I know a little bit about cryptography. Most of the "middle ground" that you're interested in is truly just pure math. You need to learn the pure math before you can deal with the cryptography.
There are a variety of different ways that cryptography has been implemented; both in the past and currently. The most secure of cryptography is the one-time pad which uses a simple replacement cypher. By not reusing any elements of the key, it is theoretecially (not practically) impossible to break the encryption. If any of the key is repeated, it then becomes possible to break the encryption. This is done by looking at the frequency of certain parts of the encrypted text. There are references on line about this (I once looked them up).
The two encryption systems used most often on the internet are public key encryption and symmetrical encryption systems. Symmetrical encryption systems use the same key for encrypting something and the same key for decrypting something. Public key encryption uses one key for encryption (the public key) and one key for decryption. RSA is a public key encryption system. It does involve the factoring of large psuedo-primes into primes. Currently, this is a hard problem (in the mathematical sense of hard). There are other public key encryption systems that use different hard problems in them (elliptical encryption for one).
That's about the sum total of my encryption knowledge.
Matt