In this paper, we introduce a novel inference attack that we coin as the reconstruction attack whose objective is to reconstruct a probabilistic version of the original dataset on which a classifier was learnt from the description of this classifier and possibly some auxiliary information. In a nutshell, the reconstruction attack exploits the structure of the classifier in order to derive a probabilistic version of dataset on which this model has been trained. Moreover, we propose a general framework that can be used to assess the success of a reconstruction attack in terms of a novel distance between the reconstructed and original datasets. In case of multiple releases of classifiers, we also give a strategy that can be used to merge the different reconstructed datasets into a single coherent one that is closer to the original dataset than any of the simple reconstructed datasets. Finally, we give an instantiation of this reconstruction attack on a decision tree classifier that was learnt using the algorithm C4.5 and evaluate experimentally its efficiency. The results of this experimentation demonstrate that the proposed attack is able to reconstruct a significant part of the original dataset, thus highlighting the need to develop new learning algorithms whose output is specifically tailored to mitigate the success of this type of attack.