Alan Turing was not shy about his homosexuality. Voss (2013) tells us "to become a close friend meant accepting his homosexuality, and Turing would gently raise the issue on the third or fourth meeting with friendly colleagues to ascertain their opinions." Some of Turing's most famous work came from his time working at Bletchley Park during WWII. While here Turing worked on finding a way to decode messages from the enigma machines that had been intercepted. "In 1939, Turing created a method called "the bombe," an electromechanical device that could detect the settings for ENIGMA, allowing the Allied powers to decipher German encryptions (Central Intelligence Agency, 2015)."

Modular Arithmetic is heavily used in cryptography and is what Alan Turing used to break the Enigma code. In Modular Arithmetic we say that a is congruent to b modulo n if n | (a-b)and is denoted as a=b (mod n) (Leighton & Rubinfeld, 2006). Use the applet below to explore modular arithmetic and see the relationship between a,b, and n.

A simple use of Modular Arithmetic is the Caesar Cypher. In a Caesar Cypher a number is agreed upon that shifts the letters of the alphabet (Buchanan Obe, 2017, 14). For example "the letters for the cipher have been moved forward by two positions, where a 'c' becomes an 'A'. Thus 'the' will be coded as 'RFC' (Buchanan Obe, 2017, 14)." The Caesar Cypher encryption is represented in Modular Arithmetic as C=(M+k) mod 26 with C being the encrypted character, M being the input character and k being the number of positions moved. The decryption will be displayed as M=(C-k) mod 26 with the same corresponding character definitions. Use the Applet below to explore the Caesar cypher.

The problem with this cypher is it is relatively easy to break using brute force. To avoid the possibility of brute force the enigma machine used 3 rotors to further encrypt any messages (Roberts & Cain, 2017). Watch the video below to get a better understanding of this machine.