1. Generate the ssh key pair on the desktop computer:
ssh-keygen
2. Copy the public key to the server:
scp ~/.ssh/id_rsa.pub user@10.10.10.1:
3. Connect to the server:
ssh user@10.10.10.1
4. Append the public key to authorized_keys and remove the uploaded copy:
cat id_rsa.pub >> ~/.ssh/authorized_keys
rm id_rsa.pub
5. Edit the ssh server configuration to make sure that public key authentication is enabled (it should be enabled by default):
sudo nano /etc/ssh/sshd_config
5.1 These entries must be set to yes:
RSAAuthentication yes
PubkeyAuthentication yes
6. Reload the configuration:
sudo /etc/init.d/ssh reload
7. Disconnect from the server:
exit
8. Try connecting without the need to give the password to the ssh-client:
ssh user@10.10.10.1
You might need to give a password now to access your private key file, but you should not need to give the password to the ssh program.
9. Disable password authentication:
sudo nano /etc/ssh/sshd_config
9.1 The following settings should be set to no:
ChallengeResponseAuthentication no
PasswordAuthentication no
UsePAM no
9.2. Reload the configuration:
sudo /etc/init.d/ssh reload
10. Test that password authentication really is disabled:
10.1 Disconnect from the server:
exit
10.2 Rename your private key file:
mv ~/.ssh/id_rsa ~/.ssh/id_rsa.backup
10.3 Try to reconnect to the server:
ssh user@10.10.10.1
This should produce a permission denied message: “Permission denied (publickey).”
10.4 Restore your private key file:
mv ~/.ssh/id_rsa.backup ~/.ssh/id_rsa
Done 
Referens
Thank you VERY MUCH for this useful guide. May I point out that you left out one step beetween 9 and 10:Reload the configuration:
sudo /etc/init.d/ssh reload
Thank you jb, I’ve updated the post to include the missing step.
Thanks a lot. That was very helpful
I had to take two extra permission steps on the machine i was sshing into to make it work due to this error: “SSH Error: Permission denied (publickey,gssapi-with-mic)” . Not sure if they’re relevant but here are the steps that did the trick.
chmod 600 .ssh/authorized_keys
chmod 700 .ssh
After that, my sshing without password worked great.
Thanks for the great tutorial!