Would love to know more about the "Pairing and Crypt attacks" along with "Cryptovariable management". Probably the pairing here is referring to the pairing between client and server rather than the cryptographic technique of using pairings ... but it seems this hasn't surfaced in any of the other snowden docs. I often wish the journalists working on that story had released more source material.
They're only slides. We don't have audio of the presentations. :) I did wonder about that, but no "common" internet encryption protocols use pairing-friendly (in the open source cryptographic community sense) primitives. I think you're about right and it probably refers to matching public and private keys for CAs in SSL/TLS, looking up suitable intermediate CAs, for which they may have a few keys stashed away. They d…
Compromise of a CA's key does not permit decryption of traffic encrypted by server keys that use certificates (signatures) from those CAs. This is a common misconception.
It would allow for issuing (signing) a rogue, second key that could then be used to silently active MITM a connection - but getting the CA's key does not give you the VPN server's key.
(Remember, a certificate is just a signature by a CA over the hash of the VPN server's public key. The CA never sees the private key of the VPN server, nor is the CA's key used for anything other than signing.)