The rapid progress of human genome studies leads to a strong demand of aggregate human DNA data (e.g, allele frequencies, test statistics, etc.), whose public dissemination, however, has been impeded by privacy concerns. Prior research shows that it is possible to identify the presence of some participants in a study from such data, and in some cases, even fully recover their DNA sequences. A critical issue, therefore, becomes how to evaluate such a risk on individual data-sets and determine when they are safe to release. In this paper, we report our research that makes the first attempt to address this issue. We first identified the space of the aggregate-data-release problem, through examining common types of aggregate data and the typical threats they are facing. Then, we performed an in-depth study on different scenarios of attacks on different types of data, which sheds light on several fundamental questions in this problem domain. Particularly, we found that attacks on aggrega...