Could affine transformation mod 2^128 be a side-channel attack problem
I do not know of this cipher; however, if you explicitly calculate everything, ie: do not use arrays or lookup tables, you are not susceptible to timing attacks.  Basically, you treat the mathematics like you are on hardware, using only base logic, and it's quite slow, but it's safe because it takes equal time to calculate every value.
Having said that, you basically could not easily calculate something that large in this manner.  $2^{64}$ is a huge number, and 64-bits quickly explodes into something large in the world of logic gates.