I can say this at the moment: an NDA exists

I've been looking at the text of an NDA (for something completely unrelated to any work activity, I should add), which includes the clause that the recipients cannot even acknowledge that the NDA exists, despite the fact that the invitation to take part in the activity which will be covered by the NDA was advertised to a reasonably wide audience (and certainly to more people than will volunteer to sign the NDA) -- ie meaning the existance of the activity is known about by people under no obligation to keep it secret.

But this means that even if someone asks "did you sign an NDA with X" you can't say 'yes' or 'no' as that would infer an NDA exists with X.
It certainly seems rather OTT and I dont see how this benefits the other party in terms of keeping their proprietary information secret.

Of course, I'm not a legal person. But I have sat in meetings in the past where 'legal people' have inserted clauses to see what they can 'get away with', on the expectation that the other side will argue these ones and presumably overlook the more contentious ones.