Cryptography Basics: Exploring Functions, Domains, and Finite Fields 🔐

In this first episode, we set out on our journey into cryptography by exploring the fundamental concepts of functions, domains, and codomains, and then stepping into the fascinating structure of finite fields. Using the metaphor of a “magic clock,” we discovered how addition and subtraction in a finite field can be visualized as clockwise and counterclockwise rotations, always keeping us within the set—an idea known as closure. With this foundation, we introduced encryption as a mathematical shield for protecting messages, and brought history to life through the Caesar cipher, an ancient scheme once used by Julius Caesar himself. By mapping numbers to letters, we saw how a simple shift by 3 can transform plain text into secret code, and how reversing the process decrypts it just as easily. This led us to the broader category of symmetric encryption, where the same key is used for both locking and unlocking information. While the Caesar cipher is long broken by today’s standards, it provided us with a powerful first glimpse into the art of encryption—revealing how mathematics has been used for centuries to secure secrets and shape history.