Im just reading a book on the basics of blockchain and I encountered a confusion regarding the 51% attack. If I'm right, it says that an attacker holding 51% or more of the network's computing power can rewrite the blockchain to his own favor.
What confuses me is the following: Blocks in the mainchain can only be added sequentially, hence the growth speed of the blockchain is at most the speed of the fastest miner in the network. So if a attacker is faster than the fastest miner of the rest of the network can start at some lower block (maybe even the genesis block) and add his own blocks on a new branch one after the other. Since he is faster than the official main-chain, his branch will eventually be longer than the latter and consequently become the new main-chain.
So the attacker does not need 51% of the whole computing power, only more than any other node, which is usually much less than 51%. What is wrong here?