Where to find a comprehensive content on security proof systems in cryptography Proof systems (provable security) are seen in many research papers related to cryptography and security. Where would I be able to find a comprehensive resource covering the purpose and the fundamentals of proof systems, and its common approaches such as the random oracle model method?
First, as a heads up &quot;approaches to provable security&quot; or &quot;approaches to security proofs&quot; (which it sounds like you are interested in) means something different than &quot;proof systems&quot; in cryptography. Proof systems are a specific construct that are studied within cryptography (similar to encryption or signatures), of which zero-knowledge proofs are the best known example. The fact that there is a naming collision here is unfortunate, but its best to just keep it in mind and sometimes uses more awkward phrasing to avoid the collision.
There are a number of slightly different competing notions of &quot;proof systems&quot;. I don't know a resource that collects them all into one document, but two popular ones are:

Bellare and Rogaway's &quot;Game-playing&quot; model, which you can find exposition on here

The &quot;simulation&quot; proof technique, which you can find exposition on here


As for the random oracle model, I believe chapter 6 from Katz's book Digital Signatures is probably a good pointer, although if you do not have institutional access it may not be freely available.
EDIT: Browsing eprint, I found this chapter on hybrid arguments, which also may be interesting.