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Almost the same question as my “Why are the shiftrows in AES in a fixed order? Can the order be changed?” but this time it’s about the AES MixColumns.

Why are the mixcols fixed? Can we keep adequate security by changing the order? If not 'any' order, what about some other arrangements? Or is this arrangement the only one suitable?

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What do you mean by "order"? Each column is "mixed" independently using the same operation. If you are talking about the MixColumns matrix, of course you can change it, but

  1. the operation defined by the matrix must be bijective;
  2. the matrix should have low linear and differential branching numbers (optimal in case of the AES MixColumns).
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