Re: Variable length rotor machines: was: how to detect breakage -- lures etc.??

On Wed, 2020-01-08 at 13:59 +0000, Peter Fairbrother wrote:
> This makes the rotors non-interchangeable. 

All of this is true.  With a machine using reflecting rotors, it is
simple to have two independent wirings in a rotor, and just turn it
over for a second option.  Or if you don't care so much about
"independent" you can just wire the contacts on both sides together and
turn it over for a mirror-inversion of the wiring. But, yeah, you're
never going to use a size-27 rotor in the size-25 or size-29 slot, so
you do miss out on the way rotor sequence can add a permutation to the
key space.

A thing that has some implications though is that a reflecting rotor 
of, say, size 27, must have 54 contacts on its face, because both 
ends of the 27 connections have to be there.  Thus, the size-27 rotor
can be in any of 54 different positions.  The odd-to-even mappings
around the rotor turn into even-to-odd mappings every time the rotor
advances one position, then back into odd-to-even mappings when the
rotor advances again. 

This doubles the cryptoperiod of the system by adding a (shared) factor
of '2' to the least-common-multiple.  But it does much more than double
the key space (assuming rotor positions are part of the key).  The keys
would be divided into 2^(n-1) sets for n=number of rotors, each set
having the same number of keys as the cryptoperiod, corresponding to
positions on a different sequence of cipher alphabets.

			Bear


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