"The security certificate has expired or is not yet valid" is an error message you may get while trying to access secure pages. Some times you may get different but similar type error messages for the same issue like Secure Connection Failed. Common type of error messages are:
1. "website name " uses an invalid security certificate
2. This connection is untrusted
3. The security certificate has expired or is not yet valid
Screen shots of the error message are provided below.

"Secure Connection failed" error message looks like.

Common troubleshooting steps for the "the security certificate has expired or is not yet valid" error message are listed below.
1. check the system date
In most of the cases, wrong system date cause the certificate expired or invalid error message. Just by correcting the system date the error message will go.
2. Change the security preference in web browsers
Another step is to change the security preference in web browser. By changing the security level to lower level may solve the issue.
3. Try to open the website in another browser
If you face the issue in Firefox, try to open the same website in another browser.
4. Do Browser and OS update
Regular browser and OS updates can avoid many errors.
1. "website name " uses an invalid security certificate
2. This connection is untrusted
3. The security certificate has expired or is not yet valid
Screen shots of the error message are provided below.

"Secure Connection failed" error message looks like.

Common troubleshooting steps for the "the security certificate has expired or is not yet valid" error message are listed below.
1. check the system date
In most of the cases, wrong system date cause the certificate expired or invalid error message. Just by correcting the system date the error message will go.
2. Change the security preference in web browsers
Another step is to change the security preference in web browser. By changing the security level to lower level may solve the issue.
3. Try to open the website in another browser
If you face the issue in Firefox, try to open the same website in another browser.
4. Do Browser and OS update
Regular browser and OS updates can avoid many errors.
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