SSH login without password

Every time using SSH to login, we should type enter our passwords in to login successfully. Here is a method which make SSH login without entering password.

First, use ssh-keygen to generate the public/private RSA key pair

willy@LOCAL_COMPUTER:~$ ssh-keygen
Generating public/private rsa key pair.
Enter file in which to save the key (/home/willy/.ssh/id_rsa):
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/willy/.ssh/id_rsa.
Your public key has been saved in /home/willy/.ssh/id_rsa.pub.
The key fingerprint is:
8c:ee:fc:2f:62:b8:84:78:43:0b:1b:d7:7b:72:32:cd willy@willy-System-Product-Name
The key's randomart image is:
+--[ RSA 2048]----+
|                 |
|                 |
|                 |
|   .   o         |
|o o . . S        |
| B o =           |
|o = *.E          |
| . o.Oo .        |
|    .ooo.o.      |
+-----------------+

Second, copy the public key ~/.ssh/id_rsa.pub to the remote server

willy@LOCAL_COMPUTER:~$ sftp willy@REMOTE_SERVER
sftp> put id_rsa.pub
sftp> quit

Third, login the REMOTE_SERVER and append the id_rsa.pub to ~/.ssh/authorized_keys

willy@LOCAL_COMPUTER:~$ ssh willy@REMOTE_SERVER
willy@REMOTE_COMPUTER:~$ cat id_rsa.pub ~/.ssh/authorized_keys
willy@REMOTE_COMPUTER:~$ exit

Finally, login again, this time, we need not to enter the password.