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From: http://rcsg-gsir.imsb-dsgi.nrc-cnrc.gc.ca/documents/internet/node31.html

ssh-keygen is used to generate that key pair for you. Here is a session where your own personal
private/public key pair is created:

cantin@sodium:~> ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/home/cantin/.ssh/id_rsa):
Enter passphrase (empty for no passphrase): <– press Enter…
Enter same passphrase again: <– press Enter again ..
Your identification has been saved in /home/cantin/.ssh/id_rsa.
Your public key has been saved in /home/cantin/.ssh/id_rsa.pub.
The key fingerprint is:
f6:61:a8:27:35:cf:4c:6d:13:22:70:cf:4c:c8:a0:23 cantin@sodium

The command ssh-keygen -t rsa initiated the creation of the key pair.

No passphrase was entered (Enter key was pressed instead).

The private key was saved in .ssh/id_rsa. This file is read-only and only for you. No one else must see
the content of that file, as it is used to decrypt all correspondence encrypted with the public key.

The public key is save in .ssh/id_rsa.pub.

In this case, the content of file id_rsa.pub is

ssh-rsa AAAAB3NzaC1yc2EAAAABIwAAAIEArkwv9X8eTVK4F7pMlSt45pWoiakFkZMw
G9BjydOJPGH0RFNAy1QqIWBGWv7vS5K2tr+EEO+F8WL2Y/jK4ZkUoQgoi+n7DWQVOHsR
ijcS3LvtO+50Np4yjXYWJKh29JL6GHcp8o7+YKEyVUMB2CSDOP99eF9g5Q0d+1U2WVdB
WQM= cantin@sodium

It is one line in length.

Its content is then copied in file .ssh/authorized_keys of the system you wish to SSH to without being
prompted for a password.

The example shown here generated keys on sodium by user cantin. If the public key generated,
file .ssh/id_rsa.pub, was copied to your account, file .ssh/authorized_keys on nickel.sao.nrc.ca, then
user cantin@sodium is allowed to SSH into your own account on nickel.sao.nrc.ca without the use of
a password.

To summarize, a personal private/public key pair is generated using the ssh-keygen command.
The public key is then copied onto a remote systems’ .ssh/authorized_keys file. And you can
now SSH to the remote systems’s account without the use of a password.