this is a clueluess question, but what does the Socialist Millionaire Protocol, which is typically used in conjunction with OTR-Messaging, that "conventional" Challenge-Response Mechanisms like CHAP can't do?
http://en.wikipedia.org/wiki/Socialist_millionaire
http://en.wikipedia.org/wiki/Challenge-handshake_authentication_protocol
PS: Can someone consider adding the tag "OTR"?
In the CHAP protocol the client just proves his identity through showing that he has knowledge of the key. This could also be done with asymmetric cipher. The client just has to encrypt randomly generated challenge and the serve has be able to verify the content.
The Socialist millionaire protocol tells both entities that they have either used to same value or a different value. This could also be used as a login protocol. It will then offer mutual authentication.