Title: Information Theory of Data Privacy,
Abstract: By combining Shannon's cryptography model with an assumption to the lower
bound of adversaries' uncertainty to the queried dataset, we develop a secure
Bayesian inference-based privacy model and then in some extent answer Dwork et
al.'s question [1]: "why Bayesian risk factors are the right measure for
privacy loss".
This model ensures an adversary can only obtain little information of each
individual from the model's output if the adversary's uncertainty to the
queried dataset is larger than the lower bound. Importantly, the assumption to
the lower bound almost always holds, especially for big datasets. Furthermore,
this model is flexible enough to balance privacy and utility: by using four
parameters to characterize the assumption, there are many approaches to balance
privacy and utility and to discuss the group privacy and the composition
privacy properties of this model.