Visibility of other user's tasks

Hi! We are small team which tests your resource for our own needs. Specification of our organization dictates us to hide tasks between team mebers except some it (tasks). Is it possible to create one task for me and one task assigned to other user in the same project in such way other user can see only task assigned to hem but not see my task? Because now I can see not my tasks in the project as well as tasks assigned to me. Also I can see all tasks of another user in his profile. But we want to hide this information too.