I read the RFC document, it mentioned that there are some kinds of client certificate type. So I don't understand what does this type mean. For a instance, one type named rsa_fixed_ecdh, it said, the certificate must be signed with RSA. What is the ECDH used for, for the key exchange? How does it work?

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    I'm confused about what you're asking: it starts like a generic question about how client cert authentication works in SSL/TLS and then you go on with a specific algorythm specification. If you have two questions, please open two different topics. Otherwise, please clarify. – Stephane Jun 27 '14 at 7:06

Elliptic curve Diffie–Hellman (ECDH) is an anonymous key agreement protocol that allows two parties, each having an elliptic curve public–private key pair, to establish a shared secret over an insecure channel. ECC is an enhanced encryption technique which works on 164bit key and use less computing power and battery uses. Compare to RSA and DSA algorithm ECC is much faster and holds less space and bandwidth. Visit here to get elaborate illustration of ECC and RSA.

Below is a comparison among RSA vs DSA vs ECC.

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