DES-like functions can generate the alternating group
Shimon Even, Oded Goldreich · IEEE Transactions on Information Theory · 1983
A set of transformations on binary vectors of lengthnis defined. These transformations are similar to those of the data encryption standard (DES) and therefore are called DES-like functions. It is proved that the group of permutations generated by the DES-like functions is exactly the alternating group of the set of binarynvectors.