For security
It takes me and my colleague some minutes to figure out why our machines cannot ssh their own localhost. We added -v to ssh for debugging and found that the id_rsa is offered but ignored.
Finally, we checked and changed the file permissions. Then the problem got solved.
The following is a set of correct settings.
Permissions and commands
Generate keys:
ssh-keygen -t rsa -b 4096 -N '' -C "yourname@example.com" -f ~/.ssh/id_rsa
Add keys:
eval "$(ssh-agent -s)"
ssh-add ~/.ssh/id_rsa
Change file permissions:
chmod 700 ~/.ssh
chmod 644 ~/.ssh/authorized_keys
chmod 644 ~/.ssh/known_hosts
chmod 644 ~/.ssh/config
chmod 600 ~/.ssh/id_rsa
chmod 644 ~/.ssh/id_rsa.pub