Passwordless logins

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With Linux, it is possible to log in to a remote computer without having to type a password. You authenticate yourself with your "digital signature" and your public key.

Goal
You want to log in using ssh to a remote computer without being asked for a password.
Solution
Establish a trust relationship so your desktop's ssh key is authorized on your server like this:
desktop:~ # ssh-keygen -t dsa
Generating public/private dsa key pair.
Enter file in which to save the key (/root/.ssh/id_dsa):
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /root/.ssh/id_dsa.
Your public key has been saved in /root/.ssh/id_dsa.pub.
The key fingerprint is:
1c:9a:b8:03:ab:04:b3:7b:75:49:99:8c:51:79:5d:06 root@scorpio

Now you just need to copy your public key to the remote machine so that it can recognize you:

desktop:~ # ssh-copy-id -i .ssh/id_dsa.pub root@server

In this example, you create a key pair with no passphrase and distribute the public key from the computer desktop to server. The user root from desktop no longer needs to authenticate with his password, he can log in to server from desktop with the command

desktop:~ # ssh server
Welcome to server.
server:~ #
Explanation
The ssh folder contains a file authorized keys that contains host keys of trusted hosts. ssh-copy-id adds to this file. Instead of calling ssh-copy-id, you can also issue
desktop:~ # cat ~/.ssh/id_dsa.pub | ssh root@server "cat >>.ssh/authorized_keys" 

However, this command is error-prone because on some distributions, e.g. Red Hat, the file authorized_keys needs special permission settings. Better stick to ssh-copy-id.