Difference between certain, specific and particular

All three words obviously have multiple meanings, but in the context you're taking about, specific and particular are completely interchangeable in every case I can think of.

Certain is slightly more nuanced. It can (but doesn't always) carry a sense of deliberate ambiguity. For example, I'm here looking for a certain person could mean:

• (neutrally) I'm here looking for a specific person
• (enigmaticaly) I'm here looking for a specific person, but I'm not going to say who because it's a secret
• (ironically or humorously) I'm here looking for a specific person, and you know who that is, but I'm not going to mention their name (for example because they and I recently had an argument).

Context and tone would make clear which of these was intended.

Personally, for that reason, I would avoid using certain in the context you're describing. A dictionary will tell you it's correct, but it doesn't feel quite as natural or idiomatic as specific or particular.

Good answers... and here's another nuanced difference between "Certain" and the two words "particular" or "specific."

Certain can contain a nuance of "assurance." For example... "I am certain that this is the right answer."

I could not replace "certain" with "specific" or "particular" and it have the same meaning.