OpenWRT is a linux distribution for embedded devices like a router. The installation of OpenWRT on your device instead of the original vendor’s firmware allows you to do some nifty stuff with your router like installing additional software out of openWRT’s own repository.
Although there is a package for the openSSH server available, dropbear is the default choice. To enable password-less ssh access you first need to generate the ssh keys on your client machine if you haven’t already. If you want, you can secure your key by typing in a password, otherwise just press enter.
Next you have to transfer your public key (the file ending with .pub) to your openWRT installation.
pat@earth:~$ scp ~/.ssh/id_rsa.pub 192.168.1.1:/tmp/
Replace 192.168.1.1 with the IP of your router. If you changed the Port of your ssh server, you have to define it using the -P parameter like scp -P 4321 etc.
Connect to your router and add the transferred public key file to your authorized_keys. Unlike OpenSSH, Dropbear doesn’t look in .ssh underneath your home directory for the authorized_keys file, so you have to create the file in /etc/dropbear/.
root@router:~# cd /etc/dropbear/
root@router:~# cat /tmp/id_rsa.pub >> authorized_keys
root@router:~# chmod 0600 authorized_keys
Now you should be able to ssh from your client pc to your openWRT device without the need of a password.