Is there key infrastructure allows one running as sudo remotely without prompting password?

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http://askubuntu.com – For example, I can use ssh-id-copy to get the key and login to the remote server without entering the password. Is there a similar mechanism to run as root without prompting password? I don't know. If login with a key is sort of safe, then I argue there should be a mechanism like that for sudo. NOPASSWD is not a good solution, however. Thanks. (HowTos)