  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.
