Security, Probability and Nearly Fair Coins in the Cryptographers’ Café

Abstract

Security and probability are both artefacts that we hope to bring increasingly within the reach of refinement-based Formal Methods; although we have worked on them separately, in the past, the goal has always been to bring them together. In this report we describe our ongoing work in that direction: we relate it to a well known problem in security, Chaum's Dining Cryptographers, where the various criteria of correctness that might apply to it expose precisely the issues we have found to be significant in our efforts to deal with security, probability and abstraction all at once. Taking our conviction into this unfamiliar and demanding territory, that abstraction and refinement are the key tools of software development, has turned out to be an exciting challenge.

Compositional Closure for Bayes Risk in Probabilistic Noninterference

“…Proof: The equivalence of the first and second formulations is straightforward; 20 we prove the second, reasoning…”

“…All of them however used our qualitative model for compositional noninterference [27,23]; here of course we are using instead a quantitative model. 20 First implies second:…”

“…All of them however used our qualitative model for compositional noninterference [27,23]; here of course we are using instead a quantitative model. 20 First implies second: The example is as follows. Three judges A, B, C are to give a majority decision, innocent or guilty, by exchanging messages but concealing their individual votes a, b and c, respectively.…”

“…Both require a careful distinction between what data can be observed and what data must be protected; by observing that distinction in the definition of abstraction, we allow the tractable analysis of properties which rely on "secrecy" (on the one hand) or "probabilistic local state" (on the other). This unified semantic foundation opens up the possibility for a uniform approach to the specification of security properties, along with other safety-critical features, during system design [20].…”

Probabilistic Point-to-Point Information Leakage

“…We note that our model intentionally does not consider the overwriting of secret variables to be the cause of an information leak. More recent work by McIver et al [15] develops the model further. Askarov & Sabelfield's [16] information leakage model allows for the safe public disclosure of previously-secret values during program execution, but is qualitative rather than quantitative.…”