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# AES— Brute force attack versus Known plain text attack

I am taking a codes and cryptology course and the following is a questions on a past exam that I could not and still can't solve:

 Suppose that E sub k denotes the function that encrypts a message M with AES,
where K is the 128-bit key. Suppose that a cryptographer discovers a function F
so that E sub k(M)=F sub k1(F sub k2(M)), where k1 and k2 are each 64-bits, and K
is easily computable from k1 and k2. Explain how one would use this to mount a known
plain text attack on AES that is faster than brute-forcing the 128-bit key.


If someone could provide a step by step explanation of how to do this, it would be greatly appreciate! Thanks in advance!