【Byzantine Generals Problem】Explanation of Basic Terms
How to Reach Consensus in a World Full of Liars
Good morning.
I’m Mitsui, a web3 researcher.
Every Saturday and Sunday at noon, we’ll deliver articles explaining basic vocabulary. We aim to keep each article concise enough for a quick read, while also providing content you can revisit and study.
Today’s topic is the “Byzantine Generals Problem.”
Please watch until the very end!
1. What is the Byzantine Generals Problem?
This problem was proposed in 1982 by computer scientist Leslie Lamport and others.
Let’s consider this with an analogy.
Several generals of the Byzantine Empire are besieging a city. The generals have established their camps in separate locations and communicate messages using messengers. They must take unified action: either “attack together” or “retreat together.”
The problem is that there may be a traitor among the generals.
A traitor might tell one general to “attack” and another to “retreat.” If everyone makes conflicting decisions, the army will be destroyed.
In other words, the essence of this problem is as follows.
Can everyone arrive at the same correct judgment in a situation where there may be a liar among the participants?
This is the Byzantine Generals Problem.
2. Why is this problem difficult?
At first glance, it seems simple. Why not just take a majority vote?
However, distributed environments present several fundamental challenges.
The message is not credible.Messages may be tampered with during transmission. There is no way to verify whether the received message truly reflects the sender’s intent.
I don’t know who’s being honest.On a network, it is difficult to verify participants’ identities and intentions beforehand. A traitor can pretend to be honest.
There is no central administrator.If there were a trusted “commander” everyone followed, we could simply obey their orders. But in a distributed system, there is no such privileged entity. Everyone is equal, and everyone is a potential traitor.
When these three conditions coincide, reaching a proper agreement becomes extremely difficult.
3. Byzantine Fault Tolerance in Distributed Systems
The ability to handle this problem is called “Byzantine Fault Tolerance (BFT).”
BFT refers to the property that allows a system to maintain correct consensus even if some network participants fail or act maliciously.
In classical BFT research, an important threshold has been demonstrated.
If honest participants make up more than two-thirds of the total, a correct consensus is possible.
Conversely, if traitors account for more than one-third of the total, consensus formation can no longer be guaranteed.
For example, if there are 10 participants, the group can tolerate up to 3 traitors, but if there are 4 or more, consensus may break down.
This “two-thirds rule” lies at the core of the design philosophy for many blockchain protocols.
4. How did Bitcoin solve this?
In 2008, Satoshi Nakamoto published the Bitcoin white paper. This presented a practical and groundbreaking solution to the Byzantine Generals Problem.
Bitcoin adopted a mechanism called Proof of Work (PoW).
The essence of PoW lies in “cost-based voting.”
Network participants (miners) perform massive computations to generate new blocks. These computations incur real-world costs (electricity, hardware). Contributing to a valid ledger earns a reward, but attempting to create a fraudulent ledger wastes those costs.
In other words, Bitcoin replaced the problem of trust with economic incentives.
Creating situations where lying is “not worth the trouble” encourages honest behavior.
This approach differs from classical BFT, which assumes “two-thirds honest nodes.” Rather than relying on participants’ goodwill, it leverages rational economic behavior. As long as a majority of computational resources (51% or more) are honest, the network functions correctly.
5. How is Ethereum (PoS) different?
Ethereum transitioned to Proof of Stake (PoS) following The Merge in 2022.
In PoS, voting is backed by “stake” (collateral) rather than computational power.
Validators participate in the network by staking ETH. They receive rewards for correct validation, but if they act maliciously, their staked ETH is confiscated. This confiscation mechanism is called slashing.
Let’s clarify the differences between PoW and PoS.
In PoW, proof of correctness is achieved by consuming electricity and computational resources. This structure ensures that “lying would result in wasted computational costs.”
In PoS, assets are pledged as collateral to guarantee correctness. It operates on the principle that “if you lie, your assets will be confiscated.”
Both are essentially the same.Economic rationality serves as a deterrent against betrayal.
PoS adheres to the classical 2/3 rule of BFT, guaranteeing finality (confirmation of consensus) as long as more than two-thirds of the stake is honest.
6. The Byzantine Problem Reveals the Essence of Web3
Understanding the Byzantine Generals Problem makes the design philosophy of Web3 clearer.
Design that doesn’t trust people.Blockchain is designed so that you don’t need to trust specific individuals or organizations. It doesn’t matter whether participants are good or bad. The mechanism itself ensures correctness.
What is right is decided by the majority.In blockchain, the “correct ledger” is the one selected by majority consensus. There is no absolute truth; instead, the collective judgment of participants becomes the rule.
There is no such thing as absolute safety.Byzantine fault tolerance has its limits. If a majority of participants or two-thirds of the stake become malicious, the system can fail. Blockchain is not a “magic safety device,” but a consensus system that functions under specific conditions.
Summary
Blockchain is not a “magical ledger that cannot be tampered with.” It can be described as a consensus mechanism designed to function even in a world where there are liars.
The Byzantine Generals Problem is the starting point for this design. How to reach consensus in an environment with untrustworthy parties? Bitcoin proposed a solution through computational cost, while Ethereum proposed a solution through staking.
Understanding Web3 also means accepting the premise of “cooperating under conditions of distrust.”
Disclaimer：I carefully examine and write the information that I research, but since it is personally operated and there are many parts with English sources, there may be some paraphrasing or incorrect information. Please understand. Also, there may be introductions of Dapps, NFTs, and tokens in the articles, but there is absolutely no solicitation purpose. Please purchase and use them at your own risk.
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mitsui
A web3 researcher. Operating the newsletter “web3 Research” delivered in five languages around the world.
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The author is a web3 researcher based in Japan. If you have a project that is interested in expanding to Japan, please contact the following:
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*Please note that this newsletter translates articles that are originally in Japanese. There may be translation mistakes such as mistranslations or paraphrasing, so please understand in advance.