# [Cryptography] Imitation Game: Can Enigma/Tunney be Fixed?

Ray Dillinger bear at sonic.net
Fri Jan 9 02:22:28 EST 2015

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On 01/08/2015 03:16 PM, Jon Callas wrote:
>
> On Jan 8, 2015, at 1:35 PM, Ryan Carboni <ryacko at gmail.com> wrote:
>
>> If we're doing alternate history and second guessing the decisions of the Germans while they had limited resources.... why not use a Feistel cipher with six letter blocks in ECB mode? Such a machine would only weigh 50 kg... not a major problem?
>
> That's about 45kg too heavy.

A nontrivial redesign of Enigma, but still using
mostly the same parts and the same budget for mass
and parts complexity, would be representing each
letter as a combination of *two* signals on a
selected *eight* I/O lines out of the 26 that the
manufactured wheels had. 8 x 7 (for some combination
of two out of eight) divided by 2 (because it can't
matter which order you get them in) gives an alphabet
of 28 symbols, which encompasses the 26 letters and
gives you two more - to use probably for "switch to
numbers" and "switch to numbers then look up the
number in a codebook" respectively.

Then, instead of having a reflector, you'd just
loop the other 18 connections through pluggable
patch cords from output to input.  The patch cords
would replace both the steckerbrett and the reflector.

So two signals enter from the keyboard on the eight
leads and pass through the 4 rotors. If one of them
reaches one of the eight selected contacts, that's
one of the two output signals, and if it doesn't it
just loops back through a patch cord to the input side
and passes back through the three rotors again, until
it comes out at one of the eight selected I/O contacts.

A signal can't get stuck in a cycle in the non-output
contacts, because the input and output contacts are
the only possible endpoints, and everything else loops
through without ending.  Because there's no way back
onto the same electrical path you've already traversed
except through an endpoint that you can't get mapped
back to, no electrical path can be repeated. Therefore
a path from any input contact MUST end at an output
contact.

Because a signal going in only has an 8/26 chance
of coming out in the range of I/O lines after a
single trip through the rotors, each of the two
signals would pass through the rotors something
between 1 and 18 times, with an average of about
3 times, getting redirected by a patch cord each
time through. This would be drastically better
than using the reflector plus steckerbrett.

This would fix the can't-map-to-itself problem,
and also the cyclometric attack.  It would require
the redesigned Enigma to add an encrypting/decrypting
switch (the effect of which could be as trivial as
reversing the direction of current flow with two
strategically placed diodes) but would replace the
reflector and steckerbrett with something much
simpler, so probably be less expensive overall to
produce and almost exactly the same bulk.

This would place it entirely beyond the analytical
capabilities of WWII, with pretty much the same
parts, bulk, etc, and nothing harder to manufacture
than they did manufacture.

Bear

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