I don't know about you, but I used to think of the prefix "crypto" as applying mainly to secret messages. One of the neatest takeaways from the study of cryptography as a whole is just how much more widely applicable the mathematical tools at its core are. Really this prefix serves more as an antonym for "trust" than it does as a synonym for "secrecy". One of the first times this really sank in for me was upon reading the Bitcoin white paper.
I decided to cover this topic now partially in light of the recent rise in attention towards other cryptocurrencies; a level of attention which is not always accompanied with a real understanding of what these currencies actually are. While there are a handful of really good explanations of the blockchain I've seen out there, it seems that the more prominent search results one will get when trying to learn about them lean too heavily on vague analogies with gold-mining, and the more technical ones don't always motivate why the system works the way that it does. (An excellent exception, by the way, is this post by Michael Nielsen).
Here I try to frame things in the context of you stumbling into inventing your own cryptocurrency, which hopefully helps clarify why the various technical constructs involved come into play the way that they do.
The supplemented video here was something I originally had as part of the script of the main video to illustrate what "infeasible" means in the context of digital signatures and cryptographic hash functions. It's too peripheral to justify the amount of time it would add to the main video, but I had fun thinking through the example, so it was pulled out into an isolated footnote.