Editing Ultra (cryptography) (section)

====Enigma====
{{Main|Cryptanalysis of the Enigma}}
"[[Enigma machine|Enigma]]" refers to a family of electro-mechanical [[Rotor machine|rotor cipher machines]]. These produced a [[Polyalphabetic cipher|polyalphabetic substitution cipher]] and were widely thought to be unbreakable in the 1920s, when a variant of the commercial Model D was first used by the [[Reichswehr]]. The [[German Army (1935–1945)|German Army]] (''Heer''), [[Kriegsmarine|Navy]], Air Force, [[Nazi Party|Nazi party]], [[Gestapo]] and German diplomats used Enigma machines in several variants. [[Abwehr]]  (German military intelligence) used a four-rotor machine without a plugboard and Naval Enigma used different key management from that of the army or air force, making its traffic far more difficult to cryptanalyse; each variant required different cryptanalytic treatment. The commercial versions were not as secure and [[Dilly Knox]] of GC&CS is said to have broken one before the war.

German military Enigma was first broken in December 1932 by [[Marian Rejewski]] and the [[Biuro Szyfrów|Polish Cipher Bureau]], using a combination of brilliant mathematics, the services of a spy in the German office responsible for administering encrypted communications, and good luck.{{sfn|Singh|1999|p=145}}{{sfn|Copeland|2004|pp=231, 232}} The Poles read Enigma to the outbreak of World War II and beyond, in France.{{sfn|Kozaczuk|1984|pp=81–92}} At the turn of 1939, the Germans made the systems ten times more complex, which required a tenfold increase in Polish decryption equipment, which they could not meet.{{sfn|Rejewski|1984|pp=242–43}} On 25 July 1939, the Polish Cipher Bureau handed [[Polish Enigma doubles|reconstructed Enigma machines]] and their techniques for decrypting ciphers to the French and British.{{sfn|Copeland|2004|pp=234, 235}} [[Gordon Welchman]] wrote,

{{Quote|Ultra would never have got off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military Enigma machine, and of the operating procedures that were in use.|Gordon Welchman{{sfn|Welchman|1984|p=289}}}}

At Bletchley Park, some of the key people responsible for success against Enigma included mathematicians [[Alan Turing]] and [[Conel Hugh O'Donel Alexander|Hugh Alexander]] and, at the [[British Tabulating Machine Company]], chief engineer [[Harold Keen]].<ref name="haigh"/>
After the war, interrogation of German cryptographic personnel led to the conclusion that German cryptanalysts understood that cryptanalytic attacks against Enigma were possible but were thought to require impracticable amounts of effort and investment.{{sfn|Bamford|2001|p=17}} The Poles' early start at breaking Enigma and the continuity of their success gave the Allies an advantage when World War II began.{{sfn|Welchman|1984|p=289}}