Probably not the technical part (at least not without assuming a background in complexity theory) but the cultural aspect, certainly.

In a sentence, complexity theory, mother of the computer sciences, is the math behind how hard it is to perform a given computational task.

Crypto is a mishmash of different kinds of people: there are those who view it as a branch of complexity theory, and at the other extreme there are those who just want to build secure systems and protocols without having to worry about the math. Most people are interested in constructing protocols but want to be able to justify it complexity theoretically, but are not interested in complexity theory for its own sake.

A recurring issue is the tension between the believability of a definition and the hardness of doing proofs that meet that definition. Likewise, it is common for one faction to give a proof that involves constructing a number that encodes the bit-repesentation of an algorithm (or circuit), and the other faction to respond with a giant "WTF?"

Random oracles are objects that "magically" map strings into random strings. They are defined by quantifying over all functions over a certain space. What I was pointing out was that by defining these spaces in a convenient way, rather than in the most natural way, proofs can be considerably simplified -- in particular, made combinatorial. I (like many computer scientists, I suspect) have a natural aversion for any math that is not discrete. However,

**ephermata** seems to disagree that this can be done, so don't take my word for it.