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The grill method also determined the plugboard wiring. The only remaining secret of the daily key would be the ring settings, and the Poles would attack that problem with brute force. Most messages would start with the three letters "ANX" an is German for "to" and the "X" character was used as a space. Once the ring settings were found, the Poles could read the day's traffic.
The Germans made it easy for the Poles in the beginning. The rotor order only changed every quarter, so the Poles would not have to search for the rotor order. Later the Germans changed it every month, but that would not cause much trouble, either. Eventually, the Germans would change the rotor order every day, and late in the war after Poland had been overrun the rotor order might be changed during the day. Rejewski realised that, although the letters in the cycle groups were changed by the plugboard, the number and lengths of the cycles were unaffected—in the example above, six cycle groups with lengths of 9, 9, 3, 3, 1 and 1.
He described this invariant structure as the characteristic of the indicator setting. The cycle-length method would avoid using the grill. The card catalog would index the cycle-length for all starting positions except for turnovers that occurred while enciphering an indicator. The day's traffic would be examined to discover the cycles in the permutations. The card catalog would be consulted to find the possible starting positions. There are roughly 1 million possible cycle-length combinations and only , starting positions.
Having found a starting position, the Poles would use an Enigma double to determine the cycles at that starting position without a plugboard. The Poles would then compare those cycles to the cycles with the unknown plugboard and solve for the plugboard permutation a simple substitution cipher. Then the Poles could find the remaining secret of the ring settings with the ANX method. Rejewski, in or , devised a machine to facilitate making the catalog and called it a cyclometer. This "comprised two sets of rotors Rotor N in the second set was three letters out of phase with respect to rotor N in the first set, whereas rotors L and M in the second set were always set the same way as rotors L and M in the first set".
However, on 1 November , the Germans changed the Enigma reflector , necessitating the production of a new catalog—"a task which [says Rejewski] consumed, on account of our greater experience, probably somewhat less than a year's time". This characteristics method stopped working for German naval Enigma messages on 1 May , when the indicator procedure was changed to one involving special codebooks see German Navy 3-rotor Enigma below.
Although German army message keys would still be double enciphered, the days keys would not be double enciphered at the same initial setting, so the characteristic could no longer be found or exploited. Although the characteristics method no longer worked, the inclusion of the enciphered message key twice gave rise to a phenomenon that the cryptanalyst Henryk Zygalski was able to exploit. Sometimes about one message in eight one of the repeated letters in the message key enciphered to the same letter on both occasions.
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These occurrences were called samiczki  in English, females —a term later used at Bletchley Park. Only a limited number of scrambler settings would give rise to females, and these would have been identifiable from the card catalog. The method was called Netz from Netzverfahren , "net method" , or the Zygalski sheet method as it used perforated sheets that he devised, although at Bletchley Park Zygalski's name was not used for security reasons.
There was a set of 26 of these sheets for each of the six possible sequences wheel orders. Each sheet was for the left slowest-moving rotor. The sheets contained about holes in the positions in which a female could occur. Rejewski wrote about how the device was operated:. When the sheets were superposed and moved in the proper sequence and the proper manner with respect to each other, in accordance with a strictly defined program, the number of visible apertures gradually decreased. And, if a sufficient quantity of data was available, there finally remained a single aperture, probably corresponding to the right case, that is, to the solution.
From the position of the aperture one could calculate the order of the rotors, the setting of their rings, and, by comparing the letters of the cipher keys with the letters in the machine, likewise permutation S; in other words, the entire cipher key. The holes in the sheets were painstakingly cut with razor blades and in the three months before the next major setback, the sets of sheets for only two of the possible six wheel orders had been produced. After Rejewski's characteristics method became useless, he invented an electro-mechanical device that was dubbed the bomba kryptologiczna or cryptologic bomb.
Each machine contained six sets of Enigma rotors for the six positions of the repeated three-letter key. Like the Zygalski sheet method, the bomba relied on the occurrence of females , but required only three instead of about ten for the sheet method. Six bomby  were constructed, one for each of the then possible wheel orders. Each bomba conducted an exhaustive brute-force analysis of the 17,  possible message keys. Rejewski has written about the device:. The bomb method, invented in the autumn of , consisted largely in the automation and acceleration of the process of reconstructing daily keys.
