if I configure my server to use 6144-bit or 8192-bit DH parameters, the test fails to detect DHE ciphersuites. with 8192-bit parameters, the test also fails to detect any TLS 1.2 ciphersuites.
What SSL/TLS server software are you using? I have no problems in my testing using large params (other than the expected Java client messups).
Correction: The server software is truncating the DH params to the keysize, if the DH is over the keysize. In my test case, it's effectively 4096bits. Depending on the software you're using, it might be allowing the larger params, but then unable to properly generate temp keys.
I'm using nginx. I did a bit more testing, it looks like clients that try to use DHE fail to connect... but somehow tlsenum still detects the DHE ciphersuites.
and there's still the issue of all the other TLS 1.2 ciphersuites (with ECDHE) not being detected when there server is configured with 8192-bit DH parameters... which is probably a bug in the test, since chrome can still access the site using EECDH and chacha20, and Firefox using EECDH and AES GCM (both TLS 1.2 ciphersuites that aren't detected by the test).
I've disabled DHE for now, since it's slow and I don't really care about ancient versions of android and openssl, but can re-enable it for testing if you want.
DHE gets much slower as your param size increases. If you had an interest in troubleshooting this further, the next step I'd recommend is setting the param size to <= the keysize. I don't know of anyone issuing 8192bit certs professionally, so I'd expect you probably have a 2048bit or 4096bit cert.
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