Error: An error occurred during a connection to newsgroup.foobar.com:563.
Cannot communicate securely with peer: no common encryption algorithm(s).
(Error code: ssl_error_no_cypher_overlap)
Server public key is 2048 bit
Secure Renegotiation IS supported
Protocol : SSLv3
In older Firefox Browsers (before 23), there was a menu entry to disable SSLv3 (Preferences-Advanced-Encryption).
For more recent Firefox versions you need to use the detailed configuration. Go to "about:config", search for "security.tls.version.min" and change the value to "1" at least.
The default is "0", see:
The same steps are needed for Thunderbird.