It took the place of about one hundred workers and shortened the time for obtaining a key to about two hours. The cipher message transmitted the Grundstellung in the clear, so when a bomba found a match, it revealed the rotor order, the rotor positions, and the ring settings.
The only remaining secret was the plugboard permutation. This increased the number of possible wheel orders from 6 to They did not have the resources to commission 54 more bombs or produce 58 sets of Zygalski sheets. Other Enigma users received the two new rotors at the same time. However, until 1 July the Sicherheitsdienst SD —the intelligence agency of the SS and the Nazi Party —continued to use its machines in the old way with the same indicator setting for all messages.
This allowed Rejewski to reuse his previous method, and by about the turn of the year he had worked out the wirings of the two new rotors.
Rejewski wrote, in a critique of appendix 1, volume 1 , of the official history of British Intelligence in the Second World War:. Thus the change was not qualitative but quantitative. We would have had to markedly increase the personnel to operate the bombs, to produce the perforated sheets In Dilly Knox wanted to establish whether the Italian Navy were still using the same system that he had cracked during the Spanish Civil War; he instructed his assistants to use rodding to see whether the crib PERX per being Italian for "for" and X being used to indicate a space between words worked for the first part of the message.
After three months there was no success, but Mavis Lever , a year-old student, found that rodding produced PERS for the first four letters of one message. This confirmed that the Italians were indeed using the same machines and procedures.
The subsequent breaking of Italian naval Enigma ciphers led to substantial Allied successes. The cipher-breaking was disguised by sending a reconnaissance aircraft to the known location of a warship before attacking it, so that the Italians assumed that this was how they had been discovered. As the likelihood of war increased in , Britain and France pledged support for Poland in the event of action that threatened its independence.
The Polish General Staff, realizing what was likely to happen, decided to share their work on Enigma decryption with their western allies. Marian Rejewski later wrote:. If we had had no difficulties at all we would still, or even the more so, have shared our achievements with our allies as our contribution to the struggle against Germany.
At a conference near Warsaw on 26 and 27 July , the Poles revealed to the French and British that they had broken Enigma and pledged to give each a Polish-reconstructed Enigma , along with details of their Enigma-solving techniques and equipment, including Zygalski's perforated sheets and Rejewski's cryptologic bomb.
He commented on the fragility of the Polish system's reliance on the repetition in the indicator, because it might "at any moment be cancelled". Gordon Welchman, who became head of Hut 6 at Bletchley Park, wrote:. Hut 6 Ultra would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use.
Peter Calvocoressi , who became head of the Luftwaffe section in Hut 3, wrote of the Polish contribution:. The one moot point is—how valuable? According to the best qualified judges it accelerated the breaking of Enigma by perhaps a year. The British did not adopt Polish techniques but they were enlightened by them.
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On 17 September , the day the Soviet Union began its invasion of Poland , Cipher Bureau personnel crossed their country's southeastern border into Romania. PC Bruno and Bletchley Park worked together closely, communicating via a telegraph line secured by the use of Enigma doubles. He had brought the Poles a full set of Zygalski sheets that had been punched at Bletchley Park by John Jeffreys using Polish-supplied information, and on 17 January , the Poles made the first break into wartime Enigma traffic—that from 28 October Just before opening their 10 May offensive against the Low Countries and France, the Germans made the feared change in the indicator procedure, discontinuing the duplication of the enciphered message key.
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This meant that the Zygalski sheet method no longer worked. Due to their having been in occupied France, it was thought too risky to invite them to work at Bletchley Park. Despite the dire circumstances in which some of them were held, none betrayed the secret of Enigma's decryption.
Apart from some less-than-ideal inherent characteristics of the Enigma, in practice the system's greatest weakness was the way that it was used. The basic principle of this sort of enciphering machine is that it should deliver a very long stream of transformations that are difficult for a cryptanalyst to predict.
Some of the instructions to operators, however, and their sloppy habits, had the opposite effect. Without these operating shortcomings, Enigma would, almost certainly, not have been broken. The set of shortcomings that the Polish cryptanalysts exploited to such great effect included the following:.
Other useful shortcomings that were discovered by the British and later the American cryptanalysts included the following, many of which depended on frequent solving of a particular network:. Mavis Lever, a member of Dilly Knox's team, recalled an occasion when there was an extraordinary message.