Cryptography is widely claimed to be useful in establishing trust in electronic assertions (such as an assertion that the holder of a certain public key is also the registered owner of a certain domain) . The argument goes like this: a certain operation (E) on the assertion A resulting in an artefact A is mathematically intractable (i.e. practically impossible) without knowledge of a certain secret S. Another bit of information, Pi which is not secret, but instead publicly available can be used to verify whether A was produced using a given secret Si or not using the inverse mathematical operation to E, D. Pi can only be used to prove this for only one other secret. Therefore if you know P and the binding between P and the entity owning the secret it can verify (say Bi(P,E,A)) then you can be sure that E produced A with S. In order to be sure of this binding, you can rely on a second binding which makes the statement that Bi(P,E,A) is valid. By chaining these bindings, as long as you have one binding which you are sure of (for example because someone you trust gave it to you) then you can be sure of Bi and ultimately the source of A.
This is all fine and dandy, but the problem is with the dumb user. Ultimately the way this works is that your computer performs D and tells you whether Pi corresponds to Si or not. No user is capable of checking whether D was performed correctly or whether instead the computer just said – yeah, looks good to me, without actually doing D at all, therefore the user has to trust the computer and its software. So the user, most of whom wouldn’t know a public key from a public toilet, is tasked with figuring out whether the computer was telling porkies or not. How can this be done? The options are limited to one: you trust the person who gave you the device that they neither cooked the machine deliberately nor exposed it to anyone else who could have cooked it instead. This is almost as hard as figuring by another means other than crypto whether for example, a document was really sent by a specific individual – for example by phoning them and listening to their voice telling you that they sent it.