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No, that's not really possible without blatant flaws of the implementation. Modern modes of operation of ciphers are resistent to attacks even if you know many pairs of plaintext and ciphertext - and the IV is public knowledge. Knowing it is the normal case. You also didn't mention what operation mode was used. Well, of course you could brute force the key, ...


Welcome to crypto SE. I guess, you are referring to the mix columns operation from the point of view with polynomials over $GF(2^8)$. A detailed explanation of this can be found at Wikipedia. It is a quite unusual structure, but it behaves just like you would consider any $GF$. The columns are first considered as polynomial, or better: as coefficients ...

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