# How does the Rijndael 192/256 bits block size mix column works?

I am quite comfortable about the 128 bits block size mix column operation, the maths behind it and how to implement it.

However, what about the 192 and 256 bits block size? I can't find any paper describing it.

Do you simply do two times the operation? For 192 one full time and one with half the bits being set to 0 as place holders, and two full time for the 256 bits block size?

Since I'm not supposed to have link-only answers, I'll try to explain it myself. The state in Rijndael is represented by a $4 \times n$ matrix of bytes (where $n=4$ for 128 bit blocks, the AES case, and $n=6$ for 192 bit blocks and $n=8$ for 256 bit blocks). When you perform the Mix Column step, you take each column in the matrix, and multiply it by the fixed polynomial $03x^3 + x^2 + x + 02$ modulo $x^4 + 1$. This operation is precisely the same as in AES, except that if you have a larger block size, you have more columns; you still apply this multiplication only once for each column in the matrix.