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Yes, there are a few reasons to prefer ECDH over RSA: ECDH will perform much better; ECDH can provide forward security when used with ephemeral key pairs without a large performance overhead for creating those key pairs; ECDH should be impervious to most oracle attacks, i.e. timing based padding oracle attacks on OAEP. For the forward secrecy you require ...


I don't see how the server can directly learn $x$; what a server would be able to is perform a single exchange with the client (recording the initial parts of the protocol), and then go through a dictionary, and test various passwords (that is, various possible $x$ values), and realize when he finds the right one. The idea here would be to select a prime ...

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