Editing Enigma machine (section)

=== Turnover ===
[[File:Enigma ratchet.png|thumb|The Enigma stepping motion seen from the side away from the operator. All three ratchet pawls (green) push in unison as a key is depressed. For the first rotor (1), which to the operator is the right-hand rotor, the ratchet (red) is always engaged, and steps with each keypress. Here, the middle rotor (2) is engaged, because the notch in the first rotor is aligned with the pawl; it will step (''turn over'') with the first rotor. The third rotor (3) is not engaged, because the notch in the second rotor is not aligned to the pawl, so it will not engage with the rachet.]]
The advancement of a rotor other than the left-hand one was called a ''turnover'' by the British. This was achieved by a [[Ratchet (device)|ratchet and pawl]] mechanism. Each rotor had a ratchet with 26 teeth and every time a key was pressed, the set of spring-loaded pawls moved forward in unison, trying to engage with a ratchet. The alphabet ring of the rotor to the right normally prevented this. As this ring rotated with its rotor, a notch machined into it would eventually align itself with the pawl, allowing it to engage with the ratchet, and advance the rotor on its left. The right-hand pawl, having no rotor and ring to its right, stepped its rotor with every key depression.<ref name="doublestepping" /> For a single-notch rotor in the right-hand position, the middle rotor stepped once for every 26 steps of the right-hand rotor. Similarly for rotors two and three. For a two-notch rotor, the rotor to its left would turn over twice for each rotation.

The first five rotors to be introduced (I–V) contained one notch each, while the additional naval rotors VI, VII and VIII each had two notches. The position of the notch on each rotor was determined by the letter ring which could be adjusted in relation to the core containing the interconnections. The points on the rings at which they caused the next wheel to move were as follows.<ref>{{cite web| last=Sale|first=Tony|author-link=Tony Sale|title=Technical specifications of the Enigma rotors| work=Technical Specification of the Enigma|url=http://www.codesandciphers.org.uk/enigma/rotorspec.htm|access-date=15 November 2009}}</ref>

{|class="wikitable" style="margin: 1em auto 1em auto"
|+Position of turnover notches
|-
! style="width:130pt;"| Rotor
! style="width:130pt;"| Turnover position(s)
! style="width:130pt;"| BP mnemonic
|- style="text-align:center;"
| |I|| style="text-align:center;"|R|| style="text-align:center;"|Royal
|- style="text-align:center;"
| |II|| style="text-align:center;"|F|| style="text-align:center;"|Flags
|- style="text-align:center;"
| |III|| style="text-align:center;"|W|| style="text-align:center;"|Wave
|- style="text-align:center;"
| |IV|| style="text-align:center;"|K|| style="text-align:center;"|Kings
|- style="text-align:center;"
| |V|| style="text-align:center;"|A|| style="text-align:center;"|Above
|-
| style="text-align:center;"|VI, VII and VIII|| style="text-align:center;"|A and N|||
|}

The design also included a feature known as ''double-stepping''. This occurred when each pawl aligned with both the ratchet of its rotor and the rotating notched ring of the neighbouring rotor. If a pawl engaged with a ratchet through alignment with a notch, as it moved forward it pushed against both the ratchet and the notch, advancing both rotors. In a three-rotor machine, double-stepping affected rotor two only. If, in moving forward, the ratchet of rotor three was engaged, rotor two would move again on the subsequent keystroke, resulting in two consecutive steps. Rotor two also pushes rotor one forward after 26 steps, but since rotor one moves forward with every keystroke anyway, there is no double-stepping.<ref name="doublestepping">{{cite journal |first=David |last=Hamer |title=Enigma: Actions Involved in the 'Double-Stepping' of the Middle Rotor |journal=Cryptologia |volume=21 |issue=1 |date=January 1997 |pages=47–50 |url=http://www.eclipse.net/~dhamer/downloads/rotorpdf.zip |archive-date=19 July 2011 |archive-url=https://web.archive.org/web/20110719081659/http://www.eclipse.net/~dhamer/downloads/rotorpdf.zip |format=zip |doi=10.1080/0161-119791885779|url-access=subscription }}</ref> This double-stepping caused the rotors to deviate from [[odometer]]-style regular motion.

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With three wheels and only single notches in the first and second wheels, the machine had a period of 26×25×26&nbsp;= 16,900 (not 26×26×26, because of double-stepping).<ref name="doublestepping" /> Historically, messages were limited to a few hundred letters, and so there was no chance of repeating any combined rotor position during a single session, denying cryptanalysts valuable clues.

To make room for the Naval fourth rotors, the reflector was made much thinner. The fourth rotor fitted into the space made available. No other changes were made, which eased the changeover. Since there were only three pawls, the fourth rotor never stepped, but could be manually set into one of 26 possible positions.

A device that was designed, but not implemented before the war's end, was the ''Lückenfüllerwalze'' (gap-fill wheel) that implemented irregular stepping. It allowed field configuration of notches in all 26 positions. If the number of notches was a [[Coprime integers|relative prime]] of 26 and the number of notches were different for each wheel, the stepping would be more unpredictable. Like the Umkehrwalze-D it also allowed the internal wiring to be reconfigured.<ref>{{cite web|url=http://www.cryptomuseum.com/crypto/enigma/lf/index.htm |title=Lückenfüllerwalze |publisher=Cryptomuseum.com |access-date=17 July 2012}}</ref>{{Clear}}