[mananaysiempre]

Incidentally, how is it a GF(2^8) affine transform? As best as I can tell, it’s a GF(2)^8 affine transform, i.e. an affine transform of vectors of bits with normal XOR addition and AND multiplication, and the polynomial defining GF(2^8) just does not enter anywhere. It does enter into GF2P8AFFINEINVQB, but I’m having difficulties finding a geometric description for that one at all.

[pclmulqdq]

I believe that the polynomial for GF2P8AFFINEQB is user-defined. One argument is an 8x8 matrix in GF(2) and the result is [A.x + b] in GF(2)^8 for each 8-bit section. Don't quote me on this, but I believe that matrix multiply in GF(2)^8 gets you a transform in GF(2^8).