Proof of non-knowledge I pretty recently understood the concept of zero-knowledge proof (on a purely logical level, not mathematically speaking, thanks to this article). Despite being a very counter-intuitive principle, it turned out to be an actual and applicable system.
I am now wondering if another counter intuitive problem is solvable: is it possible to prove that we don't (or are unable to) know an information? Or to rephrase it in a more formal way, is it possible to prove that such a system is impossible to create?
Regards
Yes. ​ Just prove that such information doesn't exist.

(For example, that can be used to prove that one

doesn't know a boolean value x such that ​ x and not x .)

For P/poly provers, if such proofs exist then UNSAT has a usually-correct promiseMA protocol.

However, if public-coin collision-resistant hash families exist, then

a common random string is enough for arguments of non-knowledge.

For example, to argue that one does not know a string

such that ​ Hcommon_random_string(0||x) = y , ​ argue that one

does know a string x such that ​ Hcommon_random_string(1||x) = y .