I'm seeing the fundamental function in open source code for Rijndael MixColumns implementation. (Picture below) If i translate the 8'h1b correctly, it is represent the polynomial of $x^4+x^3+x+1$.

However looking at the wikipedia explanation, the multiplied modulo is $x^4+1$. May i know how to link them together? Anything I interpret wrongly?

enter image description here

  • $\begingroup$ Did you read the first paragraph Rijndael MixColumns. I'm pretty sure that there are dupes for your question. $\endgroup$
    – kelalaka
    Apr 24, 2020 at 16:51
  • $\begingroup$ @kelalaka, Thanks for guidance. So it is due to the shift operation, so the IP from x^8+x^4+x^3+x+1 become x^4+x^3+x+1 ? But i still don't understand how the multiplied module x^4+1 come into the picture? $\endgroup$
    – Pi-Turn
    Apr 24, 2020 at 17:41
  • 3
    $\begingroup$ 8'b1 is the AES(Rijndael)'s s Galois field. $ x^4+1$ is used when each column is multiplied with fixed $a(x)$. There is a nice tutorial A Stick Figure Guide to the Advanced Encryption Standard (AES) $\endgroup$
    – kelalaka
    Apr 24, 2020 at 18:53


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