which transactions have taken place and when.
Nodes have the potential to supply faulty data about transactions either by choice or by accident, and their information must be sorted out. Bitcoin (BTC) and other cryptocurrencies solve this problem via technical solutions such as the proof-of-work and proof-of-stake algorithms.
See Byzantine Fault Tolerance (BFT).