MySQL root-login with SSH private key?
Suppose Mysql -dbs and an admin with a bad habbit to forget the passwords (or paranoid enough wanting more creative authentication, not just password). Is it possible to access Mysql -root shell for example in a way that the Ssh-agent stores the private keys and then I could just login by "mysql -u root" (without typing the passwords or a combination of private-key and a password)?
Answer
You can certainly use the normal SSH key authentication to log on to your shell account and then use a ~/.my.cnf file with your password inside. This will be used by default by the mysql command line client.
Its content should be:
[client]
user=the_user_name
password=the_password
Beware that whoever can read this file will be able to use those credentials. Protect it so that only the owner can read it (and lock your terminal if you go away from your keyboard).
If you want direct key-based authentication, you could also use SSL client-certificate authentication. You could create your own small CA and issue yourself with these client-certificates. A number of tools support this if you require direct remote access.