Topology of Privacy: Lattice Structures and Information Bubbles for Inference and Obfuscation

Abstract : Information has intrinsic geometric and topological structure, arising from relative relationships beyond absolute values or types. For instance, the fact that two people did or did not share a meal describes a relationship independent of the meal's ingredients. Such relationships give rise to lattices. Lattices have topology. That topology informs the ways in which information may be observed, hidden, inferred, and dissembled. Privacy preservation may be understood as finding isotropic topologies, in which relationships appear homogeneous. Moreover, the underlying lattice structure of those topologies has a temporal aspect, which reveals how isotropy may degrade over time, thereby puncturing privacy.