Definition of the term "key" I've looked in many places (NIST, text books, online resources) and I cannot find an answer to the definition of the term "key" from a semantic point of view. 

Is it the "key" to cipher-texts (i.e. like a door key to lock/unlock), or is the the "key" to the algorithm (i.e. a crucial factor to make it work, like a keystone)?

I was taught that it was the latter, but I cannot find proof either way. I can understand if the difference is too minor to discuss, but I was wondering if the original intent of the term is known.

Edit:

To further clarify how I understand the semantics: because the key is required for the algorithm to function at all, the key is 'meant' for the algorithm (e.g. a keystone for an arch or a punch card for a IBM computer) the term 'key' is meant as an enabler for a process, not as a lock/unlocker for a secret. This is especially true because cryptographic keys can be used for algorithms that do not 'hide' or 'protect' data.
In the context of encryption schemes, the key is whatever piece of information the legitimate recipient of an encrypted message possesses, which allows him to decrypt the ciphertext efficiently. Hence, the key must be kept hidden from an attacker, since otherwise the attacker could decrypt efficiently just as the legitimate recipent does.