An interesting aspect of Linux permissions is that the default permission is typically 777 (-rwxrwxrwx) and then umask is used to automatically remove permissions, so that when new directories or files are created, the newly created directory or file is not 777, and instead is something like 644 (-rw-r--r--) or 666 (-rw-rw-rw-). If you wish to remove the default read permission for all files/directories, you can adjust the umask. However, changing umask is probably not the solution to the task you face.
I think the solution would be to control access using chmod and chown or setfacl and getfacl. For example, lets say only root should have access to /var/private. You could use the following commands so that only root can read, write and access the directory and files in the directory.
Set root as both the owner and group owner of /var/private:
chown -R root:root /var/private
You could also set the permission on the directory so that only root can access the directory (-rwx------):
chmod 0700 /var/private
You could then recursively set the permission on all files in the directory so that only root can read, write and execute files in the directory (-rwx-----):
chmod 0700 -R /var/private/*
Note: I do not know how you are using your database. If your database files are accessible from a Web browser, such as through PHP or ASP.Net, this permission change may prevent PHP or ASP.Net from being able to interact with database records.