I was just at another school where I had the opportunity to talk about the mathematics involved in communication. One of my favorite subjects in math is number theory, so when I was asked to speak my mind when straight to encryption.
The class was fun, and students (and teachers) had a great time manipulating the cipher wheel. One student even shouted out “Can all of the teachers please leave so Mr. Wolf can teach us this encryption without them knowing how to decrypt?”
I only had the opportunity to speak about a simple shift cipher; how to encrypt, decrypt, and break the code. I also had about 1 minute to speak about the Vigenere Cipher, but alas, I ran out of time. If I had a whole semester I would have spoken about public key cryptography, the discrete logarithm problem, Diffie-Hellman, and RSA.
What fascinates me about encryption is that such simple math can be the cause for extremely tight and secure encryption. Until you get into complex code breaking and sieves, the entire process of encryption and decryption is totally arithmetic: anybody with half a high school education can learn it.