How to cache private files created with image_style_url()?

Question

PHP

field_file puts the files in the private directory then I need to render images styled with image_style_url() , drupal creates them and puts them in /private/styles/posts/private/attachments and renders them to the page but every time the page is loaded it is re-created and this takes quite a lot of time, since there are about 200 pictures, how to cache them?