What is Reconstruction attack?

A reconstruction attack is any method for partially reconstructing a private dataset from public aggregate information. Typically, the dataset contains sensitive information about individuals, whose privacy needs to be protected. The attacker has no or only partial access to the dataset, but has access to public aggregate statistics about the datasets, which could be exact or distorted, for example by adding noise. If the public statistics are not sufficiently distorted, the attacker is able to accurately reconstruct a large portion of the original private data. Reconstruction attacks are relevant to the analysis of private data, as they show that, in order to preserve even a very weak notion of individual privacy, any published statistics need to be sufficiently distorted. This phenomenon was called the Fundamental Law of Information Recovery by Dwork and Roth, and formulated as "overly accurate answers to too many questions will destroy privacy in a spectacular way."