I had searched a lot but I don't undestand how work the operation on binary (How to solve MixColumns). What I don't undestand is from where he catch 0001 1011 to do the XOR operation.

Can someone explain me? Thanks in advance for the replies.


1 Answer 1


Do you mean where we come up with 0001 1011 (also known as 0x1B)? That's actually mentioned in the answer:

Multiplying by $2$ is what your question is about: it is equivalent to shifting the number left by one, and then exclusiving-or'ing the value 0x1B if the high bit had been one (where, in case you're wondering, the value 0x1B came from the field representation)

That is, the $GF(2^8)$ representation that AES uses is a polynomial representation, based on the irreducible polynomial $x^8 + x^4 + x^3 + x + 1$; 0001 1011 (or 0x1B) are the lower 8 bits of that polynomial.

If you don't understand that, well, just assume that 0x1B is a magic value that just happens to make things work...

  • $\begingroup$ Thanks poncho for the help. Is this correct root25.com/2012/12/…? $\endgroup$ Commented Oct 24, 2017 at 9:50
  • $\begingroup$ @Dragonfighter: it looks about right $\endgroup$
    – poncho
    Commented Oct 24, 2017 at 15:05

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