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A Little Cryptography

May 28, 2021 pm31 11:51 pm

I’m teaching a Number Theory elective this Spring, and trying to have some fun.

I chose a text, and I knew we would finish it in April, which we did.

And I gave students some choices of what to explore next. While they were choosing, I started a unit on old encryption systems, biding time, figuring they would pick a new direction.

But the direction most picked was to learn a bit of math that underpins modern cryptosystems, so learning a bit more about old systems made sense. Plus, they were having some fun. It’s one thing for me to claim that a code is easy to break, it’s another for me to post gibberish, and for my students figure out what it says.

They don’t own Captain Midnight Decoder Rings, but if they did, the rings would have been perfect for the first few lessons.

I told them to dial the rings to G and to decode the text I gave them. Wow! they all got it. Then I told them to encode a text (sounds bad, but just 250 characters). Not a problem.

Then they looked at encrypted stuff without knowing the key, but the one-letter words gave the key away.

Then we took away the spaces. Who needs them? And they make it too easy to break the code. But letter frequency gives it away. English has lots of As and Es and Ns and Ts, and not so many Qs or Zs.

Once students learned to break codes by letter frequency, even with the spaces gone, we decided it was a good thing we didn’t invest in Decoder Rings.

Next we looked at Napoleonic systems, that involved FOUR (4) or MORE (more) Captain Midnight Decoder Rings. That takes us historically up to the US Civil War (the slaveholders used this outdated cipher, some surprise), and in today’s time, up to today. I can show students how to break this system, and why it is eminently breakable, but breaking it is still hard, and only a few will even attempt it on their own. That’s ok. This has been fun. And next i’ll show them some of the mechanics of Enigma, and some of the basics behind modern stuff (Enigma shouldn’t count as modern).

But that’s all background.


Any part of that I got right, I owe to Dr. Kent Boklan of Queens College who taught a massively enjoyable class on Cryptography when I was on sabbatical. My group (we did group work) got some cipher text encrypted with Enigma, and we broke it. (Yay!).

And any part of the above I got wrong, I owe to not paying close enough attention in class.

That’s also background.

Choice of Text

I have to choose things to encrypt. And then ask a question. I could ask “first three sentences” “blah blah” “name of author” etc etc. Or I could ask things like, “Who wrote this, and why is he so angry?” Which I did ask (George Wallace on the passage of the Civil Rights Act of 1964)

I have picked some righteous words. Frederick Douglas, on Caribbean emancipation. Mohammad Ali, on why he would not fight in Viet Nam, Leonard Peltier: “America, when will you live up to your own principles?”

There was a boring abstract from the World Health Organization. It was so loaded down with Cs and Vs (Covid vaccines and variants) that it made the frequencies challenging.

There are classics. Edgar Allen Poe’s The Bells (letter frequencies go off in poetry), the prologue to the Canterbury Tales (some English looks funny, and has skewed frequencies).

Songs. Mail Myself to You (really cute, if you’ve never listened, you should). The Guns of Brixton. This Land is Your Land (lots of As, not so many Es in that one). My Rambling Boy was yesterday.

There was an unfair one (I think I got the key, but it doesn’t look like English). They were correct, it was the first few of the 95 theses. I don’t think anyone broke that one.

Another time they couldn’t get the key. But there were only 12 letters, which was a clue. And a few of them checked, and that sounded like something Polynesian. One guessed, correctly, Hawaiian. And then decrypted the Lords Prayer. Pretty impressive.

Choice of Text

I have also assigned students to encrypt texts of their choice. That’s fun, too.

I get popular songs.

I got “I Have a Dream”

I got a Sponge Bob song.

I got an excerpt from the Hobbit.

I have gotten philosophers. And poets.

An excerpt from the Communist Manifesto.

And a bicycle repair manual.

Last week I got a guide to answering questions on the AP English Language exam.

And a reading from an economics class.

More Fun Than Teaching Logarithms

It’s true.

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