AES has been rigorously tested against all known attacks. However, I believe there are 30 suitable irreducible polynomials that could be used for AES. If we were to change the current irreducible poly to another suitable one:
- how can we be sure it will still be protected against DCA and LCA attacks?
- can we show it is still protected against DCA, LCA and other attacks without having to test large amounts of data? If so, how?
- how, if at all, would this change other parts of the cipher (e.g. MixCols)
I have tried to find clear answers on this but they seem hard to come by. Many books have merely asserted that changing the irreducible poly (to one of the other 29) would not adversely affect security, but I cannot find a clear reasoning.
A simple answer with clear examples would be much appreciated. I am still very much a beginner in cryptography.