<html>
<head>
<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
<p>Da <a class="moz-txt-link-freetext" href="https://weakdh.org/">https://weakdh.org/</a><br>
</p>
<p><a
href="https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange">Diffie-Hellman
key exchange</a> 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.</p>
<p>We have uncovered several weaknesses in how Diffie-Hellman key
exchange has been deployed:</p>
<ol>
<li> <b>Logjam Attack against the TLS Protocol.</b> 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 <a
href="http://freakattack.com">FREAK attack</a>, 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 <tt>DHE_EXPORT</tt> ciphers, and affects all modern
web browsers. 8.4% of the Top 1 Million domains were initially
vulnerable.</li>
<li>
<p><b>Threats from state-level adversaries.</b> 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.</p>
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 DHE EXPORT servers.
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.</li>
</ol>
</body>
</html>