Variants of AES?

Question

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.?

Answer 1

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, ...