If secure connections are failing on a lot of websites, this can indicate one of these problems:

• Date, time, or time zone not correct. Firefox only allows a small margin of error.

• Firefox not set up to work with your security software's filtering feature. avast! 2015 (Web Shield), Kaspersky (SSL Scan), ESET, and BitDefender, for example, will intercept requests for web pages to filter them. For secure sites, this requires presenting a "fake" certificate to Firefox, which indicates that it was issued by your security software instead of the true issuer.

• Malware may have been installed and is presenting fake certificates to Firefox.

• Your connection to the web is being proxied through another system.

As a starting point for diagnosing this, does the error page contain a bottom section entitled "I understand the risks" that contains an "Add Exception" button? You can use this button to view the certificate without actually adding an exception. Click the button, then the "View" button to check the "Issued by" section of the certificate. Could you report what it says there? Then you can cancel out of adding an exception.

If the button is not available, you may be able to call up the Add an Exception dialog by pasting the following URL in the address bar and pressing Enter/Return to load it. Then type/paste in the address of the site you were trying to reach and see whether you can Get and View the certificate:

chrome://pippki/content/exceptionDialog.xul

I should add that as a Windows user, I'm not in a good position to recommend malware cleanup tools for MacOS X. You might try a search on Apple's forums for recommendations.

• https://discussions.apple.com/docs/DOC-2435
• https://www.google.com/search?q=remove+malware+site:discussions.apple.com

Clear the cache and remove cookies only from websites that cause problems.

"Clear the Cache":

• Firefox > Preferences > Advanced > Network > Cached Web Content: "Clear Now"

"Remove Cookies" from sites causing problems:

• Firefox > Preferences > Privacy > "Use custom settings for history" > Cookies: "Show Cookies"

You can check the connection settings.

• Firefox > Preferences > Advanced > Network : Connection > Settings
• https://support.mozilla.org/kb/Options+window+-+Advanced+panel

If you do not need to use a proxy to connect to internet then try to select "No Proxy" if "Use the system proxy settings" or one of the others do not work properly.

See "Firefox connection settings":

• https://support.mozilla.org/kb/Firefox+cannot+load+websites+but+other+programs+can

See also:

• https://support.mozilla.org/kb/connection-untrusted-error-message
• https://support.mozilla.org/kb/secure-connection-failed-error-message