In this episode of Bitcoin, Explained, hosts Aaron van Wirdum and Sjors Provoost go back to basics. They explain one of the most fundamental building blocks in all of Bitcoin: hash functions.
To start the episode off, Aaron and Sjors explain that hash functions are a type of mathematical one-way functions. That means that they can easily convert one piece of data into another piece of data, a hash, but anyone who knows only this hash can not convert it back to the original data. Additionally, a hash is supposed to be unique: no two (different) pieces of data should result in the same hash. If either of these things is no longer true, a hash function is considered to be broken.
Then, Aaron and Sjors go on to explain in a little bit more detail how hash functions actually work. They discuss some aspects of the history and evolution of different hash functions, they mention some hash functions that have indeed been broken over time, and they pinpoint which hash functions are used in Bitcoin.
Finally, Aaron and Sjors explain how hash functions are used in Bitcoin, exactly. This includes almost every aspect of the Bitcoin system, they point out, ranging from transactions (in multiple ways) and blocks, to addresses and the proof of work mechanism, as well as in relatively new upgrades like Taproot, and hash functions are even used to create some randomness needed to establish connections on the peer-to-peer network.