It is widely believed that public/private keys or certificates are “more secure” than passwords. E.g., an SSH login via key rather than using a password. Or a site-to-site VPN with certificate authentication rather than a pre-shared key (PSK). However, even certificates and private keys are not unlimited secure. They can be compromised, too, since the public-key cryptography only implies that private keys won’t be exposed if a brute-force attack is nearly impossible.
So, what’s the real security level of passwords compared to public keys/certificates?