The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy pp 397-416 | Cite as

# Refinement Metrics for Quantitative Information Flow

Chapter

First Online:

## Abstract

In Quantitative Information Flow, *refinement* ( Open image in new window ) expresses the strong property that one channel never leaks more than another. Since two channels are then typically incomparable, here we explore a family of *refinement quasimetrics* offering greater flexibility. We show these quasimetrics let us unify refinement and capacity, we show that some of them can be computed efficiently via linear programming, and we establish upper bounds via the Earth Mover’s distance. We illustrate our techniques on the Crowds protocol.

## Supplementary material

## References

- 1.LIBQIF : Quantitative information flow C++ library. https://github.com/chatziko/libqif
- 2.Alvim, M.S., Chatzikokolakis, K., McIver, A., Morgan, C., Palamidessi, C., Smith, G.: Additive and multiplicative notions of leakage, and their capacities. In: Proceedings of the 27th IEEE Computer Security Foundations Symposium (CSF 2014), pp. 308–322 (2014)Google Scholar
- 3.Alvim, M.S., Chatzikokolakis, K., McIver, A., Morgan, C., Palamidessi, C., Smith, G.: The Science of Quantitative Information Flow. Springer, Heidelberg (2019)zbMATHGoogle Scholar
- 4.Alvim, M.S., Chatzikokolakis, K., Palamidessi, C., Smith, G.: Measuring information leakage using generalized gain functions. In: Proceedings of 25th IEEE Computer Security Foundations Symposium (CSF 2012), pp. 265–279, June 2012Google Scholar
- 5.Chatzikokolakis, K.: On the additive capacity problem for quantitative information flow. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 1–19. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_1CrossRefGoogle Scholar
- 6.Clark, D., Hunt, S., Malacaria, P.: Quantitative analysis of the leakage of confidential data. Electr. Notes Theor. Comput. Sci.
**59**(3), 238–251 (2001). (Proceedings of Workshop on Quantitative Aspects of Programming Languages)CrossRefGoogle Scholar - 7.Clarkson, M., Myers, A., Schneider, F.: Belief in information flow. In: Proceedings of 18th IEEE Computer Security Foundations Workshop (CSFW 2005), pp. 31–45 (2005)Google Scholar
- 8.Espinoza, B., Smith, G.: Min-entropy as a resource. Inf. Comput.
**226**, 57–75 (2013). (Special Issue on Information Security as a Resource)MathSciNetCrossRefGoogle Scholar - 9.Köpf, B., Basin, D.: An information-theoretic model for adaptive side-channel attacks. In: Proceedings of 14th ACM Conference on Computer and Communications Security (CCS 2007), pp. 286–296 (2007)Google Scholar
- 10.McIver, A., Morgan, C., Smith, G., Espinoza, B., Meinicke, L.: Abstract channels and their robust information-leakage ordering. In: Abadi, M., Kremer, S. (eds.) POST 2014. LNCS, vol. 8414, pp. 83–102. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54792-8_5CrossRefGoogle Scholar
- 11.Pele, O., Werman, M.: Fast and robust earth mover’s distances. In: ICCV (2009)Google Scholar
- 12.Reiter, M.K., Rubin, A.D.: Crowds: anonymity for web transactions. ACM Trans. Inf. Syst. Secur.
**1**(1), 66–92 (1998)CrossRefGoogle Scholar - 13.Villani, C.: Topics in optimal transportation, no. 58. American Mathematical Society (2003)Google Scholar

## Copyright information

© Springer Nature Switzerland AG 2019