Is it beautiful? Reflections on teaching Cryptography!

Today, we had a professional learning day where we concentrated on 5 principles of curriculum implementation. The final principle was: Is it beautiful? Immediately, I thought of some 3D animations that some students were creating. My second thought was: Cryptography! Bear with me, I will explain it! If you cannot "bear with me", feel free to skip to the section: How I know it is beautiful!

Cryptography in Year Eight

For the last three years, we have been teaching some basic cryptographic techniques to our Year Eight Digital Technology students. This is where you take a message and, using a mutually agreed system of encoding text, you make it incomprehensible to all but the intended recipient. The unit is challenging and well designed. Credit goes to my brilliant colleague, Luisa Ochoa, who was the first to teach the course and who put the unit togther. Let me give you an example:

A Caesar Cipher is possibly the earliest method of encrypting text: Shift the letters of the alphabet. Figure 1 below shows an example of this, where the A has been lined up with T, the B with U and so on.

Figure 1: Cipher Wheel

Using the Cipher Wheel in figure 1, we can encrypt Hello. Writing the letters on the inside of the wheel, we get Axeeh. In theory, only someone who knows how our wheel was set up can decrypt the message and recover our "Hello".

In the Year Eight course, we teach students how to use Caesar Ciphers to encrypt and decrypt. We also teach them the flaws that make them easy to "crack" and then we move on to stronger Ciphers.

The students are challenged, especially when we start writing computer programs to encrypt and decrypt a letter at a time, leading up to entire messages. However, they seem to enjoy the topic!

Cryptography in Year Ten

In Year 10, we discuss modern day cryptography: The kind used to encrypt our passwords when we log on to Instagram or when we connect to our bank account.

They learn that all of the methods used until World War II suffered from one major flaw: The sender and receiver needed to exchange the "key", the wheel setup in the above example. Failing a secure exchange of the key, our messages would be susceptible to being read by our "enemies".

Modern day cryptography uses clever mathematics to obviate the need for the exchange of keys. Instead, each person can have two keys, a public key and a private key. It is OK to share your public key with the entire world, including your enemies! They can only use it to encrypt messages and send them to you. You can then use your private key to decrypt those messages. Knowing your public key does not help people work out your private key! 

The image often used to illustrate modern-day cryptography is this: You distribute locks to the world. Anyone who wants to send you a secret message needs to put the message in a box and secure it with your own lock. Only you have the key to the lock.

When we practise using this kind of cryptography, using the students' CAS calculators, they find it fascinating that such a thing can happen!

How I know it is a "beautiful" piece of curriculum

Well, there's the ability that we, teachers, claim to have to "read the classroom". Apart from that, at the end of each cryptography unit, I tell students about Simon Singh's very good book: The Code Book for Young People. No student ever read a popular science book I recommend! That was until this week.

 

Earlier this week, a student in Year 8 and another, in Year 10, showed me their copies of the book! They wanted to spend time finding out more about the topic and that is Beautiful!