JSF: How to get the x509 certificate list stored in the browser ?

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Java

security

certificate

JSF

(sorry for my english)
Hello. Firstly, I have to say that I'm new in Web development. I'm learning by myself thanks to the information I find on the Internet.

I'm developing a JSF application with Eclipse, JSF 2, Tomcat 7 and primefaces 5. I'm quite happy with my progression, but I'm stopped now.
I've achieved to establish a SSL connection (https) with openssl.

I'd like my application to press a buttom in the login form, and show the list of personal X509 certificates which are in the browser's store.
Many webs implement this functionality, so I realize that this is posible, and without using applets.
Is this so hard?
I'm looking for examples but I can't find anything.
Can anyone help me?
Thanks

Julián