Two-Bit Pattern Analysis For Quantitative Information Flow

Protecting confidential information from improper disclosure is a fundamental security goal. While encryption and access control are important tools for ensuring confidentiality, they cannot prevent an authorized system from leaking confidential information to its publicly observable outputs, whether inadvertently or maliciously. Hence, secure information flow aims to provide end-to-end control of information flow. Unfortunately, the traditionally-adopted policy of noninterference, which forbids all improper leakage, is often too restrictive. Theories of quantitative information flow address this issue by quantifying the amount of confidential information leaked by a system, with the goal of showing that it is intuitively “small” enough to be tolerated. Given such a theory, it is crucial to develop automated techniques for calculating the leakage in a system. This dissertation is concerned with program analysis for calculating the maximum leakage, or capacity, of confidential information in the context of deterministic systems and under three proposed entropy measures of information leakage: Shannon entropy leakage, min-entropy leakage, and g-leakage. In this context, it turns out that calculating the maximum leakage of a program reduces to counting the number of possible outputs that it can produce. The new approach introduced in this dissertation is to determine two-bit patterns, the relationships among pairs of bits in the output; for instance we might determine that two bits must be unequal. By counting the number of solutions to the two-bit patterns, we obtain an upper bound on the number of possible outputs. Hence, the maximum leakage can be bounded. We first describe a straightforward computation of the two-bit patterns using an automated prover. We then show a more efficient implementation that uses an implication graph to represent the two- bit patterns. It efficiently constructs the graph through the use of an automated prover, random executions, STP counterexamples, and deductive closure. The effectiveness of our techniques, both in terms of efficiency and accuracy, is shown through a number of case studies found in recent literature