Weak Diffie-Hellman and the Logjam Attack

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
    , 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

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 |

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

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.

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

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