How to decrypt data when you can't get the private key in Windows?

I'm very confuse. My english is poor, but I try to say my question clearly.
When browser connects to a https website which needs client certificate to authenticate the identity, the browser will send client certificate to web server.
Then the web server will use the certificate to encrypt some data and send it to browser.
Then broswer should have private key to decrypt that.
But as I know, if I install a pfx format personal certificate, I can set can't export private key, which means you can't get the private key to use it. So how can
the browser decrypt the data without private key?
By the way, what is CSP, use CSP's interface can we use CryptoAPI
to decrypt data without private key?

Answer for question is "you cant"..
"How to decrypt data when you can't get the private key in Windows?"
Read more
http://msdn.microsoft.com/en-us/library/windows/desktop/aa387460(v=vs.85).aspx
http://msdn.microsoft.com/en-us/library/windows/desktop/bb427432(v=vs.85).aspx
http://technet.microsoft.com/en-us/library/dd277320.aspx
http://en.wikipedia.org/wiki/Public-key_cryptography

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