I think the disconnect is that you assume that being able to do useful computation on some data implies that it must be possible to derive some insight into what the data is (side-channels or the like).
It's a fair assumption to start with. But the folks building FHE basically claim "nuh-uh", and I haven't seen anything to indicate they're wrong. Maybe some new Math grad will sort it out.
I too have been playing with the conjecture for fun. Your insight is interesting because of the appearance of 2^n, given that that always resolves to 1 for all n.
PMapper author here: I can't give PMapper the love it deserves, but I fully support the work done in Fennerr's fork at https://github.com/Fennerr/PMapper .
I remember hearing about this sort of thing from a grad student a few years back. She pointed out that there were interesting privacy concerns with these microbiomes, given how we leave traces of it.
I remember planning to do something in video games as I was growing up. Ended up in a different but fairly related field. Maybe this is just a sign of the next generation of people that'll work in advertising/marketing/PR/media/fashion?
I ran into a similar issue. It took a Google search plus following a nicely documented guide to reset, and I was back at it. Way easier fix process than dealing with <PC Laptop Manufacturing Company> support.
