Abstract. In 2002, algebraic attacks using overdefined systems of equations have been proposed as a potentially very powerful cryptanalysis technique against block ciphers. However, although a number of convincing experiments have been performed against certain reduced algorithms, it is not clear wether these attacks can be successfully applied in general and to a large class of ciphers. In this paper, we show that algebraic techniques can be combined with side-channel attacks in a very effective and natural fashion. As an illustration, we apply them to the block cipher PRESENT that is a stimulating first target, due to its simple algebraic structure. The proposed attacks have a number of interesting features: (1) they exploit the information leakages of all the cipher rounds, (2) in common implementation contexts (e.g. assuming a Hamming weight leakage model), they recover the block cipher keys after the observation of a single encryption, (3) these attacks can succeed in an unknown-p...