## Spy Training 101: How to Encode and Decode Messages like an Expert

### Course Description

The course provides an introduction to the history and mathematics behind cryptography. From Julius Caesar's encoded messages to his generals and Thomas Jefferson's wooden cipher to modern day encryption systems, codes have always been used to protect important or personal information. In this course we study the mathematical concepts behind encoding and decoding messages, as well as the role these systems have played in shaping historical events.

We will study a variety of ciphers, starting with the Caesar and Jefferson ciphers and moving on up to modern day methods of encrypting information. For each of those ciphers we will talk about their discovery, when and where they were used, and how we can employ them to encode or decode messages.

In the process of discussing the basics of cryptography we will encounter some very interesting new mathematics: modular or "clock" arithmetic, prime numbers, and even Fermat's little theorem. We will study these topics from an intuitive point of view, focusing less on the abstract concepts and much more on the way in which they arise naturally in the context of cryptography.

Replicas will be built of the physical devices that were used historically to perform encryptions, while other times we will ask a computer or calculator for help. In all cases, we will discuss the issue of information security: is our message safe if we encode it using a certain method? If not, just how easy is it for a third person to break the code and read our message? And, more importantly, what options do we have to keep our information safe?

By the end of this course, students will have a better understanding of the challenges of modern data encryption and the way mathematics is used to solve such problems. The introduction to cryptography will set a good foundation for future mathematics and science courses by exposing students to problem solving in the context of an everyday life question.

The course has no prerequisites beyond knowledge of basic multiplication and division. In fact it is recommended for students who may feel intimidated or uncomfortable with mathematics, since it provides a more hands-on, less abstract learning experience.