# Tag Archives: Group theory

November 7, 2011, 7:45 am

# Math Monday: Columnar transposition ciphers and permutations, oh my

I hope you enjoyed Ed’s guest posts on NP-complete problems on TV the last couple of Mondays. It’s always great to hear from others on math that they are thinking about. This week it’s me again, and we’re going to get back to the notion of columnar transposition ciphers. In the first post about CTCs, we discussed what they are and in particular the rail fence cipher which is a CTC with two columns. This post is going to get into the math behind CTCs, and in doing so we’ll be able to work with CTCs on several different levels.

A CTC is just one of many transposition ciphers, which is one of the basic cryptographic primitives. Transposition ciphers work by shuffling the characters in the message according to some predefined rule. The way these ciphers work is easy to understand if we put a little structure on the situation.

First, label all the positions in the message from $$0$$ to …

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