Recently I've been looking at Signal Protocol, and it made me think about security protocols in general. There are protocols that work very well for protecting messages (or data), signing data so you know the authenticity, etc… All of these things are based off of securities that we have in the physical world.
An analogy can be made to sending mail. When a letter is sent, the sender could seal the letter with their wax seal, showing the authenticity of who it is from. If they wanted to be more sure no one read it, they could walk the letter over to the recipient's mailbox (which only the recipient has the key for), and slip it in their mailbox.
Out of this mail example, you can obviously pull out the relationship to computer security. The "wax seal" is signing with a private key (in a pair… sort of), the "mailbox" is asymmetric encryption. These relationships are not perfect, but pretty close. But we have really limited this example. There are things which we have not modeled in computer security that exist in physical security (or at least if they exist, they are not popular).
Let's talk about the "wax seal". Wax seals can help to determine if a message has been opened. We have logging in computer security, but that is not the same concept. In the real world, there is something intrinsically different about the message (letter) itself when it has been opened. You don't have to go to a separate system to see if your message (letter) was opened.
Really, it seems like cryptography is a way of modeling things in the physical world. It uses math to be able to create irreversible modifications to something completely digital. Think about if you had a list in which each element had its hash, hashed with the hash of the previous element in the list (the zeroth element being only a hash of the data). As you add to this structure, you have made a irreversible modification to this structure, where you can never modify anything in the middle of the structure, only add to it in the end (this is what a blockchain is). Blockchain could then be used to assign people assets. Not just money, but objects. Imagine you use the blockchain to say you have a car, then when you get in a car accident with me you and I could say "Abbergie totaled my car", it would go on the blockchain, and everyone would see something which happened, and it is irreversible. Just like if I actually hit your car in the real world.
But I'm not just talking about blockchain when I mention modeling the real world with cryptography, the wax seal example shows another case of something we could model.
I think we can keep pushing cryptography to continue to model physical things in on a computer. Now the question is what has not been modeled yet by a computer which exists in the real world, and does there exist a mathematical function which can be used to make it difficult or infeasible to break our digital models of the physical world.