Diffie-Hellman key exchange is a popular cryptographic algorithm that allows Internet protocols to agree on a shared key and negotiate a secure connection.
It is fundamental to many protocols including HTTPS, SSH, IPsec, SMTPS, and protocols that rely on TLS.
Researchers have uncovered several weaknesses in how Diffie-Hellman key exchange has been deployed.
Logjam Attack against the TLS Protocol
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 is reminiscent of the FREAK attack, but is due to a flaw in the TLS protocol rather than an implementation vulnerability, and attacks a Diffie-Hellman key exchange rather than an RSA key exchange.
The attack affects any server that supports DHE_EXPORT ciphers, and affects all modern web browsers. 8.4% of the Top 1 Million domains were initially vulnerable.
Threats from state-level adversaries
Millions of HTTPS, SSH, and VPN servers all use the same prime numbers for Diffie-Hellman key exchange.
Practitioners believed this was safe as long as new key exchange messages were generated for every connection. However, the first step in the number field sieve—the most efficient algorithm for breaking a Diffie-Hellman connection—is dependent only on this prime.
After this first step, an attacker can quickly break individual connections.We carried out this computation against the most common 512-bit prime used for TLS and demonstrate that the Logjam attack can be used to downgrade connections to 80% of TLS servers supporting DHE_EXPORT.
We further estimate that an academic team can break a 768-bit prime and that a nation-state can break a 1024-bit prime.
Breaking the single, most common 1024-bit prime used by web servers would allow passive eavesdropping on connections to 18% of the Top 1 Million HTTPS domains. 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.
