Hey guys,

I have a question regarding sidechains in the proof-of-stake cryptocurrency NXT but I guess it can also be expanded to any other cryptocurrency.

In a paper called "A Probabilistic Analysis of the Nxt Forging Algorithm", the author states the following attack:

"The attacker spends in the main chain and waits for some confirmations, and then broadcasts a (long) sidechain that would be accepted by the nodes as the main one."
And continues with:
"Therefore, in this section we analyse how many blocks in a row can be typically generated by a given account over a long period n of time."

Now I have read some things about sidechains but I still don't see what is happening in the mentioned attack. In particular, why is it necessary to generate consecutive blocks and not just generate more blocks than the mainchain does in a certain period of time?

I hope someone can help me here.