Reply To: !

[the_cryptographer_formerly_known_as_madness]

Speaking of commutation, and speaking of ciphers, have you noticed that if you encrypt a document with a Vigenère cipher and then encrypt the result with another Vigenère cipher, then the overall result is the same as if you switch the order of the two encryptions?

Now try it with two Beaufort encryptions. Here the order matters. Why?

The way I like to think about it is by putting the 26 letters evenly spaced on a circle. A Vigenère cipher is like a set of rotations of that circle, but Beaufort is like a set of reflections. Each key letter is a different angle of rotation for the V, and a different axis of reflection for the B.

Now here is something to really blow your mind: That text that was encrypted with two Beauforts can be decrypted with one Vigenère. Figure out what that means.

For the mathematicians in the audience, think dihedral group.