Apply Security Settings to Multiple Files
You should be apply to apply security settings, i.e. password protect multiple files at once just like you can add a header/footer to multiple files at once.
You can create a new policy template from Protect—Encrypt—Manage Security Policies—New (create the new security settings that you want to apply) and save it as a template.
You will still need to open the files individually and apply the template on each file. But this would be an easier way around.