How secure is 256 bit security?
Supplement to the cryptocurrency video: How hard is it to find a 256-bit hash just by guessing and checking? What kind of computer would that take?
==========
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 let's give it a try. 2^256 is the same as 2^32, multiplied by itself 8 times. Now what's nice about that split is that 2^32 is 4 billion. Which is at least a numb...
==========
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 let's give it a try. 2^256 is the same as 2^32, multiplied by itself 8 times. Now what's nice about that split is that 2^32 is 4 billion. Which is at least a numb...
