There are three key components that should be specified in any security definition/protocol.
1. Adversarial power under which the protocol is secure
2. Network model in which the protocol operates
3. Security guarantees that the protocol provides
Security is not something absolute. We may not be able to protect a protocol against any type of adversary. A security protocol is meaningless if it does not specify the capabilities of the adversaries under which the protocol is still secure. The capabilities of adversaries are specified in the adversarial model. For example, if the adversary is computationally bounded or have unbounded computational power, if the adversary is honest, semi-honest or malicious, etc.
Your protocol may need a trusted third party to work. It may not be secure without a trusted third party. Your protocols may need certain parties to online at all times. Such information is specified in the network model. Like the adversarial power, your protocol is meaningless without a proper network model.
As I mentioned earlier, security is moving line; your protocol may solve only certain problems. It is crucial to specify what problems it solves up front as part of the security guarantees.
In short, you need to specify what security guarantees your security protocol provides under which adversarial and network model. Otherwise, a security protocol is as useless as zero security protocol.
A big mistake people, especially in the database community, make is to say "our protocol is secure for this data set and it does not reveal any useful information to the adversary". This is very wrong. You cannot define security based on a input data set. What happens when you have a different data set? Will your protocol still be secure? Probably not. Security should never be analyzed by a set of examples. Rather, it should be based on the above 3 objective measures.