How does a server certificate work?

The end-user's browser requests a secure channel (via "https:") from the server, and then - if the server has a cert - the browser and the server negotiate their highest common encryption strength (e.g., 128-bits), and then exchange the corresponding encryption keys (this exchange is normally done using 1024-bit encryption strength). The 128-bit encryption key is then used for this particular instance of SSL, for all from-to exchanges between the browser and the server. The next https session will have a new session key.

The certificate guarantees the security of the connection between the browser and the server. Once data is in the server, it is up to the server admin to make sure the data remains protected.
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