Abstract
Quantitative analysis of information flow is widely used to measure how much information was leaked from the secret inputs to the outputs or public inputs of a program. We propose to conduct the quantitative analysis of information flow within the trusted kernel of a higher-order-logic theorem prover in order to overcome the inaccuracy limitations of traditional analysis techniques used in this domain. For this purpose, we present the formalization of the Kullback-Leibler divergence that can be used as a unified measure of information leakage. Furthermore, we propose two new measures of information leakage, namely the information leakage degree and the conditional information leakage degree. We also formalize the notion of anonymity-based single MIX and use the channel capacity as a measure of information leakage in the MIX. Finally, for illustration purposes, we show how our framework allowed us to find a counter-example for a theorem that was reported in the literature to describe the leakage properties of the anonymity-based single MIX.
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References
Chatzikokolakis, K., Palamidessi, C., Panangaden, P.: Anonymity Protocols as Noisy Channels. In: Montanari, U., Sannella, D., Bruni, R. (eds.) TGC 2006. LNCS, vol. 4661, pp. 281–300. Springer, Heidelberg (2007)
Chaum, D.: The Dining Cryptographers Problem: Unconditional Sender and Recipient Untraceability. Journal of Cryptology 1(1), 65–75 (1988)
Coble, A.R.: Formalized Information-Theoretic Proofs of Privacy Using the HOL4 Theorem-Prover. In: Borisov, N., Goldberg, I. (eds.) PETS 2008. LNCS, vol. 5134, pp. 77–98. Springer, Heidelberg (2008)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience (1991)
Deng, Y., Pang, J., Wu, P.: Measuring Anonymity with Relative Entropy. In: Dimitrakos, T., Martinelli, F., Ryan, P.Y.A., Schneider, S. (eds.) FAST 2006. LNCS, vol. 4691, pp. 65–79. Springer, Heidelberg (2007)
DÃaz, C., Seys, S., Claessens, J., Preneel, B.: Towards Measuring Anonymity. In: Dingledine, R., Syverson, P.F. (eds.) PET 2002. LNCS, vol. 2482, pp. 54–68. Springer, Heidelberg (2003)
Gallager, R.G.: Information Theory and Reliable Communication. John Wiley & Sons, Inc. (1968)
Goldberg, R.R.: Methods of Real Analysis. Wiley (1976)
Gordon, M.J.C.: Mechanizing Programming Logics in Higher-Order Logic. In: Current Trends in Hardware Verification and Automated Theorem Proving, pp. 387–439. Springer (1989)
Gordon, M.J.C., Melham, T.F.: Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press (1993)
Kwiatkowska, M., Norman, G., Parker, D.: Quantitative Analysis with the Probabilistic Model Checker PRISM. Electronic Notes in Theoretical Computer Science 153(2), 5–31 (2005)
Malacaria, P.: Assessing Security Threats of Looping Constructs. SIGPLAN Notes 42(1), 225–235 (2007)
Mhamdi, T., Hasan, O., Tahar, S.: On the Formalization of the Lebesgue Integration Theory in HOL. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 387–402. Springer, Heidelberg (2010)
Mhamdi, T., Hasan, O., Tahar, S.: Formalization of Entropy Measures in HOL. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 233–248. Springer, Heidelberg (2011)
Mhamdi, T., Hasan, O., Tahar, S.: Quantitative Information Flow Analysis in HOL (2012), http://hvg.ece.concordia.ca/code/hol/information-flow/
Reiter, M.K., Rubin, A.D.: Crowds: Anonymity for Web Transactions. ACM Transactions on Information and System Security 1(1), 66–92 (1998)
Sabelfeld, A., Myers, A.C.: Language-Based Information-Flow Security. IEEE Journal on Selected Areas in Communications 21(1), 5–19 (2003)
Serjantov, A., Danezis, G.: Towards an Information Theoretic Metric for Anonymity. In: Dingledine, R., Syverson, P.F. (eds.) PET 2002. LNCS, vol. 2482, pp. 41–53. Springer, Heidelberg (2003)
Smith, G.: On the Foundations of Quantitative Information Flow. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 288–302. Springer, Heidelberg (2009)
Zhu, Y., Bettati, R.: Information Leakage as a Model for Quality of Anonymity Networks. IEEE Transactions on Parallel and Distributed Systems 20(4), 540–552 (2009)
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Mhamdi, T., Hasan, O., Tahar, S. (2012). Quantitative Analysis of Information Flow Using Theorem Proving. In: Aoki, T., Taguchi, K. (eds) Formal Methods and Software Engineering. ICFEM 2012. Lecture Notes in Computer Science, vol 7635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34281-3_11
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DOI: https://doi.org/10.1007/978-3-642-34281-3_11
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