The most popular algorithm used for key-based authentication is RSA. The asymmetric keys using at present consist of thousand of bits (as for year 2016, the recommended lengths are 20 bits). Of course, the brute force attacks may still be performed by an attacker, but the complexity of long and unreadable keys is much larger, and such attacks would have significantly smaller chance of success. During establishing the connection, the server would use the public key to authenticate the client, for example by encrypting some number and asking the client to decrypt it, by using his corresponding private key. Users would store their public keys in each system they want to use, while at the some time their private keys would be kept secure on the computers, the users want to use to connect with those secured systems. The idea is to assign a pair of asymmetric keys to every user. Public key authentication offers a solution to these problems. Moreover, this method requires the users to remember their (ideally difficult and complex) passwords. A disadvantage of this method is that, when a server is publicly available, it may be targeted by various types of brute force and dictionary attacks, and the password may eventually be broken and revealed. In order to log into a server, users have to provide their secret passwords, which are verified by the server. It does not require much preparation (at least, from the client's point of view), and perhaps is generally more intuitive. Nowadays, password authentication is more popular than public key authentication. Instead of requiring a user's password, it is possible to confirm the client's identity by using asymmetric cryptography algorithms, with public and private keys. Key-based authentication is a kind of authentication that may be used as an alternative to password authentication. Key-Based Authentication (Public Key Authentication)

Ssh keys explained