Why do you need an exception in the first place? The certificate exception prompt usually gives an exact error message.

dyoung115 said

I can no longer use Firefox for many of the sites that I know to be perfectly fine as they are ours. Firefox used to simply ask what I wanted to do and I had the ability to add a security exception and then I was able to access the site. Now it just fails to connect and even if I go to the Tools-> Options-> Advanced and go to Certificates, I have not yet been able to figure out how to be able to access a site once you decide it is insecure (even when I want to access it). If I can't find a way to solve this problem, I will be forced to use a different browser as it makes Firefox quite limited for my purposes - only useful for general browsing.

All I get for a message is...

Secure Connection Failed

An error occurred during a connection to {The Address In question}. SSL received a weak ephemeral Diffie-Hellman key in Server Key Exchange handshake message. (Error code: ssl_error_weak_server_ephemeral_dh_key)

   The page you are trying to view cannot be shown because the authenticity of the received data could not be verified.
   Please contact the web site owners to inform them of this problem.

This message is not of any use to me as I already know the site is fine - I just want to accesss it - how do I do that?

See https://developer.mozilla.org/en-US/Firefox/Releases/39/Site_Compatibility#Security

sites that I know to be perfectly fine as they are ours.

I don't know what that means, but you should adjust the configuration of 'your' sites. Using a different browser does not help to solve the underlying problem, and does not help to keep your visitors secure either.

christ1 said

See https://developer.mozilla.org/en-US/Firefox/Releases/39/Site_Compatibility#Security

sites that I know to be perfectly fine as they are ours.

I don't know what that means, but you should adjust the configuration of 'your' sites. Using a different browser does not help to solve the underlying problem, and does not help to keep your visitors secure either.

=================

What that means is that I am trying to access our own internal webapp that is running on the same machine (ie: localhost) as the Firefox instance I am using, and I still can't access the thing. This webapp is not for external consumption - internal use only and we don't need to prove to ourselves that it is a safe app.

Well, then all you need to do is to fix the web server configuration so that it's not vulnerable anymore to the Logjam attack. Google is your friend.