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¿Can it be proved that both AES's ShiftRows and MixColumns are linear transformation? (if we leave out subBytes and key addition)

sy flag

I've been researching a bit and found that the mixColumns step could be expressed as matrix multiplication like this:

matrix permutation example

But I'm not sure what's the mathematical proof for it and I can't find an example for the ShiftRows step.

Any hints? (thanks in advance)

DannyNiu avatar
vu flag
To prove it, just express it as a vector of 128 bits multiplying with an 128x128 bit matrix in GF(2).
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