I understand how hashing and encryption/decryption work at a very high level, where the functions work as a black box. Hashing scrambles the input in a non-uniquely reversible way, whereas encryption uses a key to scramble the input in a reversible way where it's highly unlikely that any other key could produce the same output. Salts can be added to prevent rainbow attacks by randomising the output more.
Over time, collisions are detected in hashing functions, and encryption/decryption functions are cracked, leading to stronger functions being developed usually with more bits.
However, I would be interested in studying low-bit concrete hashing/encryption functions in order to understand how it can be mathematically proven to be uncrackable except by brute force (if that is indeed possible).
Are there any such low-bit functions that can be followed through step by step and analysed mathematically without the maths getting too complex? Ones that would be considered cryptographically secure except for their length?