Hmmm.. the description for GF2P8AFFINEQB states it is performing computations in the field GF(2^8). However, afaict in actuality it's performing computations in the vector space GF(2)^8, which is of course a very different algebraic structure. What am I missing?
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Now if you have a multiplication with a constant in GF(p^n), that's a linear map. This is still true in the corresponding vector space, so it can be respresented by a matrix in GF(p)^n. The converse is not true, as linearity in GF(p)^n is a weaker condition than in GF(p^n).
Thanks! This makes sense. I think that's also the method Knuth describes for doing CRC with the MMIX MXOR instruction. But that's essentially a scalar operation in a finite field, right? Not sure I'd call it an "affine transformation". Never seen that term used in 1D.
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I'm not aware of that method, but it sounds like it could be this. Over GF(2^8) it's just a scalar operation. The naming is a bit confusing because ax + b is often called linear function, but when talking about properties of functions, it's affine and only linear when b = 0.
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So, "affine transformation" in English is just the same as "inhomogene lineare Funktion" in German, and "linear function" in English is the same as "homogene lineare Funktion" in German? How did I make it this far without knowing this? :D
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