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Would variants of AES provide the same level of security as AES, say by just replacing the S-box with another one, MDS matrix of Mixcolumn, etc.?

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    $\begingroup$ What research did you do? I’m asking, because you seem to be unaware of already existing questions like… Replacing the Rijndael S-Box? $\endgroup$ – e-sushi Aug 21 '14 at 14:33
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There is book Algebraic Aspects of the Advanced Encryption Standard thats gives a good algebraic description of the AES algorithm. Reading it you'll see that there was some freedom in choosing some parametres to fix a standard. Changing this choices, but keeping the algebric properties should give you an equivalent algorithm. This mainly means you can change the irreductible polynomial used to define the field, ...

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