Defining privacy is supposed to be easy

Formally specifying privacy goals is not trivial. The most widely used approach in formal methods is based on the static equivalence of frames in the applied pi-calculus, basically asking whether or not the intruder is able to distinguish two given worlds. A subtle question is how we can be sure that we have specified all pairs of worlds to properly reflect our intuitive privacy goal. To address this problem, we introduce in this paper a novel and declarative way to specify privacy goals, called α-β privacy, and relate it to static equivalence. This new approach is based on specifying two formulae α and β in first-order logic with Herbrand universes, where α reflects the intentionally released information and β includes the actual cryptographic ("technical") messages the intruder can see. Then α-β privacy means that the intruder cannot derive any "non-technical" statement from β that he cannot derive from α already. We describe by a variety of examples how this notion can be used in practice. Even though α-β privacy does not directly contain a notion of distinguishing between worlds, there is a close relationship to static equivalence of frames that we investigate formally. This allows us to justify (and criticize) the specifications that are currently used in verification tools, and obtain partial tool support for α-β privacy.