The decorrelation theory provides a different point of view on the security of block cipher primitives. Results on some statistical attacks obtained in this context can support or provide new insight on the security of symmetric cryptographic primitives. In this paper, we study, for the first time, the multidimensional linear attacks as well as the truncated differential attacks in this context. We show that the cipher should be decorrelated of order two to be resistant against some multidimensional linear and truncated differential attacks. Previous results obtained with this theory for linear, differential, differential-linear and boomerang attacks are also resumed and improved in this paper.