I’ve seen something like this before in the forums, it was related to a proxy server and ssl.

Does your web connection go through a proxy? Do you have a caching server like squid?

Here’s related issues, they all seem to have the same answer:
http://askubuntu.com/questions/186847/error-gnutls-handshake-failed-when-connecting-to-https-servers
http://unix.stackexchange.com/questions/302839/gnutls-handshake-failed
http://devopscube.com/gnutls-handshake-failed-aws-codecommit/