A Precise Information Flow Measure from Imprecise Probabilities

TL;DR

This paper introduces a generalized, precise measure of information flow within Dempster-Shafer theory, capable of handling complex uncertainties and providing bounds related to secret information, improving upon previous Bayesian-based methods.

Contribution

It extends a Bayesian information flow measure to handle multiple inputs, non-singleton belief sets, and provides bounds linked to search effort, addressing previous limitations.

Findings

Handles any number of secret inputs.

Supports belief sets of all types.

Provides bounds related to search effort.

Abstract

Dempster-Shafer theory of imprecise probabilities has proved useful to incorporate both nonspecificity and conflict uncertainties in an inference mechanism. The traditional Bayesian approach cannot differentiate between the two, and is unable to handle non-specific, ambiguous, and conflicting information without making strong assumptions. This paper presents a generalization of a recent Bayesian-based method of quantifying information flow in Dempster-Shafer theory. The generalization concretely enhances the original method removing all its weaknesses that are highlighted in this paper. In so many words, our generalized method can handle any number of secret inputs to a program, it enables the capturing of an attacker's beliefs in all kinds of sets (singleton or not), and it supports a new and precise quantitative information flow measure whose reported flow results are plausible in that they are bounded by the size of a program's secret input, and can be easily associated with the exhaustive search effort needed to uncover a program's secret information, unlike the results reported by the original metric.