I have a website hosted on a server on which I have installed self signed certificate. If I install the same self signed certificate on the client device that is on the internet and access the public domain, will that be trusted? if not why?
1. yes. certificate can be use for public domain too
2. will not trust, to make it trusted, users need to install CA certificate from the CA server which created the self signed certificate.
3. since self signed certificate's CA certificate is not publicly advertised, web browsers cannot identify the trustworthiness from self signed certs. you need to install CA certificate from server to enforce web browsers to trust them.
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The technical point is already answered. I would ask myself "Is it worth it doing it that dirty way" with probably every web-provider supporting free Lets Encrypt certificates with automatic enrolment.