Security is based on a combination of:

* The integrity of registrar accounts that are the root of trust for most DNS zones (this was, last I checked, the overwhelming source of DNS corruption attacks),

* The security of one or more DNS lookups, depending (some CAs, like LetsEncrypt, do multi-perspective lookups), and

* The WebPKI Certificate Transparency system, which tracks the issuance of all certificates that Chrome and Mozilla will accept in a public ledger.