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Code and ciphers: Julius Caesar, the Enigma and the internet

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124<br />

chapter 9<br />

Figure 9. 3.<br />

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during <strong>the</strong> encipherment of <strong>the</strong> six-letter double indicator <strong>the</strong>re is an 80%<br />

chance that only wheel R1 moves.<br />

For wheel R2 can only move if R1 is on a notch position <strong>and</strong> on <strong>the</strong> original<br />

<strong>Enigma</strong> <strong>the</strong>re was only one notch on <strong>the</strong> 26-position notch ring. Thus<br />

if <strong>the</strong> notch was effective when R1 was in position Z it could only cause R2<br />

to move during <strong>the</strong> six-letter encipherment if <strong>the</strong> original setting of R1<br />

was U, V, W, X or Y. (If <strong>the</strong> original setting of R1 was Z wheel R2 would turn<br />

immediately before <strong>the</strong> encipherment of <strong>the</strong> first letter <strong>and</strong> would remain<br />

<strong>the</strong>re for <strong>the</strong> next five letter encipherments unless R2 itself was now at its<br />

notch position <strong>and</strong> so caused both R3 <strong>and</strong> itself to move at <strong>the</strong> next letter<br />

encipherment; this hardly affects <strong>the</strong> probabilities <strong>and</strong>, for simplicity,<br />

will be ignored. The cryptanalytic attack is easily modified to cover this<br />

unlikely possibility.) Therefore <strong>the</strong>re are, normally, 21 of <strong>the</strong> starting<br />

positions of R1 which ensure that R2, <strong>and</strong> <strong>the</strong>refore R3, remain stationary<br />

throughout <strong>the</strong> encipherment of <strong>the</strong> six-letter indicator <strong>and</strong> so <strong>the</strong> probability<br />

that only R1 moves is 21/26, which is more than 0.8. Had <strong>the</strong>re<br />

been more notches on <strong>the</strong> notch ring <strong>the</strong> probability would obviously<br />

have been lower. In <strong>the</strong> later stages of <strong>the</strong> War some notch rings had two<br />

notches <strong>and</strong> <strong>the</strong> notch rings of <strong>the</strong> Abwehr <strong>Enigma</strong> had many more, as we<br />

see later.<br />

If R2 <strong>and</strong> R3 don’t move during <strong>the</strong> encipherment of <strong>the</strong> six-letter<br />

indicator <strong>the</strong> <strong>Enigma</strong> becomes, effectively, a one-wheel machine, consisting<br />

of R1 <strong>and</strong> a composite reflector, made up of U, R3 <strong>and</strong> R2, none of<br />

which move during <strong>the</strong> encipherment. This is illustrated in Figure 9.3.<br />

The composite reflector, formed by <strong>the</strong> stationary wheels R2 <strong>and</strong> R3<br />

with <strong>the</strong> fixed reflector, U, is on <strong>the</strong> left. R1, <strong>the</strong> only wheel that moves<br />

during <strong>the</strong> six-letter encipherment, is on <strong>the</strong> right. The internal lines<br />

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