To summarise: the authors speculate that the NSA invested in a lot of resources into breaking Diffie-Hellman key exchange for certain 1024-bit primes. Just a few hardcoded 1024-bit primes were used in the majority of VPN handshakes and a significant minority of HTTPS and SSH handshakes worldwide in 2015. This would give the NSA the ability to recover the shared symmetric key used in these encrypted communications, and therefore decrypt them.
Since then several protocols have shifted towards preferring Elliptic Curve Diffie-Hellman key exchange which doesn't suffer from the same attack, or at least using larger primes for plain DHKE (1536-bit and above). However I don't know the extent of this - a lot of VPNs at least are still using the old, weak DH keys.
Since then several protocols have shifted towards preferring Elliptic Curve Diffie-Hellman key exchange which doesn't suffer from the same attack, or at least using larger primes for plain DHKE (1536-bit and above). However I don't know the extent of this - a lot of VPNs at least are still using the old, weak DH keys.