The idea of a reconstruction attack can be illustrated by an attack on a small dataset of 2 points. Point A is (1) point B is (2). If an attacker can query the database for min, max, and count. Min would be 1, max would be 2, and count would be 2. Given this the attacker knows the dataset has a 1 and a 2, and is no other points. Hence the attacker has reconstructed the original dataset without ever seeing it.

This example is purposefully simple, but a similar approach is used for datasets in the wild. Attacks tend to use more queries with tools such as SAT Solvers to find the Dataset that returns the same values for each of the queries made by the attacker.

Protections against reconstruction attacks try to keep the utility of queries while making the set of queries and results have no satisfiable dataset, hence, the attacker would not be able to reconstruct the data the queries were made on and the SAT Solver will return unsat.

‍