This is possible. This is actually what Kerberos authentication does, only with a little bit of added spice. To ensure that your authentication mechanism is secure, you need the following:
- A common hashing algorithm on both the client and server.
- A one-time salt value generated on the server and shared with the client.
- The original password stored in a database.
To securely authenticate a user via hash code, so you avoid sending the actual password across the wire, first generate a random, single-use salt value on the server. Send this salt value to the client, and generate a hash code from the salted version of the password the user has input. Send the resulting hash code to the server, and compare it with a hash code generated from the salted version of the stored password. If the comparison fails, discard the salt, regenerate a new salt value, and repeat the process.
The reason for the single-use salt is to prevent anyone listening to the conversation from capturing the hash code of the users password, which, when you use hash code comparison, is just as good as having the password itself.
Note that you need to keep the original password around, you can't hash it once on the server and save the hash in the database. If you need to ensure that the passwords stored in your database are also secure, then you will need to encrypt them before storing them. I believe that ASP.NET membership providers do allow you to store passwords encrypted, however, if you really wish to have a secure authentication mechanism that is difficult for a hacker to crack, then I would recommend handling password storage and retrieval entirely on your own.
Finally, I should note, that such a complex password transfer mechanism should be largely unnecessary if you use SSL to encrypt your connection during authentication.
References (for those who have never heard of Kerberos or SRP):
http://en.wikipedia.org/wiki/Kerberos_(protocol)
http://en.wikipedia.org/wiki/Secure_remote_password_protocol