In this video, I discuss the creation of SHA-256, how it works, and whether it can be used by the NSA to control Bitcoin.
SHA-256, as used in Bitcoin's proof of work, provides a concrete way of proving that a Bitcoin miner "has done the work." There are no shortcuts: a Bitcoin miner must burn electricity and keep guessing numbers until he gets an output with the correct number of zeroes at the beginning.
SHA-256 is perfect for this, since once you know the input, you can easily check it to see if the hashing algorithm spits out the correct hash. But it is difficult to come up with that input in the first place. This asymmetry lies at the heart of Bitcoin's security proposal.
SHA-256 is not a secret or a black box. Further, there is no way that the NSA can use it to control or attack Bitcoin.