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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?

Answers appreciated. Thanks

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Found an answer here:

For each group of 256 plaintexts, this filter rejects 255/256 of all wrong key guesses. As we guess a total of nine key bytes, we will need 10 or so groups of 256 encryptions to find the key.

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