The private key file should be protected. In my case i have been using the public_key authentication for a long time and i used to set the permission as 600 (rw- --- ---) for private key and 644 (rw- r-- r--) and for the .ssh folder in the home folder you will have 700 permission (rwx --- ---). For setting this go to the user's home folder and run the following command
Set the 700 permission for .ssh folder
chmod 700 .ssh
Set the 600 permission for private key file
chmod 600 .ssh/id_rsa
Set 644 permission for public key file
chmod 644 .ssh/id_rsa.pub