Editing Cryptanalysis of the Enigma (section)

===Key setting===
Enigma featured the major operational convenience of being [[involution (mathematics)|symmetrical]] (or [[inverse function|self-inverse]]). This meant that [[decipherment]] worked in the same way as [[encryption|encipherment]], so that when the [[ciphertext]] was typed in, the sequence of lamps that lit yielded the [[plaintext]].

Identical setting of the machines at the transmitting and receiving ends was achieved by key setting procedures. These varied from time to time and across different [[telecommunications network|networks]]. They consisted of ''setting sheets'' in a ''[[codebook]]''<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |title=Military Use of the Enigma: The Message Key and Setting Sheets |series=Codes and Ciphers in the Second World War: The history, science and engineering of cryptanalysis in World War II |url=https://www.codesandciphers.org.uk/enigma/enigma3.htm |access-date=21 October 2008}}</ref><ref>{{citation |last=Rijmenants |first=Dirk |title=Enigma Message Procedures |work=Cipher Machines and Cryptology |url=https://www.ciphermachinesandcryptology.com/en/enigmaproc.htm |access-date=19 November 2009}}</ref> which were distributed to all users of a network, and were changed regularly. The message key was transmitted in an ''[[Enigma machine#Indicator|indicator]]''<ref>{{Harvnb|Churchhouse|2002|pp=33, 86}}</ref> as part of the message preamble. The word ''key'' was also used at Bletchley Park to describe the network that used the same Enigma setting sheets. Initially these were recorded using coloured pencils and were given the names ''red'', ''light blue'' etc., and later the names of birds such as ''kestrel''.<ref>[[Harry Hinsley|Hinsley, F.H.]] and Stripp, Alan (1993) p. xviii and [[Harry Hinsley|Hinsley]] (1992) p. 2</ref> During World War II the settings for most networks lasted for 24 hours, although some were changed more often towards the end of the war.<ref>One element of the key, the sequence of rotors in the machine, was at first changed quarterly; but from 1 January 1936 it was changed monthly; from 1 October 1936, daily; and later, during World War II, as often as every eight hours. [[Marian Rejewski]], ''Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys...'', Appendix C to [[Władysław Kozaczuk]], ''Enigma'' (1984) p. 242</ref> The sheets had columns specifying, for each day of the month, the rotors to be used and their positions, the ring positions and the plugboard connections. For security, the dates were in reverse chronological order down the page, so that each row could be cut off and destroyed when it was finished with.<ref>{{Harvnb|US Army|1945|p=2}}</ref>

{| class="wikitable" style="margin: auto; border: none; text-align:center"
|+The top part of an early setting sheet looked something like this<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |title=Bigrams, Trigrams and Naval Enigma: The Daily Key, (Tagschluessel) |series=Lecture on Naval Enigma |url=https://www.codesandciphers.org.uk/lectures/naval1.htm |access-date=7 June 2010}}</ref>
|-
! {{langx|de|Datum||Date}}
! {{langx|de|Walzenlage||Rotors|link=no}}
! {{langx|de|Ringstellung||Ring settings|link=no}}
! {{langx|de|Steckerverbindungen||Plugboard settings|link=no}}
! {{langx|de|Grundstellung||Initial rotor settings|link=no}}
|-
| style="text-align: center; font-family: monospace;" | 31 || style="text-align: center; font-family: monospace;" | I II III || style="text-align: center; font-family: monospace;" | W N M || style="text-align: center; font-family: monospace;" | HK CN IO FY JM LW || style="text-align: center; font-family: monospace;" | RAO
|-
| style="text-align: center; font-family: monospace;" | 30 || style="text-align: center; font-family: monospace;" | III I II || style="text-align: center; font-family: monospace;" | C K U || style="text-align: center; font-family: monospace;" | CK IZ QT NP JY GW || style="text-align: center; font-family: monospace;" | VQN
|-
| style="text-align: center; font-family: monospace;" | 29 || style="text-align: center; font-family: monospace;" | II III I || style="text-align: center; font-family: monospace;" | B H N || style="text-align: center; font-family: monospace;" | FR LY OX IT BM GJ || style="text-align: center; font-family: monospace;" | XIO
|}

Until 15 September 1938,<ref>The German Navy adopted a more complex and secure indicator procedure on 1 May 1937—see "[[#German Naval Enigma|German naval Enigma]]".</ref> the transmitting operator indicated to the receiving operator(s) how to set their rotors, by choosing a three-letter ''message key'' (the key specific to that message) and enciphering it twice using the specified initial ring positions (the ''Grundstellung''). The resultant six-letter indicator was then transmitted before the enciphered text of the message.<ref>{{citation |last1=Gaj |first1=Kris |last2=Orłowski |first2=Arkadiusz |title=Advances in Cryptology — EUROCRYPT 2003 |chapter=Facts and myths of Enigma: breaking stereotypes |series=Lecture Notes in Computer Science |date=2003 |volume=2656 |publisher=George Mason University, Fairfax, VA 22030, U.S.A.; Institute of Physics, Polish Academy of Sciences Warszawa, Poland |at=Section 3.2 |doi=10.1007/3-540-39200-9_7 |isbn=978-3-540-14039-9 |chapter-url=https://link.springer.com/content/pdf/10.1007/3-540-39200-9_7.pdf |access-date=6 May 2024 |url-status=live |archive-url=https://web.archive.org/web/20080414141147/http://teal.gmu.edu/courses/ECE543/viewgraphs_F03/EUROCRYPT_2003.pdf |archive-date=14 April 2008}}</ref> Suppose that the specified ''Grundstellung'' was ''RAO'', and the chosen three-letter message key was ''IHL'', the operator would set the rotors to ''RAO'' and encipher ''IHL'' twice. The resultant ciphertext, ''DQYQQT'', would be transmitted, at which point the rotors would be changed to the message key (''IHL'') and then the message itself enciphered. The receiving operator would use the specified ''Grundstellung RAO'' to decipher the first six letters, yielding ''IHLIHL''. On seeing the repeated message key, they would know there had been no corruption and use ''IHL'' to decipher the message.

The weakness in this [[Enigma machine#Indicator|indicator procedure]] came from two factors. First, use of a global ''Grundstellung''; this was changed in September 1938 so that the operator selected his initial position to encrypt the message key, and sent the initial position [[Plaintext|in clear]] followed by the enciphered message key. The second problem was the repetition of the message key within the indicator, which was a serious security flaw.<ref>{{citation |last1=Gaj |first1=Kris |last2=Orłowski |first2=Arkadiusz |title=Advances in Cryptology — EUROCRYPT 2003 |chapter=Facts and myths of Enigma: breaking stereotypes |series=Lecture Notes in Computer Science |date=2003 |volume=2656 |publisher=George Mason University, Fairfax, VA 22030, U.S.A.; Institute of Physics, Polish Academy of Sciences Warszawa, Poland |at=Section 7 |doi=10.1007/3-540-39200-9_7 |isbn=978-3-540-14039-9 |chapter-url=https://link.springer.com/content/pdf/10.1007/3-540-39200-9_7.pdf |access-date=6 May 2024 |url-status=live |archive-url=https://web.archive.org/web/20080414141147/http://teal.gmu.edu/courses/ECE543/viewgraphs_F03/EUROCRYPT_2003.pdf |archive-date=14 April 2008}}</ref> The message setting was encoded twice, resulting in a relation between the first and fourth, second and fifth, and third and sixth characters. This weakness enabled the [[Cipher Bureau (Poland)|Polish Cipher Bureau]] to break the pre-war Enigma system as early as 1932. On 1 May 1940 the Germans changed the procedures to encipher the message key only once.