"eXpande Shperic Linearization" - hey, i know this one - it's used to prove the Riemann hypothesis as well as Fermat's last theorem. AFAIR it can also be used for prime factorization in O(1)
I think everybody here knows that AES has been broken.
But a key space of 2^126 or 2^254 is still not feasible.
And 'side channel attacks' (eg. timing, power consumption) do not attack the algorithm but the implementation. Hence if the algorithm is properly implemented you won't get any results - unless you analyze the entire key space.