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AES with linear s-box

suppose I have made changes in AES by removing the non-linear S-box and replacing it with a linear function. I know that by removing the non-linearity of the S-box I'm making the AES vulnerable to known-plaintext attack. how can I determine the amount of (P, C) pairs I need in order to perform the attack and how much time it will take? is there a calculation I can make? couldn't find anything about the calculation.

for example, if my new function is to do right shifting on the binary representation of each bit instead of the usual S-box.


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