If I understand the handshaking of TLS/SSL between a host a client, the client sends a 
certificate 
to the host, then performs a RSA encryption operation using the certificate private 
key on 
challenge data sent by the host.

If the certificate and private key is located on a USB token/Smart Card, and the 
private key is 
marked as "sensitive" or "cannot be exported", then how does the Microsoft Browser 
perform the 
private key encryption using cryptoapi, when the private key cannot be exported?  I 
have searched 
the cryptoapi documentation and cannot find any way to do this without using 
CryptExportKey to 
obtain the private key.

Ken
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