ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 16 Feb 2018 14:06:40 +0100How do you calculate the branch number of a matrix?https://ask.sagemath.org/question/41152/how-do-you-calculate-the-branch-number-of-a-matrix/ Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:
$$02\quad 03\quad 01\quad 01$$
$$01\quad 02\quad 03\quad 01$$
$$01\quad 01\quad 02\quad 03$$
$$03\quad 01\quad 01\quad 02$$
These entries are hexadecimals (or bytes), e.g. in bits $\{02\}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).
I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.
I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.
A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.
Redbook1Fri, 16 Feb 2018 14:06:40 +0100https://ask.sagemath.org/question/41152/