This paper reviews some possible design criteria for the permutation P in a DES style cryptosystem. These permutations provide the diffusion component in a substitution-permutation network. Some empirical rules which seem to account for the derivation of the permutation used in the DES are first presented. Then it is noted that these permutations may be regarded as latin-squares which link the outputs of S-boxes to their inputs at the next stage. A subset of these which perform well in a dependency analysis are then presented and suggested for use in future schemes.