Just a quick tip for anyone facing this error. If you are doing customization of your themes or functions, you could face with the following error when trying to connect Jetpack:
Jetpack could not contact WordPress.com: register_http_request_failed. This usually means something is incorrectly configured on your web host.
SSL certificate problem: self signed certificate in certificate chain
If you go to your jetpack.php file and change https://jetpack.wordpress.com/jetpack to http://… you will get a different error which is closer to the real reason:
Your Jetpack has a glitch. Something went wrong that’s never supposed to happen. Guess you’re just lucky: xml_rpc-32700
Try connecting again.
Error Details: The Jetpack server could not communicate with your site’s XML-RPC URL. Please check to make sure http://zigman.altinet.eu/xmlrpc.php is working properly. It should show ‘XML‑RPC server accepts POST requests only.’ on a line by itself when viewed in a browser and should not have any blank links or extra output anywhere.
And when you go to that file you’ll probably see some empty lines or something like that. Ok, so you can now return the url to https, and start hunting inside your files for extra spaces on top or bottom (usually some functions.php file is to blame).
I’ve added a file which can help you find the trailing spaces that helped me. (got it originally from following link)
Note: I had to leave http instead of https for the connection to work. Didn’t have any problems so far with it but YMMV.
Hope that helps!