Re: double encyphering with an enigma

From: David Hamer (dhamer_at_bletchleypark.org.uk)
Date: 02/26/04 

Date: Thu, 26 Feb 2004 12:47:18 -0500
To: Peter Fairbrother <zenadsl6186@zen.co.uk>

Peter Fairbrother wrote:

> John A. Malley wrote:
>
> > I'd assume cascading two ENIGMA machines with independent key settings
> > results in a longer periodic polyalphabetic key sequence than periodic
> polyalphabetic key sequence that from
> > a single ENIGMA machine stage.
>
> Why? The overall periods of each machine would be the same, 17,576 letters
> for a 3-rotor machine.
>
> I may be making assumptions about what you mean by a "periodic
> polyalphabetic key sequence" though.

If the "periodic polyalphabetic key sequence" is the total
number of mixed alphabets produced by a given initial setting
of a 3-wheel Enigma with single-notch wheels that total is
not 17,756 [26^3] but 16,900 [26*25*26]. The general formula
for wheels with multiple turnover notches [e.g. navy wheels
VI-VIII] is 26.(26/m)-1.26/f where m and f are the number of
turnover notches on the middle and 'fast' [right hand] wheels
respectively. If 2-notch wheels are used the period can be as
short as 4056.

David Hamer
dhamer@bletchleypark.org.uk