In the two indicators UJOOBL and UANODR the repetition of the first letters is followed by a repetition of the fourth letters. That this must always happen is clear from the fact that the fourth letter arises from the first by enciphering at position directly after the Grundstellung and re-enciphering three places further on. This phenomenon enables us to tell very quickly with any cipher whether the Boxing form of indication is being used. From the indicators we can find the effects of the three repeated encipherments. In Fig 66 we have entered in one of the columns against each letter the effect of enciphering it first at the position immediately after the Grundstellung and then at the position four places after the Grundstellung: thus we have the entry J against A, with five dots. This means that A enciphered at the first and fourth positions gives J, and that this information has been given us from six indicators, which are actually ALAJMB, AYIJPI, AFIJVI, APTJNA, AVRJKK, AUXJJJ. The other two columns give us the results of the encipherments at the second and then the fifth position, and at the third and then the sixth. We get for the results of these double encipherments

G_{4}G_{1}

...NEQAJSKP...TGE.ZW...(DMHUGVEXBRCYT)

G_{5}G_{2}

(PNUJBQCLMFVKY)(OHIWSADXETGRZ)

G_{6}G_{3}

(V)(I)(JFNRKPWSHOLX)...DUQEZGTABYMC...

G_{4}G_{1} here means the encipherment with the first alphabet and then with the
fourth, the reversal of the natural order being in agreement with mathematical
tradition. There can be no doubt as to how the substitution G_{6}G_{3} is to be
completed, but at first sight it might appear that there are two possibilities
for G_{4}G_{1}. However if we remember what we found out in the section 'alphabets
and boxes' we see that it must be possible to pair off the cycles of G_{4}G_{1}
into ones of equal length.

-130-

Back to Turing's Treatise on the Enigma. Chapter VII.