Ben Gilbert: belief

Transcript context

…If you own a bitcoin, and the first people who own that bitcoin when it's created are the people who mined it, and then it gets transacted. You own some, I own some, people who buy and invest. What you actually own is you own a piece of the computing power that has gone into making the system robust, secure, viable, and good for everyone. Yeah. Before we move on to the story here, I think there's a couple of little rabbit holes I want to go down. We've talked about this cryptographic work a few times. I want to talk a little bit about the idea of one-way functions in computer science. There are certain types of math that are very easy to do in one direction but very difficult to undo in the other direction. A classic example of this is the product of two prime numbers. If you multiplied prime number A by prime number B, it's fairly easy to do that math. You can imagine literally doing it on paper, you can imagine writing a computer program to do it, bringing those numbers into the registers and assembly code, multiplying them together. But if you’re given the product of those two numbers, especially when all the numbers you were dealing with are very large, you can imagine that it gets extremely difficult and would be very inefficient to try and figure out what the initial two prime numbers were that created that product. The magic that makes this one-way function work is the fact that it’s easy to multiply two prime numbers together, but very difficult to factor large primes. Of course, it’s gotten much more complex since this initial insight. But I do want to pause on that for a minute and say, the implication here is that it’s very easy to check someone’s work when they tell you they have the answer to this product and they provide you one of the factors or one of those initial prime numbers. You can very quickly do that math and say, yup, checks out. But it’s super hard for you to stumble onto the exact two initial numbers without knowing any other piece of information. This system is totally ingenious. I want to David Rosenthal-style here, rewind back to 1874. William Stanley Jevons wrote in the Principles of Science—keep in mind this is little under a hundred years before the personal computer was created. “Can the reader say what two numbers multiplied together will produce the number 8,616,469,799? I think it will be quite unlikely that anyone but myself will ever know.” He came on to the very first idea of the one-way function. Obviously, now a computer can very quickly, through brute force, figure out what the two—guess and check, guess and check, guess and check—factors of that number are. But you can imagine if that number were extremely large, then it would take modern computers a very long time. Or frankly, if you make them large enough, it makes it impossible, to our knowledge, for computers today to undo that problem. It requires just way, way, way too much work. If you make them bigger than that, then you can say, assuming computers get better at a certain rate, this problem is never undoable. There’s a scary thing that exists here which is at some point, we have not proven for sure that one-way functions exist. We’ve tried to undo them a bunch of different ways and mathematicians everywhere have tried to prove this problem. ere which is at some point, we have not proven for sure that one-way functions exist. We’ve tried to undo them a bunch of different ways and mathematicians everywhere have tried to prove this problem. It’s a scary thing where we rely on this for public/private key encryption, encryption of all kinds, hashing. Everything in Bitcoin is based on anything with any password that you log into anywhere is based on this. Your email is based on it. We’re pretty sure that you can’t [...] from the other direction in a computationally efficient way, but we’re not provably sure.…

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