There are a few different means of authentication with SSH. First, let me say that having no authentication would be extremely risky, even with a completely isolated machine. Whether SSH can even be configured in such a manner I am not certain, nor would I ever attempt it.
The best option to avoid password prompting would be to use key based authentication. If this will not work for you, you might want to look into something such as Kerberos + LDAP or even host authentication.
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