I am working on a confidential research project. I'm not allowed to talk to anybody outside of the group without explicit permission. However, my colleagues from other groups are curious of what I am doing. I don't want to damage the working relationship but I just can't share too much details. Should I lie something (they won't know) or ask them to shut up?
It is perfectly fine to say: "I am working on something, but I was told by my boss Dr Who to keep it confidential. You can ask Dr Who if you are interested."
Simply tell them you are not at liberty to discuss the details of the project.
The fact that you are working on a confidential research project is not the confidential part, so you are free to mention that.
Lying is unnecessary, and has the potential to backfire. Simply reiterate that you do not have permission to speak about it.
If they persist, then they are damaging the working relationship, as they would be a nuisance.