There is a way to do it but it would be awkward if you have a lot of users. You could create a role for each user and you can use an instance of Shared Files for each user and set the view permissions to the role for the corresponding user.
The Shared Files feature allows secure storage and access to files and it protects file access by roles, but not at the file level, it is for the whole instance of the Shared Files. You can use as many instances as you need but as I said it would be awkward.
Hope it helps,
Joe