What does trust mean in cryptography? Terms like "trustless protocol", "trusted third party", "trusted platform", "trusted server", etc. require a notion of trust. I already wrote


  The term trust when used in the context of cryptography does not refer to personal confidence in whether a person is reliable or has good intentions but instead describes whether an entity can be assumed to always behave according to protocol within the given model.


and went looking for a source to back this claim up. Unfortunately, I wasn't able to find one, nor was I able to find one to say that my notion of what "trust" means in cryptography is wrong.

So what does this term refer to formally?
A most common use of "trusted" in cryptography is to state that what's qualified as "trusted", by hypothesis, behaves/works/performs per a certain precise set of rules (which depends on context), and will perform no less and no more. That's the case in trusted third party, and trusted server.

A special case is "trusted" applied to data, e.g. trusted key. There, trusted means that the data is assumed to possess some property, which depends on context. Typically, having been generated by a certain party in a certain way and not having been altered by any adversary; or/and being unknown to any adversary. Data can become trusted after having passed a cryptographic check, e.g. a digital signature or Message Authentication Code verification; or be initially trusted (e.g. a Root Certification Authority public key).

In marketing talk like trusted platform module or trusted computing, "trusted" means intended for implementation of something trusted in the above cryptographic sense. Experience often shows otherwise, but confusion between intent and fact is the lesser of the many kinds of lies in marketing (which also has plain lies, damned lies, and statistics).



"Trustless" means not requiring something "trusted". For a protocol, that's not requiring a trusted arbitrator, typically replacing that with users that still are expected to largely play by some rule, because they have no long-term interest in doing otherwise (perhaps, unless enough users band together to rip the others).