In the Classroom: Algebra II Cryptography and Computer Science

Linda D'Arco
Algebra II students are learning about cryptography, from Caesar’s time through World War II and present day. The class invited me to join in. Codes? Mystery? My inner Indiana Jones had to say, “Yes!” Read on for more about their cryptography and computer science Project Block class.

Math teacher Jeff Bush started the class off with a great historical introduction to cryptography. As someone who always sided more with the “humanities” programs than the math department, his introduction made the math approachable and interesting. Here are a few things Jeff taught us to get us started.

We learned that cryptography by definition is a means of sharing private information between two parties separated by a distance. It is an ancient form of communication. But, what happens if a third party intercepts the message? Students in Jeff Bush’s Algebra II class took some time to explore ciphers during project block today. We looked first at Caesar ciphers.

The Caesar cipher method of encryption is achieved by shifting a message by a certain number of letters in the alphabet. It was the first well-known cipher. Around 58 BC, Caesar shifted each letter in his military commands so they would appear meaningless to his enemies. This basic cipher was used for hundreds of years after Caesar, by military leaders. 

We discussed as a class what some of the flaws of a Caesar cipher would be. We talked first about single letter words. If the coded messages retained spaces between the words, it would be easy to discover the encryption method by figuring out how the letters “i” and “a” were coded. We considered doubled letters next because there are few letters that are doubled in English words. (This sparked a fun little side conversation on the number of words we could think of that had unusual double letters, like “z.”) Then we looked at the frequency of letters. If certain letters appear more frequently in a language (like “e” in English), it can be easier to break a code by looking for the way that one letter is represented. 

Then Jeff asked us? “How can a computer break this encrypted message easily?” Students replied, “It can make guesses more efficiently.” That’s right, said Jeff, “a computer can make the guesses much more quickly, and with the Caesar code, there are just 25 guesses. But, before the time of computers, and paper, and even broader literacy, an encryption method like the Caesar cipher would have been pretty effective.” Jeff showed the class a simple computer program and the code for it that could change their messages into encrypted language quickly through a digital Caesar cipher conversion.

We learned from a Khan academy video clip that the weaknesses of the Caesar cipher weren’t exposed until 800 years later when people started to consider letter frequency. The longer the message was, the easier it was to pick out repeated letters, like the letter “e.” We then had a chance to look at letter frequency as a code breaking method in class, as the students worked to crack a coded message Jeff gave them through an on line portal.

After a minute or two a weird spat of coughing erupted in class. It prompted me to lift me eyes from typing this article to ask an obviously over-zealously coughing Christian Brown ’17, if he needed a lozenge. Christian just laughed and said, “you’ll get it soon.” I took a peek over his shoulder and found that the message he’d cracked asked him to cough when he knew the answer.

The class also covered polyalphabetic ciphers, a “perfect secrecy” exploration, and a “frequency stability exploration.” By the end of the class, students were able to decipher this message and some others that I haven’t quite caught up to!

Leave a Reply