Decrypt client certificate

I'm trying to authenticate my site's users by verifying their credentials from their DOD CAC (Common Access Card).
When I look through the key/value pairs in Request.ClientCertificate.Keys is see some fields are encrypted, and some that are not.
I assume that the encrypted fields were encrypted using the client's private key, and I can decrypt them using the supplied public key (right?).
I also assume in order to do this, I need to convert the public key and one of the encrypted fields to a Base64 string first.


Given the public key, and some other encrypted field (now in Base64 string) how do I perform that actual decryption?

...