There are also some very important facets to Information security that you are missing. You describe security as being "based on knowing, doing, or owning something that no one else can". But this is not quite right. You are speaking to only one aspect of security - confidentiality. There is also integrity and availability. Additionally, you are only speaking to the authentication aspect of confidentiality. Your "knowing, doing, or owning" could be more succinctly described as authorization based off of "something you know, something you have, or something you are" which are the 3 main ways that someone could be identified as you they claim to be. Your signature example would generally fall under something you are - but an argument could be made for it being something you know as well.

EDIT:

You also described Public key cryptography as having "2 different keys. One allows for encryption and the other for decryption. In this case, the decryption key is public so everyone can decrypt." This misses the mark a little bit. The public key could be used to encrypt as well, so that only the holder of the private key can read the information. Using the private key to encrypt is generally used in digital signatures so that the recipient can verify that the sender is who they claim to be. This scenario doesn't attempt to keep the data secret, because anyone with access to the public key can decrypt the data.