November 21, 2011, 7:45 am

By Robert Talbert

It’s been a couple of Math Mondays since we last looked at columnar transposition ciphers, so let’s jump back in. In the last post, we learned that CTC’s are really just permutations on the set of character positions in a message. That is, a CTC is a bijective function \( \{0, 1, 2, \dots, L-1\} \rightarrow \{0, 1, 2, \dots, L-1\}\) where \(L\) is the length of the message. One of the big questions we left hanging was whether there was a systematic way of specifying that function — for example, with a formula. The answer is YES, and in this post we’re going to develop that formula.

Before we start, let me just mention again that all of the following ideas are from my paper “The cycle structure and order of the rail fence cipher”, which was published in the journal *Cryptologia*. However, the formula you’re about to see here is a newer (and I think improved) version of the one in the…

Read More

October 10, 2011, 10:53 am

By Robert Talbert

http://www.flickr.com/photos/maistora/

We all have secrets to keep. Those secrets could be personal dirt we want to keep from others, or they could be something as mundane as our credit card numbers or medical histories. But all of us have information that we want to keep to ourselves or at least to a small circle of people whom we select. This is why the field of **cryptology** — the science of making and breaking coded messages, or more generally the notion of communicating in a secure way — is a viable and extremely active field of study these days.

I’ve been interested in cryptology ever since a student came to me in 1999 and asked me to direct an independent study on the subject for her. I’ve since taught topics courses in cryptology to math majors and to liberal arts students, and it always…

Read More