The Complexity of Quantitative Information Flow Problems

—In this paper, we investigate the computational complexity of quantitative information flow (QIF) problems. Information-theoretic quantitative relaxations of noninterference (based on Shannon entropy) have been introduced to enable more fine-grained reasoning about programs in situations where limited information flow is acceptable. The QIF bounding problem asks whether the information flow in a given program is bounded by a constant d. Our first result is that the QIF bounding problem is PSPACE-complete. The QIF memoryless synthesis problem asks whether it is possible to resolve nondeterministic choices in a given partial program in such a way that in the resulting deterministic program, the quantitative information flow is bounded by a given constant d. Our second result is that the QIF memoryless synthesis problem is also PSPACE-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that ...

• Type: Journal
• Year: 2011
• Where: CSFW
• Authors: Pavol Cerný, Krishnendu Chatterjee, Thomas A. Henzinger
• Keywords: Computational Complexity, CSFW 2011, Security Privacy, Shannon Entropy, Synthesis Problem