Enigma machine
A 3-rotor Enigma machine, possibly military
However, the Enigma cypher was not as strong as believed, having two flaws in its design: the machine guaranteed that a letter would never be encrypted to itself and the rightmost rotor would rotate a set number of places before the next would rotate (26 in the initial version). Moreover, in German military usage, the failure to replace the rotors over many years of service, and discernable patterns in messages further weakened the system. In fact, messages used in many Enigma networks were frequently decrypted, and that fact is sometimes credited with ending World War II at least a year earlier than it would have otherwise.
The similar British encryption machine, Typex, and several American ones, e.g. the SIGABA (or M-134-C in Army use), were similar in principle to Enigma, but far more secure. The first modern rotor cypher machine, by Edward Hebern, was considerably less secure, a fact promptly noted by William F. Friedman when it was offered to the US Government.
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2 Operation 3 Strengths of Enigma 4 Encryption method 5 Breaking the Enigma 6 Ultra 7 After the War; public disclosure 8 Further reading 9 See also 10 External links |
History
Enigma was developed by Arthur Scherbius in various versions dating back to 1919. He set up a Berlin company to produce the machine, and the first commercial version (Enigma-A) was offered for sale in 1923. Three more commercial versions followed, and the Enigma-D became the most important when several copies were purchased by the German Navy, the Reichsmarine, in 1926, leading to adoption of the machine (with different rotor wirings) by the Navy. In the German Navy, it was called the "M" machine. The basic design was then picked up by the Army in 1929, slightly modified by adding the plugboard mechanism, and thereafter by most German military organizations and by many parts of the Nazi hierarchy.
Versions of Enigma were used for practically all German (and much other European Axis) radio, and often telegraph, communications throughout the war; even weather reports were encrypted with an Enigma machine. Both the Spanish (during the Civil War) and Italians (during World War II) are said to have used one of the commercial models, unchanged, for military communications. This was unwise, for the British (and one presumes, others) had succeeded in breaking the plain commercial version(s) or their equivalents. This contributed to the British defeat of a large part of the Italian fleet at Matapan.
The Enigma machine was electro-mechanical, meaning it used a combination of electrical and mechanical parts. The mechanical mechanism consisted of a typewriter-style keyboard, which operated electrical switches as well as a gearing mechanism which caused the rotors to move with each key press.
The electrical portion consisted of a battery attached through the keys to lamps. In general terms, when a key was held down on the keyboard, one of the lamps would light. In the picture to the right you can see the typewriter keys at the front of the machine, and the lights are the small, barely visible circles "above" the keyboard in the middle of the machine. The plugboard mechanism (stecker in German) is visible on the front panel and some of the patch cords can be seen in the lid.
Enigma rotors in most versions consisted of flat disks, somewhat resembling hockey pucks, with 26 contacts on each side, arranged in a circular manner around the outer edge of both disk faces. Every contact on one side of each disk is wired to a different contact on the other side. For instance, in a particular rotor the 1st contact on one side of the rotor might be wired to the 14th contact on the other side, the 2nd one on the first side to the 25th on the other, and so forth. Each rotor in the set supplied with an Enigma was wired differently than the others, and the German military/party models used different rotor wirings than did any of the commercial models.
In most variants, within the machine were three slots into which the rotors could be placed. The rotors were "stacked" so that the contacts on the "output" side of one rotor were in contact with the "input" contacts on the next. The third rotor in most versions was followed by a reflector (unique to the Enigma family amongst the various rotor machines designed in the period) which was fixed and fed outputs of the third rotor back into different contacts of the third rotor, thence to the second, and thru to the first, but by a different route. In the picture you can see the three stacked rotors at the top of the machine, with teeth protruding from the panel surface which allowed each rotor to be turned by hand.
When a key was pressed, battery current flowed from the switch controlled by that key, say A, into one of the contacts on the first rotor. From there it traveled to a contact on the other side, into the second rotor, the third, and into the reflector, traveling back into the third rotor, the second, and finally out of the first and to one of the lamps, perhaps J. A in the plaintext would thus be substituted for by J, the fundamental mechanism in all substitution cypher systems. The reflector was a unique patented
feature of the Engimas not found in other rotor machines.
