Editing Cryptanalysis of the Enigma (section)

===Security properties===
The various Enigma models provided different levels of security. The presence of a plugboard (''Steckerbrett'') substantially increased the security of the encipherment. Each pair of letters that were connected together by a plugboard lead were referred to as ''stecker partners'', and the letters that remained unconnected were said to be ''self-steckered''.<ref>{{Harvnb|Copeland|2004|p=245}}</ref> In general, the unsteckered Enigma was used for commercial and diplomatic traffic and could be broken relatively easily using hand methods, while attacking versions with a plugboard was much more difficult. The British read unsteckered Enigma messages sent during the [[Spanish Civil War]],<ref>{{Harvnb|Smith|2006|p=23}}</ref> and also some [[#Italian naval Enigma|Italian naval traffic]] enciphered early in World War II.

The strength of the security of the ciphers that were produced by the Enigma machine was a product of the large numbers associated with the scrambling process.
#It produced a polyalphabetic substitution cipher with a period ({{thinspace|16|900}}) that was many times the length of the longest message.
#The 3-rotor scrambler could be set in 26 × 26 × 26 = {{thinspace|17|576}} ways, and the 4-rotor scrambler in 26 × {{thinspace|17|576}} = {{thinspace|456|976}} ways.
#With ''L'' leads on the plugboard, the number of ways that pairs of letters could be interchanged was <math>\tfrac{26!}{(26-2L)! \cdot L! \cdot 2^L}</math>
#*With ''L''=6, the number of combinations was {{thinspace|100|391|791|500}} (100 billion)<ref>{{Harvnb|Singh|1999|p=136}}</ref> and with ten leads, it was {{thinspace|150|738|274|937|250}} (151 trillion).<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |title=Military Use of the Enigma: The complexity of the Enigma machine |url=https://www.codesandciphers.org.uk/enigma/enigma3.htm |access-date=2 June 2010}}</ref>

However, the way that Enigma was used by the Germans meant that, if the settings for one day (or whatever period was represented by each row of the setting sheet) were established, the rest of the messages for that network on that day could quickly be deciphered.<ref>{{Harvnb|Copeland|2004|p=250}}</ref>

The security of Enigma ciphers did have fundamental weaknesses that proved helpful to cryptanalysts.
#A letter could never be [[encrypt]]ed to itself, a consequence of the reflector.<ref>{{Harvnb|Mahon|1945|p=3}}</ref> This property was of great help in using ''[[known-plaintext attack|cribs]]''—short sections of plaintext thought to be somewhere in the ciphertext—and could be used to eliminate a crib in a particular position. For a possible location, if any letter in the crib matched a letter in the ciphertext at the same position, the location could be ruled out.<ref name="Mahon 1945 16">{{Harvnb|Mahon|1945|p=16}}</ref> It was this feature that the British [[mathematician]] and [[logic]]ian [[Alan Turing]] exploited in designing the British [[bombe]].
#The plugboard connections were reciprocal, so that if A was plugged to N, then N likewise became A. It was this property that led mathematician [[Gordon Welchman]] at Bletchley Park to propose that a ''diagonal board'' be introduced into the bombe, substantially reducing the number of incorrect rotor settings that the bombes found.<ref name="Welchman97p245">{{Harvnb|Welchman|1997|p=245}}</ref>
#The notches in the ''alphabet rings'' of rotors I to V were in different positions, which helped cryptanalysts to work out the ''wheel order'' by observing when the middle rotor was turned over by the right-hand rotor.<ref>{{Harvnb|Bauer|2002|p=135}}</ref>
#There were weaknesses, in both policies and practice, in the way some Enigma versions were used.{{Clarify|date=July 2023}}
#Critical material was disclosed without notice.{{Clarify|date=July 2023}}