# What is the required group theory knowledge needed to understand Verhoeff's algorithm?

The Wikipedia page tells me I need to understand permutation groups and dihedral groups. Can someone clearly outline what exactly the perquisites of understanding this is and how much time I'll take to understand this ?

I know some basic group theory. I don't know what dihedral groups are and I haven't studied information theory.

• This is a nice question -- just learned that this sort of checksum was used for pre-Euro German banknotes earlier today; what a happy coincidence! – pjs36 Jun 7 '16 at 5:10
• here it is the dihedral group $D_5$ which is used, not very complicated, see its operation table en.wikipedia.org/wiki/Verhoeff_algorithm#Table-based_algorithm . in a regular checksum, the group operation used is the addition modulo $10$, while here we send the digits to $D_5$, and the operation are computed in this group. – reuns Jun 7 '16 at 5:32
• at first you need to understand what is a checksum. en.wikipedia.org/wiki/Checksum , then think to how it is possible to improve it for detecting the most frequent errors in this particular case of Dutch postal system – reuns Jun 7 '16 at 5:34
• I understand what a checksum and an invariant is. But, not so much what a dihedral group is. – user230452 Jun 7 '16 at 6:16