Because the rotors changed position, like an automobile odometer, with every key press, A might become J this time, but the next A would turn into something different, perhaps T. After 26 letters were pressed, a cam on the rotor advanced the rotor in the next slot by one position. The substitution alphabet used thus changed with every plaintext letter, and kept changing with every plaintext letter for a very long time; the Engimas implemented a formidable polyalphabetic substitution cypher.
Better yet, from an Engima user's perspective, the exact sequence of substitution alphabets used depended on the internal wiring of the rotors installed, initial position of the rotors, their installed order, and the setting of the alphabet ring on each rotor. These settings were the key for the message to be encrypted (to use modern terms) and were referred to as the initial settings.
Operation
Cyphers can, of course, be attacked, and the most effective attack method depends on the cypher and its vulnerabilities. By the opening of World War I cryptanalysis departments were often good enough that most cyphers used could be broken with enough effort. However, most direct of cryptanalytic techniques then (and as of 2004 as well) used relied on gaining access to sufficient quantities of text encyphered with a particular key, from which patterns might be discerned with much statistics and hard work. Enigma was designed to defeat these basic cryptanalysis techniques.
The most fundamental basic technique was frequency analysis, in which characteristic letter patterns unique to every language could be used to discover information about the substitution alphabet(s) being used. For instance, in English, E, T, A, O, I, N and S, are usually easy to identify in cyphertext -- being very frequent (see ETAOIN SHRDLU); as well, the combinations NG, ST and others, also very frequent. Simple frequency analysis relies on one letter always being substituted for another plaintext letter in the cypher: if this is not the case the situation is more difficult. For many years, cryptographers attempted to hide the telltale frequencies by using several different substitutions for common letters, but this is unable to fully hide patterns in the substitutions for plaintext letters. Such codes were being widely broken by the 1500s.
In the mid-1400s, a new technique was invented by Alberti, now known generally as polyalphabetic ciphers, which provided a simple technique for "creating" a multitude of substitution patterns. The two parties would exchange a small amount of information (referred to as the key) and follow a simple technique that used many substitution alphabets, and so many different substitutions for each plaintext letter over the course of a single plaintext. The idea is simple and effective, but proved more difficult to use than one might have expected. Many cyphers were only partial implementations of the concept, and so were easier to break than they might have been (eg, the Vigenère Cipher).
But not until the 1840s (Babbage) was any technique developed which could reliably break any polyalphabetic cyphers. These techniques also look for repeating patterns in the ciphertext, which provide clues about the length of the key. Once this is known the message essentially becomes a series of messages, each as long as the length of the key, to which normal frequency analysis can be applied. Charles Babbage, Friedrich Kasiski, and William F. Friedman are among those who did most to develop these techniques.
Cypher designers tried to get users to not only use a different substitution for every letter, but also to use a very long key, so the new techniques would fail (or at least be a lot harder). However this is very difficult to arrange; a long key takes longer to convey to the parties who need it, and mistakes are more likely. Also, most users haven't the patience to carryout lengthy, letter perfect, evolutions, and certainly not under time pressure or battlefield stress. The 'ultimate' cypher of this type would be one in which such a long key could be generated from a simple pattern (ideally automatically), producing a cypher in which there are so many substitution alphabets that frequency counting and statistical attacks would be effectively impossible. Enigma, and the rotor machines generally were just what was needed since they were seriously polyalphabetic, using a different substitution alphabet for each letter of plaintext; their messages were much harder to break.
Fundamentally, Enigma had a library of 26 x 26 x 26 = 17576 substitution alphabets for any given set of rotors. As long as the message was not longer than 17576 characters, there could be no repeated use of a substitution alphabet. But the Enigma machines added other possibilities. The sequence of alphabets used was different if the rotors were started in position ABC, as opposed to ACB; there was a rotating ring on each rotor which could be set in a different position, and the starting position of each rotor was also variable. And most of the military Enigmas added a 'stecker' (a plugboard) which changed several key assignments (8 or more depending on model). Even so, this 'key' can be easily communicated to another user, it's just a few simple values: rotors to use, rotor order, ring positions, starting position, and plugboard settings. This was, potentially, a very good cypher system!
