The Logjam (and Another) Vulnerability against Diffie-Hellman Key Exchange
Schneier on Security [blog]
May 21, 2015
“…. The Logjam attack allows a man-in-the-middle attacker to downgrade vulnerable TLS connections to 512-bit export-grade cryptography. This allows the attacker to read and modify any data passed over the connection. …
The attack affects any server that supports DHE_EXPORT ciphers, and affects all modern web browsers….
Much more interesting is the other vulnerability that the researchers found: Millions of HTTPS, SSH, and VPN servers all use the same prime numbers for Diffie-Hellman key exchange. … After this first step, an attacker can quickly break individual connections…. estimate that an academic team can break a 768-bit prime and that a nation-state can break a 1024-bit prime…. A second prime would allow passive decryption of connections to 66% of VPN servers and 26% of SSH servers. A close reading of published NSA leaks shows that the agency’s attacks on VPNs are consistent with having achieved such a break. …
Again, the NSA has put surveillance ahead of security. It never bothered to tell us that many of the “secure” encryption systems we were using were not secure. And we don’t know what other national intelligence agencies independently discovered and used this attack.
The good news is now that we know reusing prime numbers is a bad idea, we can stop doing it. …”
https://www.schneier.com/blog/archives/2015/05/the_logjam_and_.html