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 EXPTIME-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that is, by allowing the synthesized program to have more variables then the original partial program). Our third result is that the QIF general synthesis problem is EXPTIME-hard.
205 - 217
CSF: Computer Security Foundations
2011-06-27 – 2011-06-29
Cerny P, Chatterjee K, Henzinger TA. The complexity of quantitative information flow problems. In: IEEE; 2011:205-217. doi:10.1109/CSF.2011.21
Cerny, P., Chatterjee, K., & Henzinger, T. A. (2011). The complexity of quantitative information flow problems (pp. 205–217). Presented at the CSF: Computer Security Foundations, Cernay-la-Ville, France: IEEE. https://doi.org/10.1109/CSF.2011.21
Cerny, Pavol, Krishnendu Chatterjee, and Thomas A Henzinger. “The Complexity of Quantitative Information Flow Problems,” 205–17. IEEE, 2011. https://doi.org/10.1109/CSF.2011.21.
P. Cerny, K. Chatterjee, and T. A. Henzinger, “The complexity of quantitative information flow problems,” presented at the CSF: Computer Security Foundations, Cernay-la-Ville, France, 2011, pp. 205–217.
Cerny P, Chatterjee K, Henzinger TA. 2011. The complexity of quantitative information flow problems. CSF: Computer Security Foundations 205–217.
Cerny, Pavol, et al. The Complexity of Quantitative Information Flow Problems. IEEE, 2011, pp. 205–17, doi:10.1109/CSF.2011.21.