# M-94 disk cipher keyspace

If the M-94 had only 10 disks, what would be the keyspace of the resulting cipher and what is the useful keypspace of the 10 disk cipher?

• Hint: in M-94, "the wheels could be assembled on the rod in any order; the ordering used during encoding comprised the key"; where I understand comprised means precisely was, based in part on an earlier version of the wikipedia article. – fgrieu Aug 24 '16 at 20:09
• I caught myself thinking if "useful keyspace" means something specific in this case? – ilkkachu Aug 24 '16 at 20:14

In a disk cipher like the M-94, each key corresponds to a permutation of the cipher disks. Thus, with $n$ disks, there are $n! = 1 \times 2 \times 3 \times \dots \times n$ distinct possible keys.