Galois fields

Galois fields, named after mathematician Évariste Galois, are special sets of numbers where you can perform addition, subtraction, multiplication, and division (except by zero), and still stay within the set. They are finite — meaning they contain a limited number of elements. These fields are fundamental in areas like coding theory and cryptography because they enable consistent and reliable computation with discrete values, such as digital data bits. Think of them as a controlled universe of numbers where all arithmetic stays within the set, allowing complex operations to be predictable and useful in technology.