A 4-rotor Enigma, possibly an Abwehr machine as there is no plugboard
Enigma operators were at first given a new book every month that contained the initial settings for the machine. For instance, on a particular day the settings might be to put rotor number 7 in slot 1, nr 4 in slot 2, and 6 in 3. They are then spun, so that slot 1 is at letter X, slot 2 at letter J and slot 3 at A. Since the rotors could be moved around in the machine, with three rotors in three slots you have another 3 x 2 x 1 = 6 combinations to consider, for a total of 105456 possible alphabets. There was also a 'ring' setting for each rotor which adds still more variation.
At this point, the operator would then select some other settings for the rotors, this time defining only the positions, or "spins" of the rotors. A particular operator might select ABC, and these become the message settings for that encryption session. They then typed their message settings into the machine, which is still set up in the initial settings. To be on the safe side, they typed it twice. The results would be encrypted, so the ABC typed twice might turn into XHTLOA. The operator then spins the rotors to his message settings, ABC. The rest of the message is then typed in, and sent it over the radio.
At the receiving end the operation is reversed. The operator sets the machine to the inital settings and types in the first six letters of the message. Upon doing this he will see ABCABC light up on the machine. He then spins the rotors to ABC and types in the rest of the encrypted message, decyphering as he goes.
Although many messages would be sent in any one day with six letters from the initial settings, those letters were intended to be random. While an attack on the cypher itself ought to have been possible, every message used a different cypher key, making frequency counting useless in practice. With modern computers, things might have been different, but with pencil and paper...
Enigma was very secure. The Germans relied very heavily on it, and they were justified in believing it to be effectively secure. Enigma-encrypted traffic included everything from high-level messages about tactics and plans, to trivialities such as weather reports and even birthday congratulations.
The commercial Engima machine was good, but not good enough. The British are said to have broken some messages when it was used in Spain during the Civil War there. And they are also said to have read some Italian traffic encrypted with one of the commercial versions. But, when the German Navy began using Enigma in the mid-20s, no one was able to read the traffic. When the German Army began to use a slightly different version in the early 30's, no one was able to read any of that traffic either. There are reports that British cryptanalysts of the GC&CS (Government Code and Cypher School) and the French too gave up, regarding the German military Enigmas as unbreakable.
The effort which broke the German Enigma cyphers began in 1929 when the Poles intercepted an Enigma machine being shipped from Berlin to Warsaw and mistakenly not protected as diplomatic baggage. It was not one of the military versions (Navy only at that time), but it provided a hint about Germans intentions. When the German Army first began using modified Enigmas a few years later, the Poles attempted to 'break the system' by finding the wirings of the rotors used in the Army version and by finding a way to recover the settings used for particular messages.
A young Polish mathematician, Marian Rejewski, made one of the most signficant breakthroughs in all of cryptanalytic history by using techniques from pure mathematics to find a way to do both. Rejewski noticed a pattern that was to prove vital; since the message code was repeated twice at the beginning of the message, you could guess the wiring of a rotor not by the letters themselves, but by the way they changed.
For instance, let's say an operator picked QRS as their 'message setting'. They would set the machine to the day's ground settings, and then type QRSQRS. This would turn into something like JXDRFT. This looks like complete gibberish, but the clue Rejewski exploited was that the disk had moved three positions between the two sets of QRS – we know that J and R are originally the same letter, and the same for XF and DT. We don't know what the letters are, but nor do we have to, because while there are a huge number of rotor settings, there are only a small number of rotors that will have a letter go from J to R, X to F and D to T. Rejewski called these patterns chains.
Finding the proper chains from the 105456 possiblilities was quite a task. The Poles (particularly Rejewski's classmates Jerzy Rozycki and Henryk Zygalski), developed a number of methods to help. One technique used clear strips for each rotor showing which letters could be chained, with the letters that could not chain being blacked out. Users would pick up the strips and lay them over each other, looking for selections where the three letters were clear all the way through. The British had also developed such a technique when they succeeded in breaking the common commercial Enigma, though they attempted (and failed) to break the military versions of the Enigma.
Of course, a few thousand possibilites is still a lot to try. To help with this, the Poles eventually built several "parallel enigma" machines which they called the bomba kryptologiczna (ie, cryptologic bomb). (Suggestions are that the name was chosen from a kind of local ice-cream dish, or from the ticking noise the machines made as they ran through the possibilities; the French later changed the name to 'bombe' and the English (or Americans) to 'bomb'. No one traces the name to anything explosive.) Possible sets of disks would be loaded into the machine and then a message could be tried on the remaining settings one after another. Now you were down to hundreds of possibilities. Hundreds is a reasonable number to attack by hand.
