Linear cryptanalysis and differential cryptanalysis are the most important methods of attack against block ciphers. Their efficiency have been demonstrated against several ciphers, including the Data Encryption Standard. We prove that both of them can be considered, improved and joined in a more general statistical framework. We also show that the very same results as those obtained in the case of DES can be found without any linear analysis and we slightly improve them into an attack with theoretical complexity 2 42:9 . We can apply another statistical attack --- the Ø 2 -cryptanalysis --- on the same characteristics without a definite idea of what happens in the encryption process. It appears to be roughly as efficient as both differential and linear cryptanalysis. We propose a new heuristic method to find good characteristics. It has found an attack against DES absolutely equivalent to Matsui's one by following a distinct path.