How big is the company and who was interviewing? If it's HR, they genuinely might not know. I've been to interviews where the interviewer admitted they had grabbed him 5 minutes ago while he was walking past, and he had no idea about the project. They might be hiring because they have budget, for some future project (that might never happen).

Don't get me wrong, all of these scenarios aren't good, and it's a warning sign. Personally, the secrecy alone would make me think the job isn't a great fit for me.

> tell them I can't accept the job without any specifics about the project itself

This, if you aren't happy with the arrangement don't do it (if you have that luxury). Gut feeling can be quite helpful.