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

*From*: "Matt" <MattCrypto@xxxxxxxxx>*Date*: 29 Mar 2006 00:15:56 -0800

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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