Honestly SSL (https) is not as safe as people may think. There are multiple ways hackers can exploit vulnerabilities in the 'secure' socket layer using attacks such as Heartbleed, BEAST, and many others.
The little green lock and SSL stamps IMO just give the illusion of safety really. I have studied multiple things in the web developing world and security was one of them.
If you're truly concerned about your security on the internet i suggest looking into a VPN (virtual private network) these give a solid private and encrypted way of hiding your identity and other personal data while online. They are not hard to use and there are many great companies that provide them for cheap. Google some reviews and see what people say.
But the simple truth is, nothing on the web is actually secure.