Absolutely. Also, it probably is in your best interest to advertise details of your cryptography. What data is shared with whom, what algorithms are used, etc.; if you’re doing something more exotic / low-level, Alice-Bob diagrams can be helpful. I’m not sure what other people do but when looking at security-sensitive software, the first thing I do is look for the cryptographic setup and research it.

We can do math with or without Choice

Five Stages of Accepting Constructive Mathematics - Andrej Bauer very good talk on that topic

I think we have free will that operates on a sort of plane of possible actions which limits our will […]

Kant argues for something similar when he says that as humans, we are citizens of two worlds: the sensible world of phenomena in which we are bound by the laws of nature as well as the intelligible world of noumena, which is subject to reason and, by extension, freedom of will.

I think it’s important to remember that Kant doesn’t see free will in the same way for example St. Augustine or Thomas Aquinas define it — they believe free will to be the capability of arbitrary choice (‘liberum arbitrium’) — but as the product of rational thought. Freedom (autonomy), in the Kantian sense, is being able to make the reasonable, responsible choice.

Edit: Paraphrased and translated from Kaufmann, Arthur. Rechtsphilosophie. C.H. Beck. Munich: 1997. Pp.240-1 (German philosophy of law textbook)