you can do ssh key exchange between the hosts, for a particular user login. beware it will never ask for password, when you do ssh to that box, or create a shell to exit if done ssh
It does ssh key exchange without a password provided no passphrase exists for the key. In case a passphrase exists you have to put it in. Also since keys are dependent upon user account or user permission from which the command is being executed so the appropriate ssh key of that person stored in the ..ssh or appropriate directory is used.
In case you do have a passphrase you can use an ssh agent to load the private and once you key in the private key the agent takes care of the connection and for further it will not ask for the passphrase. I think you can also tell the ssh agent not to take input from a file and not standard input. Look for it other ssh agent will solve the purpose. See ssh-add it will do the trick for you. By default it loads the private key from the identity file.
Regards, Vivek