This artifact is an essay that I wrote for my Thinking Matters during my first quarter at Stanford. The course was called Breaking Codes, Finding Patterns, and introduced students to codemaking and codebreaking. Midway through the quarter, we were assigned to write an essay related to the class topic and exploring an interest of our own.

To further explore the Mathematics of codebreaking, I decided to focus on the German Enigma, how it works and how cryptanalysts before and during World War II were able to break it. I intended this paper to require no background knowledge of the Enigma, or of codemaking and codebreaking in general. I wanted to make the Math more digestible, but still complete and accurate, which is in retrospect a very hard compromise to make.

While I include formal proofs in this paper, and describe the methods used clearly, I fail to define some key terms for my audience:

“Created in the 1920s by Arthur Scherbius, the Enigma machine is an enciphering machine whose goal is to ensure total security of communications. Composed of a plugboard, three rotors, a reflector, a keyboard and a lamp board, the Enigma performs a polyalphabetic substitution on a given plaintext.”

Here, I assumed that the readers knew what a reflector, a polyalphabetic, or a plaintext were, as I knew my TAs would know what I was referring to. Since this paper is intended for a lay audience, it could have benefited from a few extra definition of key terms.

In this artifact, I also chose to include some formulas and rigorous Mathematical proofs. Looking back, I realize that I chose to include them because I found them interesting, and not because my audience needed to see those equation to understand how the Enigma worked.

If I were to write this essay again, or to rewrite it in the future, I would focus more on my audience and what it needs to know, rather than what I want to see in the paper. I would include a fully explained example of Enigma codebreaking, starting from the intercepted encrypted message and finishing with the decrypted text. I would also try to explain how each equation is linked to each other in words, rather than just in numbers.