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.
- Fifty-one percent, or
- Fifty point one percent.
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
|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
- BTF : Byzantine Fault Tolerant
- DLT : Distributed Ledger Technology
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!