In many sources, included Wikipedia, we read:
Any pool that achieves 51% hashing power can effectively overturn network transactions, resulting in double-spending.
My question is: Why do we talk about 51% attack?
If my understanding is correct, we could also say 50.1% attack or 50.01% attack.
More simply, wouldn't it be wiser to use "50% attack" idiom?
From Bitcoin Wiki;
A majority attack (usually labeled 51% attack or >50% attack) is an attack on the network.
It is also called consensus attacks.
It is only to demonstrate that one needs the majority. The majority is simply $\geq n/2$ where there are $n$ participants. If we normalize it to 100 we can say $>50\%$
51% sounds better than 50.1% and is easy to hear.
One might even ask why not 50.00000001%? Any value $> 50$ is correct. 51% easy to get the notion.
Actually, it is shown that one may need just over 30% (need a real ref than below)
This is from Antonopoulos's book; Mastering Bitcoin
Security research groups have used statistical modeling to claim that various types of consensus attacks are possible with as little as 30% of the hashing power
Unfortunately, there is no reference for this in the book. With a little search;
| Name of weakness | Description |
|---|---|
| Consensus 34% Attack | 34% Attack against BFT network, a specific instance of Consensus Majority Attack |
| Consensus 51% Attack | 51% Attack against DLT network, a specific instance of Consensus Majority Attack |
A nice website from MIT's digital currency initiative: 51% attacks
And note that this attack can only be used for double-spending, private keys are safe!