Let's start with this tweet from Bryan Ford. It links to an article that explains how a band of attackers were able to get full control of a Brazilian bank site thanks to altering the DNS records. They created a copy of the pages and got new SSL certs (we guess that the article is wrong about those 6 month old certificates from Let's Encrypt, that doesn't make sense. They are valid only for 90 days and they could have created them in a few seconds after taking over the DNS)
So losing control of DNS is really a big problem, even when they realized of the problem, they had to "fight" with NIC.br to recover control of their account and restore the proper DNS.
So what are possible solutions about this problem?
I think that something along HPKP (HTTP Public Key Pinning) is part of the answer. If everything worked correctly, the browsers would have noticed that the cert is wrong and then refused to load the page so visitors wouldn't have entered their credentials.
Bryan replied that HPKP has several problems and as you can read, it's hardly used.
So maybe the answer is not HPKP as-is now, but something developed to take into account new attacks.
Nowadays getting a HTTPS cert is finally easy thanks to Let's Encrypt, but there are still other kind of certs like EV SSL that provides verification of the company that runs the website. They aren't cheap, they require time and effort to get them, so maybe they are the starting point to get extra protection, not just showing a green url bar.
Let's say that all EV Certs are logged to a central repository (or multiple redundant copies), and that repository is the base for a new HPKP so it can't be abused by people trying to pin a free SSL cert that they got as soon as they took control of your server or your DNS. This new pinning would allow to protect those special sites that have worked and paid for a Cert that provides greater security to their users and the browsers would help to reach that goal.
A second way to use that central repository it would be that any CA should check it before issuing a new Cert. If a company has a EV Cert issued, Why would they want now a free SSL? Have they gone bankrupt? Or maybe they aren't the one requesting the new Cert? So this could close the hole that allows any CA to issue a Cert for an attacked domain.
Carlos Ferreira has replied about CAA records, but I fail to see how this is useful at all in the long run.
- The attacker doesn't have control of your server or your DNS. Then this will prevent them to get a SSL Cert, but I don't think that they could really get a Cert from any CA, maybe I'm wrong.
- The attacker has control of your server and is able to request new SSL certs. Why would they do that? If they are in your server, then they just can use your existing cert, they don't need to add a new one or create new ones.
- The attacker has control of your DNS. Then they can control CAA as they please and there's no protection at all.
There are many technologies around web security, some are old and trusted, others are proposals that didn't reach momentum for whatever reason. I'm an outsider so I can't really provide a full list of ways to get proper protection, but I feel that there are ways to get better security like promised by HPKP without risking basic sites.