In this document, I present my work in the field of symmetric cryptography during the period 2008-2011, where I did my research as Phd-student in the team SECRET at INRIA. Our results have mainly concern with the analysis and the design of block ciphers. Since the beginning of 90's, there exist a lot of statistical attacks against block ciphers. In the first part of our work, we focus on the generalizations of the so-called differential cryptanalysis. The second part is devoted to some design criteria for block ciphers. In the first part, our main interest was the determination of the complexity of statistical attacks. We notably made an extensive study on the data complexity and the success probability of most of the statistical attacks on block ciphers. Among the statistical attacks, the differential cryptanalysis and its generalizations have a crucial role because of their importance for the security of block ciphers. During our cryptanalysis of PRESENT we checked the hypotheses which are currently done in a differential cryptanalysis. The second part is dedicated to the study of the S-boxes of block ciphers. The most important criterion concerning the resistance of a block cipher against differential attacks is called the differential uniformity of its S-boxes. In this part, we introduce the notion of differential spectrum of power functions over a finite field and we explain why we have here a more general criterion which may be of great interest. In this thesis, we notably describe the differential spectra of several classes of power functions.