I am studying for an exam right now. And I wanted to make sure I got this point correct.
AES is not a Feistel cipher because the operations in AES are not invertible.
Is the above statement correct? If not, why isn't it a Feistel cipher?
Well, AES is not a Feistel cipher because it's a substitution-permutation network instead. If I were taking a test that asked me why AES was not a Feistel cipher, this would be my argument: namely, that the structure of substitution-permutation networks is fundamentally different from that of Feistel networks. (Here one could elaborate on invertibility and other differences.)
That said, your statement is not correct. In a Feistel cipher, the round function is not necessarily invertible (DES's round function is not), but in AES, like any substitution-permutation network, the rounds are invertible. This is a property of the construction itself.
By definition, a Feistel network uses a series of rounds that split the input block into two sides, uses one side to permute the other side, then swaps the sides. As always, Wikipedia has a nice diagram.
AES doesn't do this. Performing a round necessarily permutes the entire state. Each round consists of the
So only the
None of that matches the "split the block into A and B and use A to permute B" style of a Feistel network.