The Poles were able to determine the wiring of the rotors then in use by the German Army and, using them, to decrypt a large portion of German Army traffic for much of the 1930s -- until the beginning of WWII. They received some (secret) assistance from the French, who had an agent (Hans Thilo-Schmidt, codenamed Asch by the French) in Berlin who had access to Enigma key schedules, manuals, etc. Rejewski's cryptanalytic breakthrough did not, however, depend on that information; he wasn't even told of the French agent or given access to his material!
Some sources claim (without much support from informed participants' accounts) that in 1938 a Polish mechanic employed in a German factory producing Enigma machines took notes of the components before being repatriated and, with the help of the British and French secret services, constructed a wooden mockup of the machine. There's also a story about an ambush by the Polish resistance of a German Army vehicle carrying an Enigma machine... In neither case would the ground settings, much less the individual message settings chosen by the operators, be available and so that knowledge, however bravely gained, would be of little worth. These stories are, thus, less than inherently plausible.
However, in 1939 the German Army increased the complexity of their Enigma use. They had used only three rotors and simply moved them from slot to slot, but they now introduced an additional two rotors. Thus using any three out of five at any particular time. They also had their operators stop sending the individual three letter message settings twice at the beginning of each message, which eliminated the original method of attack.
The Poles, realizing time was running out before the Germans invaded, and unable to extend their techniques with the available resources, decided in mid-1939 to share their work, and passed to the French and the British some of their ersatz 'Enigmas', information on Rejewski's breakthrough, and on the other techniques they had developed. The French share was shipped to Paris in diplomatic baggage; the British share went on to Bletchley Park. Until then, German military Enigma traffic had utterly defeated both the British and French, and they faced the disturbing possibility that German communications would remain "black" for the entire war.
Nearly all the personnel of the Polish cryptography section left Poland during the invasion and most of them ended up in France, working with French cryptographers on German transmissions. Some Polish crypto workers were captured by the Germans before they left Poland or while in transit thereafter, but fortunately nothing was revealed of the Enigma work. It continued in France at 'Station PC Bruno' until the fall of France (and even somewhat after). Some of the French/Polish workers then managed to escape to England; none were used to help the British cryptanalytic effort against the Engima networks. When Rejewski himself learned (shortly before his death) of the work at Bletchley Park which he had begun in Poland in 1932, and of its importance to winning WWII, he was astonished.
With this massive Polish assistance, the British began to work on German Enigma traffic themselves. Early in 1939 Britain's secret service installed its Government Code and Cypher School (GC&CS) at Bletchley Park, 50 miles (80 km) north of London, to break enemy message traffic if possible. They also set up a large interception network to collect encyphered traffic for the code breakers at Bletchley. Eventually, there was a very large organization controlling the distribution of the resulting -- secret -- decrypted information. Strict rules were established to restrict the number of people who knew about the existence of Ultra and to ensure that no actions would alert the Axis powers that the Allies possessed such knowledge. Early in the war the product from Bletchley Park was codenamed 'Boniface' to give the impression to the uninitiated that the source was a secret agent. Such was the secrecy surrounding reports from 'Boniface' that 'his' reports were taken directly to Winston Churchill in a locked box to which the Prime Minister personally held the key. The information so produced was eventually termed Ultra.
At Bletchley Park, British mathematicians and cryptographers, chess and bridge players, and crossword puzzle fans, among them Alan Turing, confronted the problems presented by the many German Enigma variations, and found means of cracking many of them.
British attacks on the Enigmas were similar in concept to the original Polish methods, but based on different specifics. First, the German Army had changed their practices (more rotors, different 'message setting', etc), so the Polish techniques no longer worked without modification. Second, the German Navy had always used more secure practices, and no one had broken any of their traffic.
One new attack relied on the fact that the reflector (a patented feature of the Enigma machines) guaranteed that no letter could be encyphered as itself, so an A could never turn back into an A. Another technique counted on various common German phrases, like "Heil Hitler" or "please respond", which were found to likely be in this or that plaintext; successful guesses as to the plaintext were known at Bletchley as cribs. With a probable plaintext fragment and the knowledge that no letter could be encyphered as itself, it wasn't uncommon that a corresponding cyphertext fragment could be identified. This provide a large hint as to the message settings, much in the same way the message setting codes had done for the Poles before the War started.
