In our scans, we found several other exploitable security
issues in the DHE configurations used by TLS servers.
512-bit primes in non-export DHE We found 2,631
servers with browser-trusted certificates (and 118 in the
Top 1M domains) that used 512-bit or weaker primes for
non-export DHE. In these instances, active attacks may
be unnecessary. If a browser negotiates a DHE ciphersuite
with one of these servers, a passive eavesdropper can later
compute the discrete log and obtain the TLS session keys
for the connection. An active attack may still be necessary
when the client’s ordering of ciphersuites would result in the
server not selecting DHE. In this case, as in the DHE_EXPORT
downgrade attack, an active attacker can force the server to
choose a vulnerable DHE ciphersuite.
As a proof-of-concept, we implemented a passive eavesdropper
for regular DHE connections and used it to decrypt
test connections to www.fbi.gov. Until April 2015, this server
used the default 512-bit DH group from OpenSSL, which
was the third group for which we performed the NFS precomputation.
The website no longer supports DHE.