# Re: Rotor crypto devices: if you don't have a UKW (reflector) then you need to double the number of rotors (+1 extra)...

Rotor crypto devices: if you don't have a UKW (reflector) then you need to
double the number of rotors (+1 extra)...

I don't think it's that simple. It's doubtful that an N-rotor machine
with a reflector (UKW) would be as strong as a corresponding
(2N+1)-rotor machine without a reflector. Here's a vague argument as to
why: many attacks on rotor machines search through all possible
combinations of rotor orderings and start positions, performing a test
at each one (e.g. the Turing-Welchman bombe, the distributed M4 Enigma
project etc). Doubling the number of rotors greatly increases the size
of this search space. As an example:

For a 3-rotor machine with a reflector, there's some 26^3 possible
start positions of the rotor cores, and (if we assume that there are
only 3 rotors to choose from) 6 permutations for the rotor order:
105,456 possibilities in total.

For a 7-rotor machine without a reflector, you'd have 26^7 start
positions and 7! permutations for the rotor order: 40,480,323,287,040
possibilities.

It's not all about number of possibilities, of course, but this is a
rough argument.

-- Matt

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• References:

## Relevant Pages

• Re: Enigma?
... Other than for playing around with historical stuff, there is no reason to actually use Enigma. ... Each rotor had 26 wires which linked letters on each side of the rotor. ... After coming out of the third rotor, it would hit the "Reflector". ... From the above that is a very simple substitution cipher of the sort you see as easy puzzles in some US newspapers. ...
(sci.crypt)
• Re: double encyphering with an enigma
... Reflections on cascading rotor machines: ... cascade is not really any harder than a single machine. ... Now consider a machine with a reflector, ...
(sci.crypt)
• Rotor crypto devices: if you dont have a UKW (reflector) then you need to double the number of rotor
... Rotor crypto devices: if you don't have a UKW (reflector) then you need to ... Benefits of the UKW ... -- There was a similar designed Russian rotor cipher terminal that is ...
(sci.crypt)
• Re: Was the Abwehr Enigma-G stronger than the normal Enigma, dueto the rotating reflector?
... Mike Amling wrote: ... Not all enigma had movable reflectors and on some the last rotor didn't move either. ... Even so, wouldn't the probability of a reflector moving during a message of length N characters be no more than N/, assuming three rotors in addition to the reflector? ...
(sci.crypt)