Question: Recall that even if the server only stores f(p), client has to send p in clear to authenticate to the server. If the adversary is

Recall that even if the server only stores f(p), client has to send p in clear to authenticate to the server. If the adversary is watching, it learns p. Normally you have to use HTTPS to solve this problem. Alice has another idea. Instead of client sending p, client will instead only send f(p) to the server to authenticate. Then the adversary never learns p even if it can watch the whole communication. Is this a good idea? Does it improve the security of the system?

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