I am experiencing the same problem on the K3. This has started about a year ago on a handful of websites and has been getting progressively worse. Now most websites are affected.
My first guess was outdated root certificates: I therefore updated `/etc/ssl/certs/ca-certificates.crt` with the certificates extracted from Firefox.
Unfortunately this has not made any difference that I can tell. Those websites that were working before, e.g.
https://www.google.com, continue to work while those that did not, e.g.
https://premium.zeit.de, are still showing the OP's message.
Any ideas from the Kindle hackers? I would love to get my trusty K3 working again.
Update 1:
Messing with `/etc/ssl/certs/ca-certificates.crt` was a bad idea: It prevents installation of FW 3.4.1 which is the correct solution to the above described HTTPS problem.
Before I forget:
https://www.ssllabs.com/ssltest/viewMyClient.html does not load either...