I suspect (not know, not “am able to prove”, suspect) that their “breakthrough” involves being a shadow-peer-certificate-authority, getting ahold of (or even having issued) the certs being issued to authenticate and encrypt.
My real paranoia says that they invented BitCoin in order to build a giant, more-or-less free method to do a lot of cracking computation on finding certificates with hash collisions that could be used.
Or it could be as simple as they found a side-channel timing attack in many (most) implementations of TLS, similar to the one described in [Remote Timing Attacks are Still Practical⋆ Billy Bob Brumley and Nicola Tuveri].
