There's is some easy steps to follow :

• If possible change the sshd daemon listening port (How to change the listening port of Sshd)
• If you enabled login through private key (How to open an ssh session with a private key), you can disable password authentication. You just have to edit /etc/ssh/sshd_config to add :

PermitEmptyPasswords no

• You can also use fail2ban to ban script kiddies.

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