German operators themselves also gave the decrypters immense help on a number of occasions. In one instance an operator was asked to send a test message, so he simply hit the T key repeatedly and sent it. A British analyst received a long message without a single T in it from the interceptor stations, and immediately realised what had happened. In other cases, Enigma operators would constantly use the same settings for their message codes, often their own initals or those of their girlfriends. Analysts were set to finding these messages in the sea of intercepted traffic every day, allowing Bletchley to use the original Polish techniques to find the initial settings for the day. Other German operators used "form letters" for daily reports, notably weather reports, so the same crib could be used every day.
In summer 1940 British decrypters, who were successfully breaking the German Air Force codes, were able to give Churchill information about the issuance of maps of England and Ireland to the Sealion invasion forces.
From the beginning, the Naval version of Enigma used a greater variety of rotors than did the Army or Air Force versions, as well as various operational methods that made it much more secure than other Enigma variants. There was no hint at all of the initial settings for the machines, and there was little probable plaintext to use either. Different, and far more difficult methods had to be used to break into Naval Enigma traffic, and with the U-boats running freely in the Atlantic after the Fall of France, a more direct approach recommended itself.
On 7 May 1941 the Royal Navy deliberately captured a German weather ship, together with cipher equipment and codes, and 2 days later U-110 was captured, together with an Enigma machine, code book, operation manual and other information enabling the submarine message traffic to be broken until the end of June. And they did it again shortly afterwards.
In addition to U-110, Naval Enigma machines or settings books were captured from a total of 7 U-boats and 8 German surface ships, including U-boats U-505 (1944), and U-559 (1942), as well as from a number of German weather-reporting boats, from some converted trawlers, a small vessel (the Krebs) captured during the raid in the Lofoten Islands off Norway, and so on. Several other more imaginative techniques were dreamed up, including Ian Fleming's suggestion to "crash" captured German bombers into the sea near German shipping, hoping to be "rescued" by the crew, which would then be taken captive by the Commandos hiding in the plane and the crypto material captured intact.
In other cases the Allies forced the Germans to provide them with a crib. To do this they would drop mines (or take some other action), and then listen for messages being sent. In the case of mining this or that channel, they knew the word "Minen" would be in some of them. This technique was called gardening at Bletchley.
Had the Germans ever replaced every rotor at the same time, it is possible that the British would not have been able to break back into the system. However, both because of the expense and because of the difficulty of getting all those new rotors to all the necessary ships and units, it was never done. Instead the Germans simply added new rotors to the mix every so often, allowing the settings of the newest ones to be deciphered after a short period.
Even these brief periods were enough to have dramatic effects on the progress of the War. Charting the amount of traffic decoded against the British shipping losses for that month shows a strong pattern of increased loss when Naval Enigma was blacked out, and vice versa. But, by 1943, so much traffic had been decrypted that the code breakers had an excellent understanding of the messages coming from various locations and times. For instance, a message sent from the west at 6am was likely to be sent by a weather reporting boat in the Atlantic, and that meant the message would almost certainly contain these cribs, and similarly for other traffic. From this point on, Naval Enigma messages were being read constantly, even after changes to the ground settings.
However, like the Polish system, the new tricks only reduced the number of possible settings for a message. The number remaining was still huge, and due to the new rotors the Germans had added from time to time, that number was much larger than the Poles had been left with. In order to solve this problem the Allies, especially the US, "went industrial", and produced much larger versions of the Polish bomba that could test thousands of possible key settings very rapidly indeed.
Some Germans had suspicions that all was not right with Enigma. Karl Dönitz received reports of "impossible" encounters between U-boats and enemy vessels which made him suspect some compromise of his communications. In one instance, three U-boats met at a tiny island in the Caribbean, and a British destroyer promptly showed up. They all escaped and reported what had happened. Doenitz immediately asked for a review of Enigma's security. The analysis suggested that the signals problem, if there was one, wasn't due to the Enigma itself. Doenitz had the settings book changed anyway, blacking out Bletchley Park for a period. However the evidence was never enough to truly convince him that Naval Enigma was being read by the Allies. The more so, since his counterintelligence B-Dienst group, who had partially broken Royal Navy traffic (including its convoy codes during the early part of the War), supplied enough information to support the idea that the Allies were unable to read Naval Enigma. Coincidentally, German success in this respect almost exactly matched in time an Allied blackout from Naval Enigma.
