At first, huge thanks for the doxygen docs. However fundamental problem for me here is the security. Is there any good source where I can study cryptographic hash functions and digital signatures in-depth, while avoiding nasty math? I mean something like this [1] document about elliptic curve algorithm.
[1] -
http://www.secg.org/sec2-v2.pdfThere is documentation on each of the cryptographic algorithms used by Bitcoin in general as they are all standards published by other people. The hashes used are SHA256 and RIPEMD160. The digital signatures algorithm is ECDSA. There are plenty of places that explain how all of these work in general, outside of Bitcoin. Wikipedia is a pretty good place to start, especially with their references.
As for how these all work together in Bitcoin, the developer documentation on Bitcoin.org is one of the best places for this kind of documentation.
Unfortunately there is not a lot of documentation specifically about Bitcoin Core. You really have to read the code and learn about it yourself.