# AES 5 and 6 round SQUARE Attack

SQUARE attack on AES128 requires a single delta set for 4-round variant, or I assume single delta set is enough since keyspace is reduced to few keys which can be easily brute-forced. However, as we increase round number to 5, we need 5 delta sets approximately, as proposed by AES proposal. And further, for 6-round variant, we need about 10 delta sets. Is there a mathematical relation between the number of rounds and required delta sets, or is this pure heuristic? If there are any underlying mathematical relations, I couldn't spotted.

I am not able to execute a 5-round attack, since I'm following up the attack mentioned at the proposal, which requires a search on $$2^{40}$$ bits, and I'm not sure about the size of the resulting keyspace after using only one delta set. I mean, if we use a single delta set, is brute force still infeasible so that we want to use multiple delta sets, or is there any other reason?