  Recently, differential privacy (DP) is getting attention as a privacy
definition when publishing statistics of a dataset. However, when answering a
decision problem with a DP mechanism, it causes a two-sided error. This
characteristic of DP is not desirable when publishing risk information such as
concerning COVID-19. This paper proposes relaxing DP to mitigate the limitation
and improve the utility of published information. First, we define a policy
that separates information into sensitive and non-sensitive. Then, we define
asymmetric differential privacy (ADP) that provides the same privacy guarantee
as DP to sensitive information. This partial protection induces asymmetricity
in privacy protection to improve utility and allow a one-sided error mechanism.
Following ADP, we propose two mechanisms for two tasks based on counting query
with utilizing these characteristics: top-$k$ query and publishing risk
information of viruses with an accuracy guarantee. Finally, we conducted
experiments to evaluate proposed algorithms using real-world datasets and show
their practicality and improvement of the utility, comparing state-of-the-art
algorithms.
