Statement: for an attacker to change history, they must solve computational puzzles at a faster rate than the rest of the participants combined

Question

I'm new to cryptocurrency and blockchain. I just started reading the textbook Bitcoin and Cryptocurrency Technologies by Narayananm, Bonneau, Felten, Miller and Goldfeder.

The statement in the title is given in the introduction to the book (page 17 in the pre-publication draft for anyone interested)

I'm assuming it is accurate and that it is connected to the architecture of the bitcoin blockchain. However, I don't quite understand why this is the case. Is it because in order to change history you need to change the entire chain up to the block you want to change? And why do you need do be faster than all others combined?

Any explanation would be greatly appreciated!

Edit: Later, on page 33:

as long as we store the hash pointer at the head of the list in a place where the adversary cannot change it, the adversary will be unable to change any block without being detected.

Does this mean that if the head pointer is unalterable (the genesis block) the statement is false?

Answer 1

I will answer my own question for anyone that might be wondering the same.

If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes.