The increasing popularity of social networks raises critical issues regarding privacy and protection of personal information. One typical example - which is the motivation of the paper - is face images and face recognition, face recognition being ubiquitous on the web now. Assuming someone with bad intentions steals a database containing face signatures, would it be possible to reconstruct the corresponding face images, revealing who was in the database? Would these reconstructed images be good enough to allow them to gain access via a face recognition system? This paper brings a contribution to this topic by proposing a face reconstruction algorithm, based on RBF-regression in eigenspace, which is able to reconstruct face images from their signatures (i.e. neither knowing the identity of the persons nor their true facial appearance). We show that in addition to being visually realistic, the images generated by the proposed method can fool a state-of-the-art face recognition algorithm.