  Recent studies show that differential privacy is vulnerable when different
individuals' data in the dataset are correlated, and that there are many cases
where differential privacy implies poor utility. In order to treat the two
weaknesses, we traced the origin of differential privacy to Dalenius' goal, a
more rigorous privacy measure. We formalized Dalenius' goal by using Shannon's
perfect secrecy and tried to achieve Dalenius' goal with better utility. Our
first result is that, if the independence assumption is true, then differential
privacy is equivalent to Dalenius' goal, where the independence assumption
assumes that each adversary has no knowledge of the correlation among different
individuals' data in the dataset. This implies that the security of
differential privacy is based on the independence assumption. Since the
independence assumption is impractical, we introduced a new practical
assumption, which assumes that each adversary is unknown to some data of the
dataset if the dataset is large enough. Based on the assumption, we can achieve
Dalenius' goal with better utility. Furthermore, we proved a useful result
which can transplant results or approaches of information theory into data
privacy protection. We then proved that several basic privacy
mechanisms/channels satisfy Dalenuis' goal, such as the random response, the
exponential, and the Gaussian privacy channels, which are respective
counterparts of the random response, the exponential, and the Gaussian
mechanisms of differential privacy. Moreover, the group and the composition
properties were also proved. Finally, by using Yao's computational information
theory, we extend our model to the computational-bounded case.
