Verification of Quantitative Hyperproperties Using Trace Enumeration\n Relations

Abstract

Many important cryptographic primitives offer probabilistic guarantees of\nsecurity that can be specified as quantitative hyperproperties; these are\nspecifications that stipulate the existence of a certain number of traces in\nthe system satisfying certain constraints. Verification of such hyperproperties\nis extremely challenging because they involve simultaneous reasoning about an\nunbounded number of different traces. In this paper, we introduce a technique\nfor verification of quantitative hyperproperties based on the notion of trace\nenumeration relations. These relations allow us to reduce the problem of\ntrace-counting into one of model-counting of formulas in first-order logic. We\nalso introduce a set of inference rules for machine-checked reasoning about the\nnumber of satisfying solutions to first-order formulas (aka model counting).\nPutting these two components together enables semi-automated verification of\nquantitative hyperproperties on infinite state systems. We use our methodology\nto prove confidentiality of access patterns in Path ORAMs of unbounded size,\nsoundness of a simple interactive zero-knowledge proof protocol as well as\nother applications of quantitative hyperproperties studied in past work.\n