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.
You can use the Action Wizard for this.