I know there is https://www.drupal.org/project/field_permissions module, which allows to set field permissions per role, however what I need is to provide each individual field access permissions. As put on https://www.drupal.org/node/1376182
It looks that there is no module allowing to restrict access to certain files / images per role. What I think about is having checkboxes beside each file/image where to select the roles to have view access to the according entry.
I can't believe this was not implemented before, so hopefully someone can point out a viable solution.
Edit: I've got couple responses confused about what I wanted, so I believe I have to elaborate little more.
Field Permissions set role permissions for the field across all the nodes. What I am looking for is role permissions for individual field PER NODE. For example, an admin for Drupal 7 site could edit node 1 and make the file attached to it viewable to role "subscriber", but that wouldn't change any permission for another file attached to node 2. I hope it is now clear.