Could affine transformation mod 2^128 be a side-channel attack problem DFC cipher uses affine transformations mod $2^{64}+13$. Soon after DFC's publication, Ian Harvey raised the concern that reduction modulo a 65-bit number was beyond the native capabilities of most platforms, and that careful implementation would be required to protect against side-channel attacks, especially timing attacks.
Consider a cipher which is using affine transformations mod $2^{128}$. Is it still (it was 20 years ago) a problem to implement it securely? Will affine transformations mod $2^{64}$ make a big difference?
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.