I'm working on a method of user authentication. I Googled the whole web, different places like Wikipedia, and some science journals and didn't find the strategy I'm using. Can my strategy be copyrighted or patent so that nobody else can use it unless they ask for my permission? Can a strategy be registered?
At least in the US, "processes" and "methods" can fall within the range of patentable subject matter. To be at all sure of a valid patent, you'd probably want to write it to require a specific machine (e.g., "digital computer") carrying out the steps, not just the steps themselves.
For a while, the US Court of Appeals for the Federal Circuit had a rule that said to be valid, a process/method had to involve either a change in matter (e.g., mixing chemicals to give some sort of chemical reaction) or else a specific machine to carry out the steps. The US Supreme court recently said that couldn't be taken as an absolute rule, but still said it was a useful guideline.
A copyright would apply to code you wrote to implement the process/method, not (generally) to the process/method itself. There have been cases about copyrights being applied to the "look and feel" of a product (i.e., to how its user interface looks and works) but I'd tend to be wary of depending on that. Decisions in that area haven't produced a simple, easy to understand set of rules about what is or isn't likely to be covered. In any case, at least based on what you've said, chances are pretty good that your "strategy" would have little or no direct, visible representation in the UI.