It's a great article, and I've already bookmarked it to refer back to in the future whenever I need a refresher on topics I last saw in college.
I believe the confusion from the OP was that if you don't already have significant mathematical maturity (in the sense of having seen bits and pieces of number theory, linear algebra, and group theory before) you'll quickly be frustrated trying to follow along as you won't be able to reason at the necessary level of abstraction.
>Is "number theory" an appropriate title
I think "number theory from first principles" is a misleading title, and I almost skipped over it because I thought it was yet another introduction to modular arithmetic, congruences, and such. Instead, the bulk of the article lays summarizes the main results in number theory/group theory that can be put into practice to construct cryptographic primitives so I think titling it "Foundations of Cryptography" might be better.
I believe the confusion from the OP was that if you don't already have significant mathematical maturity (in the sense of having seen bits and pieces of number theory, linear algebra, and group theory before) you'll quickly be frustrated trying to follow along as you won't be able to reason at the necessary level of abstraction.
>Is "number theory" an appropriate title
I think "number theory from first principles" is a misleading title, and I almost skipped over it because I thought it was yet another introduction to modular arithmetic, congruences, and such. Instead, the bulk of the article lays summarizes the main results in number theory/group theory that can be put into practice to construct cryptographic primitives so I think titling it "Foundations of Cryptography" might be better.