Search⌘ K

Finite Field

Explore the concept of finite fields defined by modulo operations and understand Galois fields with prime elements. Learn to verify field properties such as closure, associativity, and distributivity using Python code, enhancing your grasp of algebraic structures important in data science and cryptography.

Modulo operation

Given a,m,rZa, m, r \in \Z, m>0m > 0, and 0rm10 \le r \le m-1, we write

a mod mra\ \text{mod}\ m \equiv r

when mm divides ara-r (also ...