C-Servers does not log, at any moment, any activity on our customers, and while we do have root, the root password is very, very hard (impossible) to be decrypted.
For our root password to be effectively decrypted, all root and user passwords on the Linux world would have to be automatically insecure by design, which is not possible to ever happen, as all user and root account passwords are encrypted.
Even if an attacker reached the main server, he would still have to breach over a second layer of protection: your VPS password. Which is also encrypted. Over an SSH session... which is also encrypted as well.
Therefore, it's not possible to have any sort of effective keylogging over this service.
Nevertheless, the usual precautions apply, given this is still a public service.