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In the main video on cryptocurrencies, I made two references to situations where, in order to break a given piece of security, you would have to guess a specific string of 256 bits. One of these was in the context of digital signatures and the other in the context of a cryptographic hash function. For example, if you want to find a message whose SHA-256 hash is some specific string of 256 bits, you have no better method than to just guess and check random messages, and this would require, on average, 2^256 guesses. Now this is a number so far removed from anything that we ever deal with that it can be hard to appreciate its size. But lets give it a try. 2^256 is the same as 2^32, multiplied by itself 8 times. Now whats nice about that split is that 2^32 is 4 billion. Which is at least a number we can think about, right? Its the kind of thing you might see in a headline. So what we need to do is appreciate what multiplying 4 billion times itself 8 successive times really feels like.
