I dont have any specific llms to recommend but if you do want to go that route you could always run it remotely through something like Google collab.

But I don’t know if I would trust the results of an llm doing this as any mistake would make your entire resume untrustworthy

Correct, though to be pedantic anyone can be a CA- you just generate a cert with the right bits to say it’s a ca certificate and then use it to sign any other certificate you want.

But the only devices that will consider your signature worth anything are ones you also install your ca certificate on. So it’s useful and common in internal networks but isn’t really what is being asked here.

The hard part is getting in the root CA store of operating systems and browsers. As far as I know they are all maintained independently with their own requirements.