Proving a secret is known without revealing it Let's say Alice wants to prove to Bob that she knows a secret S that Bob is also supposed to know. Alice can't be sure Bob is really who he pretends to be, so she needs to make sure Bob can't deduce S from their interaction. Additionally, S could be weak (e.g. "abc123"), so she can't simply send a hash of S to Bob, or any f(S) really since that could be brute-forced.

What are your thoughts on this? Is this even possible?
What you want is the https://en.wikipedia.org/wiki/Socialist_millionaires 
Problem. 
This problem is orignally phrased as two people want to verify if they have the same amount of money without revealing anything more. 
Alice has a value $A$ and Bob has value $B$ and they want to verify $A =? B$
without either side revealing anything more than the result of the check. 
See the wiki page for algorithm description.