Abstract
Information theory provides a range of useful methods to analyse probability distributions and these techniques have been successfully applied to measure information flow and the loss of anonymity in secure systems. However, previous work has tended to assume that the exact probabilities of every action are known, or that the system is non-deterministic. In this paper, we show that measures of information leakage based on mutual information and capacity can be calculated, automatically, from trial runs of a system alone. We find a confidence interval for this estimate based on the number of possible inputs, observations and samples. We have developed a tool to automatically perform this analysis and we demonstrate our method by analysing a Mixminon anonymous remailer node.
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References
Arimoto, S.: An algorithm for computing the capacity of arbitrary memoryless channels. IEEE Trans. on Inform. Theory IT-18(1), 14–20 (1972)
Backes, M., Köpf, B.: Formally bounding the side-channel leakage in unknown-message attacks. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 517–532. Springer, Heidelberg (2008)
Bayes, T.: An essay towards solving a problem in the doctrine of chances. Philo. Trans. of the Royal Society of London 53, 370–418 (1774)
Bickel, P.J., Doksum, K.A.: Mathematical Statistics: Basic Ideas and Selected Topics. Prentice Hall, Englewood Cliffs (2006)
Blahut, R.E.: Computation of channel capacity and rate distortion functions. IEEE Trans. on Inform. Theory IT-18(4), 460–473 (1972)
Brillinger, D.R.: Some data analysis using mutual information. Brazilian Journal of Probability and Statistics 18(6), 163–183 (2004)
Brillinger, D.R.: Personal correspondence (April 2009)
Chatzikokolakis, K., Chothia, T., Guha, A.: Calculating probabilistic anonymity from sampled data. Technical report, University of Birmingham (2009)
Chatzikokolakis, K., Palamidessi, C., Panangaden, P.: Anonymity protocols as noisy channels. Information and Computation 206, 378–401 (2008)
Chatzikokolakis, K., Palamidessi, C., Panangaden, P.: On the bayes risk in information-hiding protocols. J. Comput. Secur. 16(5), 531–571 (2008)
Chen, H., Malacaria, P.: Quantifying maximal loss of anonymity in protocols. In: ASIACCS, pp. 206–217 (2009)
Clark, D., Hunt, S., Malacaria, P.: A static analysis for quantifying information flow in a simple imperative language. J. Comput. Secur. 15(3), 321–371 (2007)
Danezis, G., Dingledine, R., Mathewson, N.: Mixminion: Design of a type iii anonymous remailer protocol. In: Proceedings of the 2003 IEEE Symposium on Security and Privacy, pp. 2–15 (2003)
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)
Díaz, 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)
Dupuis, F., Yu, W., Willems, F.M.J.: Blahut-arimoto algorithms for computing channel capacity and rate-distortion with side information. In: Proceedings of International Symposium on Information Theory. ISIT 2004, p. 179+ (2004)
Hutter, M.: Distribution of mutual information. In: Advances in Neural Information Processing Systems 14, pp. 399–406. MIT Press, Cambridge (2002)
Malacaria, P., Chen, H.: Lagrange multipliers and maximum information leakage in different observational models. In: PLAS 2008: Proceedings of the third ACM SIGPLAN workshop on Programming languages and analysis for security, pp. 135–146. ACM, New York (2008)
Mantel, H., Sudbrock, H.: Information-theoretic modeling and analysis of interrupt-related covert channels. In: Degano, P., Guttman, J., Martinelli, F. (eds.) FAST 2008. LNCS, vol. 5491, pp. 67–81. Springer, Heidelberg (2009)
Matz, G., Duhamel, P.: Information geometric formulation and interpretation of accelerated blahut-arimoto-type algorithms. In: Proceedings of the IEEE Information Theory Workshop (ITW), pp. 66–70 (2004)
McIver, A., Morgan, C.: A probabilistic approach to information hiding in Programming methodology, pp. 441–460. Springer, Heidelberg (2003)
Millen, J.K.: Covert channel capacity. In: IEEE Symposium on Security and Privacy, pp. 60–66 (1987)
Moddemejer, R.: On estimation of entropy and mutual information of continuous distributions. Signal Processing 16, 233–248 (1989)
Moskowitz, I.S., Newman, R.E., Syverson, P.F.: Quasi-anonymous channels. In: IASTED CNIS, pp. 126–131 (2003)
Paninski, L.: Estimation of entropy and mutual information. Neural Comp. 15(6), 1191–1253 (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)
Troncoso, C., Danezis, G.: The bayesian traffic analysis of mix networks. In: Proceedings of the 16th ACM conference on Computer and communications security, pp. 369–379 (2009)
Wheeler, A.J., Ganji, A.R.: Introduction to Engineering Experimentation, 3rd edn. Prentice Hall, Englewood Cliffs (2009)
Zhu, Y., Bettati, R.: Anonymity vs. information leakage in anonymity systems. In: Proc. of ICDCS, pp. 514–524. IEEE Computer Society, Los Alamitos (2005)
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Chatzikokolakis, K., Chothia, T., Guha, A. (2010). Statistical Measurement of Information Leakage. In: Esparza, J., Majumdar, R. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2010. Lecture Notes in Computer Science, vol 6015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12002-2_33
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DOI: https://doi.org/10.1007/978-3-642-12002-2_33
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