After the War, the American TICOM project teams found and detained a considerable number of German crypto personnel. Among the things they learned was that German cryptographers, at least, understood very well that Enigma messages might be read; they knew Enigma was not unbreakable. They just found it impossible to imagine anyone going to the immense effort required. (See Bamford's Body of Secrets in regard to the TICOM missions immediately after the War.)
In 1941 British intelligence learned that the German Navy was about to introduce Triton, a new version of Enigma with 4 wheels rather than 3. Fortunately, for the Allies, in December, a U boat mistakenly transmitted a messsage using Triton before it was due to be implemented. Realising the error, they re-transmitted the same message using pre-Triton 3 rotor Enigma, giving the British sufficient clues to break the new machine very shortly after it became operational on February 1 1942. The Triton network was given the name Shark and its traffic was routinely readable.
By 1945 almost all German Enigma traffic (Wehrmacht, Navy, Luftwaffe, Abwehr, SD, ...) could be decoded within a day or two, yet the Germans remained confident of its security. Had they been better informed, they simply could have, and surely would have, changed systems, forcing Allied code-breakers to start over. The Germans considered Enigma traffic so secure that they openly discussed their plans and movements, handing the Allies a huge amount of very useful information, not all of which was properly used; for example, both Rommel's actions at the Kasserine Pass, and the preparations for Battle of the Bulge were clearly foreshadowed in decrypted German Enigma traffic, but the information was not properly appreciated in either case.
It is commonly claimed that the breaks into Naval enigma resulted in the war being a year shorter, but given its effects on the Battle of the Atlantic (1940) alone, that might be an underestimate.
The fact that Enigma had been broken during the War remained a secret until the late 1960s. The important contributions to the War effort of a great many people remained unknown, and they were unable to share in the glory of what is likely one of the chief reasons the Allies won the war as quickly as they did. Eventually the story became known.
After the war ended, the British and Americans sold surplus Enigmas and Enigma-like machines to many countries around the world, who remained convinced of the security of this remarkable cypher machine. Their traffic was not so secure as they believed, which is, of course, one reason the British and Americans made the machines available.
In 1967, David Kahn released his book The Codebreakers, which described the capture of the Naval Enigma from U-505 in 1945. He went on to mention, somewhat in passing, that Enigma messages were already being read by that time, requiring machines that filled several buildings. By 1970 newer computer-based cyphers were becoming popular as the world increasingly turned to computerised communications, and the usefulness of Enigma copies (and rotor machines generally) rapidly decreased. It was decided at this point to "let the cat out of the bag", and reports about some of Bletchley Park's operations were released in 1974.
The National Security Agency retired the last of its rotor-based encryption systems in the 1980s.
Many accounts of these events, and of other World War II crypto happenings, have been published. Several are unreliable in many respects about WWII cryptographic. This can be traced to several causes:
Cryptonomicon, a novel by Neal Stephenson, was in part a fictionalized account of the breaking of the Enigma machine, as was the novel Enigma by Robert Harris, on which was based the recent movie. Neither should be relied upon as an accurate history.
Strengths of Enigma
Encryption method
Breaking the Enigma
After the War; public disclosure
Disclosure
As with other history, but more than most, the history of cryptography, especially its 'recent' history, must be read carefully.Further reading
A short and responsible account of World War II cryptography which is essentially up-to-date as of this writing is Battle of Wits by Stephen Budiansky. It covers more than just the Enigma story. Hugh Sebag-Montefiore's recent Enigma: The Battle for the Code includes some previously unknown information -- and many photographs of the individuals involved. Bletchley Park had been his grandfather's house before it was purchased for GC&CS. David Kahn's Breaking the Enigma is essentially about the problem of Naval Enigma. Finally, a brief description of the Enigma, as well as other codes/cyphers, can be found in Simon Singh's anecdotal and very readable The Code Book. The official British history of cryptography in World War II is in four volumes, edited by Sir Harry Hinsley. He also edited a one volume collection of memoirs by participants. Rejewski himself wrote some articles and a book about his 1932 breakthrough. See also
World War II Era Encryption Devices
External links