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SSL certificate
Yes, but only in the RSA key exchange.
The client and server will initially share two other random numbers, one from the client and one from the server, and both in the clear. In the Client Key Exchange message, the client derives a third random number, encrypts that with the server's public key, which it had just received in a previous message from the server, and sends that over. Using its private key the server decrypts this message and exposes the third value. Both parties then independently calculate the same master secret used to create symmetric encryption keys.
This is not, however, how it works for the Diffie-Hellman key agreement.
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