<regarding the rotor machine patent that Freidman filed in '33>
Actually, now that I have thoroughly read it, what Friedman
proposed here was actually considerably more advanced than
Enigma: While Enigma's wheels ratcheted one position each
time, and signaled overflow by ratcheting the next wheel one
position (rather like an odometer), Freidman's invention here
is different: He has a mechanism that can move each wheel
an arbitrary number of steps between each and every letter
of the message.
He then uses a set of long-period tapes to control the
positions of each rotor individually rather than just ratcheting
through positions in a "counting" mode the way Enigma did. By
putting the tapes out of phase with one another, he steps
through rotor positions in a pattern of *much* longer period
than then-extant cipher machines. The downside is that the
tapes are effectively multiple keys, each on the order of a
thousand characters long.
Freidman proposed as an example using 3 looped tapes, with
keys of 999, 1000, and 1001 characters respectively to
control 3 rotors -- these being relatively prime to one another,
this yields a period of 999,999,000 characters before all
the rotor positions would repeat. The final part of the key,
of course, would be the one that said which tapes and rotors
to use, at what position each tape and rotor started, which
rotor position each tape was to be used to control, which
rotor to mount at what position, and whether to mount each
rotor (or tape) backwards or forwards.
Hmmm. Offhand, I think that it effectively makes each
tape & Rotor combination into the mathematical equivalent
of a mega-rotor that "ratchets" in a cycle of the length
of the tape times the number of rotor positions but where
each position selects one of only twenty-six displacements
of a permutation of the alphabet.
Since alternate looped tapes don't take much space or
weight to keep, this would have been an excellent cipher
for military applications in the 40's and 50's, and probably
good for civilian application through the 60's. You have your
3-rotor machine, you have your 5 to 9 prewired rotors to pick 3
of, you have your choice of 300 or 1000 tapes to run each rotor
with, you have your little key-of-the-day book that says what
combination of rotors and tapes your unit is to use each day,
and the whole package fits in a single footlocker and has
security far superior to a 5-rotor Enigma! For "classical"
cryptography, this system is just plain slick!
I will have to check, but I don't know a good way to adapt
the algorithm that breaks rotor machines to this condition.
I especially can't think of a good technique for sorting
it out if you don't know the content, lengths, and starting
positions of the tapes. If you had multiple messages
transmitted using the same key, you could count coincidences -
but for a single message, the unicity distance is huge --
over 3000 characters if you count the contents of the tapes
as unknown.
Can anybody fully cryptanalyze this? This may actually be a
fairly secure cipher, although the key length (counting the
tape contents) is ridiculously long by modern standards.
Bear
