Say Peggy wants to prove to Victor that she knows one of his passwords. She doesn't want Victor to know which password she knows, because she knows that some passwords are more valuable to Victor than others, and wants to keep the advantage that Victor doesn't know which of his passwords she knows.
Victor wants to verify that Peggy knows one of his passwords to ensure she's not lying, but he also doesn't want Peggy to trick him into giving her any knowledge of what passwords he has/doesn't have. That is, he doesn't want to send her anything that she could use to verify that she actually does have one of his passwords, or that she could use to perform a brute force attack and reveal any additional information about his passwords.
Is there a way to prove this in zero knowledge?