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WEAK DIFFIE-HELLMAN AND THE LOGJAM ATTACK

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.

We have uncovered several weaknesses in how Diffie-Hellman key exchange has been
deployed:

 1. 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.

 2. 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.


FULL TECHNICAL PAPER

Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice
David Adrian, Karthikeyan Bhargavan, Zakir Durumeric, Pierrick Gaudry, Matthew
Green, J. Alex Halderman, Nadia Heninger, Drew Springall, Emmanuel Thomé, Luke
Valenta, Benjamin VanderSloot, Eric Wustrow, Santiago Zanella-Béguelin, and Paul
Zimmermann
22nd ACM Conference on Computer and Communications Security (CCS ’15), Denver,
CO, October 2015
Best Paper Award Winner

More: Full paper | Talk slides | Bibtex


ADDITIONAL INFORMATION

We have also created a Guide to Deploying Diffie-Hellman for TLS, and several
Proof of Concept Demos.


CONTACT THE TEAM

This study was performed by computer scientists at CNRS, Inria Nancy-Grand Est,
Inria Paris-Rocquencourt, Microsoft Research, Johns Hopkins University,
University of Michigan, and the University of Pennsylvania: David Adrian,
Karthikeyan Bhargavan, Zakir Durumeric, Pierrick Gaudry, Matthew Green, J. Alex
Halderman, Nadia Heninger, Drew Springall, Emmanuel Thomé, Luke Valenta,
Benjamin VanderSloot, Eric Wustrow, Santiago Zanella-Beguelin, and Paul
Zimmermann. The team can be contacted at weakdh-team@umich.edu.


WHO IS AFFECTED?

Websites, mail servers, and other TLS-dependent services that support DHE_EXPORT
ciphers are at risk for the Logjam attack. We use Internet-wide scanning to
measure who is vulnerable.

Protocol Vulnerable to Logjam HTTPS — Top 1 Million Domains 8.4% HTTPS — Browser
Trusted Sites 3.4% SMTP+StartTLS — IPv4 Address Space 14.8% POP3S — IPv4 Address
Space 8.9% IMAPS — IPv4 Address Space 8.4%

Websites that use one of a few commonly shared 1024-bit Diffie-Hellman groups
may be susceptible to passive eavesdropping from an attacker with nation-state
resources. Here, we show how various protocols would be affected if a single
1024-bit group were broken in each protocol, assuming a typical up-to-date
client (e.g., most recent version of OpenSSH or up-to-date installation of
Chrome).

Vulnerable if most common 1024-bit group is broken HTTPS — Top 1 Million Domains
17.9% HTTPS — Browser Trusted Sites 6.6% SSH — IPv4 Address Space 25.7% IKEv1
(IPsec VPNs) — IPv4 Address Space 66.1%


WHAT SHOULD I DO?

IF YOU RUN A SERVER…

If you have a web or mail server, you should disable support for export cipher
suites and use a 2048-bit Diffie-Hellman group. We have published a Guide to
Deploying Diffie-Hellman for TLS with step-by-step instructions. If you use SSH,
you should upgrade both your server and client installations to the most recent
version of OpenSSH, which prefers Elliptic-Curve Diffie-Hellman Key Exchange.

IF YOU USE A BROWSER…

Make sure you have the most recent version of your browser installed, and check
for updates frequently. Google Chrome (including Android Browser), Mozilla
Firefox, Microsoft Internet Explorer, and Apple Safari are all deploying fixes
for the Logjam attack.

IF YOU’RE A SYSADMIN OR DEVELOPER …

Make sure any TLS libraries you use are up-to-date, that servers you maintain
use 2048-bit or larger primes, and that clients you maintain reject
Diffie-Hellman primes smaller than 1024-bit.

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These results were first made public on May 20, 2015; peer-reviewed conference
paper published October 13, 2015.