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I have just started learning AES algorithm.

S-Box is using Galois Fields $\text{GF}(2^8)$ math behind its computation and Shiftrows & MixColumn steps also doing some math at both encryption and decryption levels.

Do these calculations ensure any security? What is the actual use of this math?

What is the use of these steps, if 128/192/256 bit key is known for decryption?

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  • $\begingroup$ AES is used to implement symmetric cryptography, where a secret key is shared between sender / receiver (which may also be the same entity of course). The idea is that nobody else learns information about the plaintext (apart from information on the message size, some of which will always be leaked). $\endgroup$ – Maarten Bodewes Jun 11 '18 at 12:13
  • $\begingroup$ Hi @MaartenBodewes,Thanks for your comment.Now i understand that plain text will be converted into cipher text after doing this Math.But Why specifically Galois Fields (or Extension Fields).Does this ensures anything other than involving in cipher text conversion? (Just asking) $\endgroup$ – iSpark Jun 11 '18 at 15:19
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SP-net consists of substitution and permutation layers. S-boxes implements substitution, Shiftrows & MixColumn implement permutation.

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The reason this mixing is done between adding in the round keys is to spread the plaintext bits all over the ciphertext. So actually the equation for a single bit of the ciphertext relies on all plaintext bits. Without these steps the repeated adding of the rounds keys would not provide any more complexity than a single round.

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