First, did you check these directives on /etc/ssh/sshd_config (toto host)?
AllowUsers root toto
If it is a production environment, I strongly suggest set these directives at this way:
Avoid root access and design other port than 22. It's safer.
If you want to access local network hosts without password prompt, just follow these steps bellow (let's suppose totXX=host client, totYY=host server ssh):
Create the same user in all machines (Ex: toto) with the same
Generate the public key on totXX
# may output a message like this:
toto@totXX:~> ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/home/toto/.ssh/id_rsa):
Created directory '/home/toto/.ssh'.
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/toto/.ssh/id_rsa.
Your public key has been saved in /home/toto/.ssh/id_rsa.pub.
The key fingerprint is:
Create ~/.ssh directory on totYY
toto@totXX:~> ssh toto@totYY mkdir -p .ssh
Put totXX public key on totYY:
toto@totXX:~> cat .ssh/id_rsa.pub | ssh toto@totoYY 'cat >> ssh/authorized_keys'
Restart ssh service on totYY:
toto@totXX:~> sudo service ssh restart
If everything is ok, the password won't be requested on ssh access.
toto@totoXX:~> ssh toto@totoYY