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I'm trying to understand how AES guarentees security. One of the named points on the web is that AES uses a non-linear step (the SubBytes step). But how exactly does the Rijndael key schedule add security? It sounds like a wide question, but for me, not exactly an expert, it's hard to understand.

Help is appreciated

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    $\begingroup$ The title asks how non-linearity (S-box) adds security. The body of the question adds how the Rijndael key schedule adds security. Please clarify what's asked. Do you understand how, regardless of the key schedule's output, non-linearity is essential for security of AES? $\endgroup$
    – fgrieu ♦
    Nov 24, 2015 at 16:48
  • $\begingroup$ I said that because the non-linearity (S-box) is part of the Rijndael key schedule. No, I don't understand. $\endgroup$
    – Thomas Wagenaar
    Nov 24, 2015 at 16:49
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    $\begingroup$ The non-linearity is also, and foremost, part of the encryption itself. In the formal specification of AES by NIST, FIPS 197, SubBytes is not even part of the key schedule (the corresponding non-linear operation is called SubWord). Hint to answer your own question without the key schedule part of it: assume that a function $f$ is said to be linear iff $\forall (x,y,z), f(x\oplus y\oplus z)=f(x)\oplus f(y)\oplus f(z)$. What can you say about the composition of linear functions? $\endgroup$
    – fgrieu ♦
    Nov 24, 2015 at 17:13
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    $\begingroup$ @fgrieu Even without the ambiguous context I find the question of how the key schedule adds security to be quite ironical given that the key schedule appears to be the weakest part of AES. $\endgroup$
    – kasperd
    Apr 10, 2016 at 12:53

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actually in most of methods like AES,DES have two important phenomena ,one is confusion and other is diffusion.so in whole process only Sbyte step bring confusion(brings non-linearity) while in diffusion data is just misplaced not changed.

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