- I have a question, does every single bit of information have a zero knowledge proof system?
- All languages in NP have a ZKP.
- How about languages in P?
- P is in NP. It makes no sense to prove ZK for a statement in P, because the verifier can compute the witness or check if the statement is in P himself.
- I think what I actually wanted to ask is that
if I have private knowledge about something with low entropy, e.g., Snoopy's birth month, can I prove it to someone else without revealing extra information? In this case, I felt it's hard to make the witness ensure both soundness and zk (as you mentioned)
I was reading through information theory where one learns things through acquiring information. Then i thought about what happens if the external world cares about ownership of information and does not let you learn freely. Is this correct?: if the knowledge is in NP\P (assuming ...), then it's possible that we do not have actual information gain; if the knowledge is in P, then we most likely learn what we need to learn.