My goal is to fully understand this answer on crypto.stackexchange by self-teaching myself all the basics.
The term I'm working on now is a "Galois field", and starting on this wiki page. The header of a page has a header like this:
Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields.
Which makes me believe that either Commutative rings is a subset of finite fields. (or the other way around, I don't know yet.)
What is the best learning path I should start on to understand finite fields?