There are basically no restriction on who can write a paper, so, clearly you can. If you have no affiliation, it might be hard go publish a "free" paper (e.g., a technical report or a pre-print on arxiv), but you can always consider submitting your idea to a workshop/conference. However, you might have to pay the conferences/travel fees (although some conferences might help you, if you can't afford it). You can also submit your idea to a journal, as many don't charge anything to publish. You can of course also just write a PDF and put it on your website, or even do a long blog post.
There is one thing you might need to be careful of, since you might not be used to write academic paper: a good paper is not just a good idea, this idea needs to be validated. In other words, you can't just write: "here is a cool idea I had", you also need to describe how it differs from existing approaches (perhaps your idea has been already published), and you need to describe why it's a good idea. There are many approaches to do so, for instance by presenting your idea in a formal setting and prove that you can mitigate DDoS attacks (probably under some assumptions). You can also run some experiments, and show that your approach mitigated x% more attacks than some known approaches.
If you're interested in eventually pursuing a career in academia, showing that you can explain and validate your work might be as important as having a good idea (because not only you have a good idea, but you can convince others that it's a good one!).
Note that another approach in your situation could be to implement your idea as an open-source software, and if it's adopted by the community, then it's another form of validation.