Abstract Algebra vs Number Theory?

[MathWarrior]

I was wondering if one wanted to pursue learning more about cryptography which of these classes would be the most important? Number theory of abstract algebra?

 

[MathWarrior]

Number theory of abstract algebra <-- should read number theory or abstract algebra.

 

[micromass]

Can't you do both? Both are quite important for crypto I think. Anyway, if you end up picking one, then I'd really suggest studying the other one too in your free time...

 

[PhDorBust]

Just take a course in abstract algebra, most number theory concepts come much easier if you can operate within a group. Many ugly proofs in number theory become quite nice if you know group theory.

That said, it's not like you're in any real rush. An graduate-level intro course in cryptography won't require more than the absolute basics. Probably just legendre symbols and basic modular arithmetic.

 

[kuahji]

I'd have to agree, I'd take the abstract algebra course. Abstract really helps open the doors to much the higher mathematics as well.

 

[Chaostamer]

I'd also say that abstract algebra is more important in general. Perhaps you should consider picking up a Number Theory book and doing some self-study. I don't think Number Theory is terribly difficult to learn if you know how to write proofs and knowledge of it might help you in algebra.

If you do want to learn Number Theory, I'd recommend the Jones and Jones book. It's well-written and affordable. Plus, it gives solutions to all the problems, so you can work through the points at which you get stuck more easily. I've had a good time with it.

 

[MathWarrior]

What do you learn in abstract algebra? Is it like normal algebra? How is it used in cryptography?

 

[Chaostamer]

What do you learn in abstract algebra? Is it like normal algebra? How is it used in cryptography?

Generally abstract algebra courses cover group theory, homomorphisms and isomorphisms, ring theory, field theory, and Galois theory. Basically, it introduces algebraic structures and explores solutions to polynomial equations. Of course, a first course generally won't cover anything beyond some ring theory.