More data is currently being collected and shared by software applications than ever before. In many cases, the user is asked if either all or none of their data can be shared. We hypothesize that in some cases, users would like to share data in more complex ways. In order to implement the sharing of data using more complicated privacy preferences, complex data sharing policies must be used. These complex sharing policies require more space to store than a simple "all or nothing" approach to data sharing. In this paper, we present a new probabilistic data structure, called the Min Mask Sketch, to efficiently store these complex data sharing policies. We describe an implementation for the Min Mask Sketch in PostgreSQL and analyze the practicality and feasibility of using a probabilistic data structure for storing complex data sharing policies.