When attempting to install a plugin or update WordPress, the process will complete successfully with the following message:
Warning: An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the support forums. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/virtual/.../wp-includes/update.php on line 119
Older hosting platforms (v4) do not support validating SHA256 certificates.
Request an automatic server migration to a newer platform that supports SHA256 certificate validation, along with a slew of other improvements. This can be done within the control panel under Help > Trouble Tickets.
Discouraged Quick fix
As a quick fix, if you are, for whatever reason, unable to migrate to a newer platform with secure software, the following filter may be added to
wp-config.php at the end of the configuration. This will disable all SSL verification, which potentially leaves you vulnerable to a man-in-the-middle attack:
add_filter( 'https_ssl_verify', '__return_false' );