Using SSH login without password

This is a simple article that provides the necessary steps to allow ssh login without the need of entering the users password
  1. on serverA generate a pair of authentication keys:
    user@serverA$ ssh-keygen -t rsa
    Generating public/private rsa key pair.
    Enter file in which to save the key (/home/usera/.ssh/id_rsa): <Enter>
    Created directory '/home/usera/.ssh'.
    Enter passphrase (empty for no passphrase): <Enter>
    Enter same passphrase again: <Enter>
    Your identification has been saved in /home/usera/.ssh/id_rsa.
    Your public key has been saved in /home/usera/.ssh/id_rsa.pub.
    The key fingerprint is:
    a1:b2:c3:d4:e5:f6:7a:8b:9c:0d:1e:2f:a3:b4:c5:d6 usera@serverA
    The key's randomart image is:
    do not enter a passphrase,

    To generate an SSH1 RSA or SSH2 DSA key pair, specify the -t rsa1 or -t dsa options.
  2. use ssh to create a directory ~/.ssh on serverB and append usera ssh public key usera@serverB:.ssh/authorized_keys and enter the users password one last time:
    usera@serverA$ ssh usera@serverB mkdir -p .ssh
    usera@serverA$ cat .ssh/id_rsa.pub | ssh usera@serverB 'cat >> .ssh/authorized_keys'

    An alternative on some Linux systems, is to use the ssh-copy-id script to append the public key in the local ~/.ssh/id_rsa.pub file to the ~/.ssh/authorized_keys file on the remote system, for example:

    usera@serverA$ ssh-copy-id usera@serverB
    usera@serverB's password: remote_password
    Now try logging into the machine, with "ssh 'usera@serverB'", and check in:
    
      .ssh/authorized_keys
    
    to make sure we haven't added extra keys that you weren't expecting.

    When prompted, enter your password for the remote system.

    The script also changes the permissions of ~/.ssh and ~/.ssh/authorized_keys on the remote system to disallow access by your group.

  3. Now it's a simple as:
    usera@serverA$ ssh usera@serverB
    usera@serverB$ 
  4. Verify that the permissions on the remote ~/.ssh directory and ~/.ssh/authorized_keys file allow access only by you:
    usera@serverA$ ssh usera@serverB ls -al .ssh
    total 4
    drwx------+ 2 usera mygrp   5 Feb 10 15:47 .
    drwxr-xr-x+ 3 usera mygrp   9 Feb 10 15:48 ..
    -rw-------+ 1 usera mygrp 397 Feb 10 15:48 authorized_keys

NOTE: On some systems you need to place the public key in the file .ssh/authorized_keys2