This depends on the way the container is configured. In the general case, the SSL configuration of the container will not be accessible by a servlet it contains. For example, in Apache Tomcat, that connector's SSL configuration can be completely independent of the settings accessible by a servlet. (In addition, SSL may be handled by APR or an Apache Httpd front-end, for example, which won't have much to do with the Java keystore configuration).
You would probably be able to gain access to the keystore if they are configured using the javax.net.ssl.*
properties. However, that's not necessarily the way the SSLContext
of the server connector is configured from. It's not generally a good idea to pass those parameters on the command line either in a production environment.
What you may be able to do is to load the keystore used by the container, from your servlet, but you'd have to know where it is, in advance. In addition, I would suppose that a hosting service would run Tomcat with a security manager turned on, which may prevent you from doing this.
Note that you could use your own keystore, shipped within your webapp (it can even be loaded from the classpath as a resource stream). Whether this keystore will contain the same private key as the one use by the server's SSL layer is up to the server's administrators (if they let you have it).