The information in the above post is a merger of like, 20 different sources of information.

Your standard cryptographic books from any undergraduate program will tell you about the basics of confusion / diffusion, but I don't think the concept is very difficult at all.

Invertibility is hugely important but not discussed very much. It seems like crypto-experts 'obviously' know about it so they just don't talk about it? Knuth and Bob Jenkins both talked about the importance of invertibility to random number generators. EDIT: Invertibility is the basis of bijective / 1-to-1 and onto permutation functions. To be fair, I think everyone discusses the concept but maybe with different words.

Here's Jenkin's discussion on (non-crypto) hash functions, including a few paragraphs on "invertibility" (or "funnels" as they put it): http://www.burtleburtle.net/bob/hash/doobs.html

The "pcg-random" generator also has a large discussion on invertibility. Honestly, one of the best writeups on the subject, and I felt like my IQ went up severely after reading the paper end-to-end: https://www.pcg-random.org/paper.html

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The study of the invertibility of (data XOR (rotate-right data) XOR (rotate-left data)) is covered in many blogposts. https://marc-b-reynolds.github.io/math/2017/10/13/XorRotate....

The study of invertibility in general was covered by Lemire: https://lemire.me/blog/2016/08/09/how-many-reversible-intege...

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So as you can see, invertibility is "important", but rarely discussed as important. Its just assumed that everyone knows how important it is. Once you realize that invertibility / lack of funnels is important, everything else makes sense.

Galois field multiplication is useful in AES because its invertible (multiply by the GF(2^8) reciprocal). Aaaaah. I see. Why didn't my undergrad teacher just start with the importance of invertibility before talking about prime numbers and extension fields?

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Ah right. Once you know that these things have great properties (ie: invertible), then you can just read the SHA256 paper directly and the rest is just "obviously" confusion + diffusion principles.

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Linear Cryptoanalysis is the "standard" run a distribution kinda thing. Anyone who has done Chi-squared tests over random numbers kinda-gets this principle. Honestly, your standard non-crypto RNGs are roughly at this level at this point, so the study of any statistical-test for any random-number generator is good. Knuth / Art of Computer Programming Vol2 is one source of information on Chi-squared tests, but the study of statistics in general also results in Chi-squared tests and the like.

Differential Cryptoanalysis is more difficult and looks at the change-of-bits at each step of every operation. I don't quite remember how I was introduced to the concept, but differential-cryptoanalysis of many popular ciphers is a well-studied thing throughout the field.

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Knowledge of "what is fast" and "what is not fast" is... not really easy to come by, and seems to change as computer architectures change. I know that memory has gotten relatively slower compared to CPU-speeds in the past 30 years. I can imagine that in the 90s, an XOR-rotate-add cipher would take "relatively more" time than today, and that SBox-based / lookup table based ciphers were far more popular back then.

I'm not sure where I learned that information. Maybe software optimization manuals in general?