June 2017 Archways

Cracking the Code

At their simplest, they are used by kids passing notes in class and at their most complex, by governments carrying out military operations. In between, they are used by people every time they pull out a credit card or shop online.

By Matt Gray

Codes substitute arbitrary symbols—typically, letters or numbers—for the components of the original message. Ciphers use algorithms to transform a message into an apparently random string of characters.

In “Codes and Ciphers,” a special topic course offered
 recently by the mathematics department, students learn the difference and get  an introduction to classical 
and modern methods for encoding secret messages (cryptography) and the science of breaking codes and ciphers (cryptanalysis). It blends the history of secret writing, the art of creating codes, and the mathematics underlying the theory and practice of encryption and decryption.

“The puzzle nature of 
the course really appeals to 
students,” says Penelope Dunham, a research associate who offers the course. “Math majors and science majors love to solve puzzles.”

The course begins during the time of the Greeks and Romans with examples such as the Caesar cipher and proceeds all the way into the modern era. The Caesar cipher is a shift cipher, one of the simplest forms of encryption in which each letter of the message is replaced by a letter a certain number of positions down in the alphabet.

Some of the key moments in history that the class studies are the decoding of the Zimmerman Telegram in 1917 and the Allies’ successful cryptanalysis of Germany’s Enigma machine during World War II.

Intercepted and decoded by British intelligence, the Zimmerman Telegram was a secret diplomatic communication that proposed a military alliance of Germany, Mexico, and Japan in the event that the U.S. entered World War I. Its release inflamed U.S. public opinion and generated support for a declaration of war.

By World War II, the Germans were transmitting encrypted messages via the Enigma machine, but the British broke that as well. “Many students have seen the film The Imitation Game,” says Dunham, “but I think they’re still surprised to 
learn just how important the 
breaking of these codes has 
been throughout history.”

“The students really enjoy the first half of the course because it’s stuff they can break,” says Dunham. “When we get to things like the Enigma machine and the computer era, the students can no longer break the ciphers, so then it becomes more about learning the mathematics 
behind them.”

Today, thanks to the need 
to send data securely online, cryptography is an unseen part 
of everyday life, and students with the right math skills are in high demand.

“I’ve had two of my students go on to work for the National Security Agency, which is now one of the top employers of 
math Ph.D.’s in the world,” 
says Dunham.

The Key

At left are the keys to solving the puzzle.

If you failed to crack the code using the puzzle that appeared in the print edition, you were on to something. We’ve posted a corrected  puzzle at the top of this post.

Scroll down for the correct answer.












I have




Comments on “Cracking the Code”

  1. This is so fantastic! It’s wonderful to hear about all the innovative courses that are being taught at Bryn Mawr. I work in Special Collections at Washington University in St. Louis, and one of our real gems is the Arnold Semeiology Collection. It features lots of rare books on ciphers and cryptography dating from the early 16th century to the present day. If anyone finds themselves in St. Louis they will have to pay us a visit!

    -Kate Goldkamp ’09