# Clarification on polynomial used in Rijndael MixColumns implementation

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?

• Did you read the first paragraph Rijndael MixColumns. I'm pretty sure that there are dupes for your question. Apr 24 '20 at 16:51
• @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? Apr 24 '20 at 17:41
• 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) Apr 24 '20 at 18:53