Quantifying vulnerability of secret generation using hyper-distributions. Mário S. Alvim, Piotr Mardziel, and Michael Hicks. In Proceedings of the Symposium on Principles of Security and Trust (POST), April 2017. Extended version of short paper that appeared at FCS 2016: http://www.cs.umd.edu/~mwh/papers/stratquant.pdf.

Traditional approaches to Quantitative Information Flow (QIF) represent the adversary's prior knowledge of possible secret values as a single probability distribution. This representation may miss important structure. For instance, representing prior knowledge about passwords of a system's users in this way overlooks the fact that many users generate passwords using some strategy. Knowledge of such strategies can help the adversary in guessing a secret, so ignoring them may underestimate the secret's vulnerability. In this paper we explicitly model strategies as distributions on secrets, and generalize the representation of the adversary's prior knowledge from a distribution on secrets to an environment, which is a distribution on strategies (and, thus, a distribution on distributions on secrets, called a hyper-distribution). By applying information-theoretic techniques to environments we derive several meaningful generalizations of the traditional approach to QIF. In particular, we disentangle the vulnerability of a secret from the vulnerability of the strategies that generate secrets, and thereby distinguish security by aggregation---which relies on the uncertainty over strategies---from security by strategy---which relies on the intrinsic uncertainty within a strategy. We also demonstrate that, in a precise way, no further generalization of prior knowledge (e.g., by using distributions of even higher order) is needed to soundly quantify the vulnerability of the secret.

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  author = {M\'{a}rio S. Alvim and Piotr Mardziel and Michael Hicks},
  title = {Quantifying vulnerability of secret generation using hyper-distributions},
  booktitle = {Proceedings of the Symposium on Principles of Security and Trust (POST)},
  year = 2017,
  month = apr,
  note = {Extended version of short paper that appeared at FCS 2016: \url{http://www.cs.umd.edu/~mwh/papers/stratquant.pdf}}

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