How to set up ssh login with no password

How to do it First log in on A as user a and generate a pair of authentication keys. Do not enter a passphrase:

a@A:~> ssh-keygen -t rsa

Generating public/private rsa key pair. Enter file in which to save the key (/home/a/.ssh/id_rsa): Created directory '/home/a/.ssh'. Enter passphrase (empty for no passphrase): Enter same passphrase again:

Your identification has been saved in /home/a/.ssh/id_rsa. Your public key has been saved in /home/a/.ssh/id_rsa.pub. The key fingerprint is: 3e:4f:05:79:3a:9f:96:7c:3b:ad:e9:58:37:bc:37:e4 a@A

Now use ssh to create a directory ~/.ssh as user b on B. (The directory may already exist, which is fine):

a@A:~> ssh b@localhost mkdir -p .ssh b@localhost's password:

Finally append a's new public key to b@B:.ssh/authorized_keys and enter b's password one last time:

a@A:~> cat .ssh/id_rsa.pub | ssh b@B 'cat >> .ssh/authorized_keys' b@B's password:

From now on you can log into B as b from A as a without password:

a@A:~> ssh b@B hostname B