The enigma of the Enigma

[Dave Saxton]

On April 9th 1974 the world of military history was rocked by the revelation that the Allies had been reading the German military messages enciphered by the Enigma cipher machines though out much of World War Two. Everything had to now be evaluated in an entirely different light. It came as complete shock to the Germans who had been reassured by their technical experts that the Enigma ciphers were impossible to break.

The German Navy had suspected that Enigma was not secure many times during the war. Each time investigators found another more likely cause of the obvious intelligence breaches and so cleared Enigma as the culprit. It was an understandable misjudgment since those other factors such as radar and radio direction finding were indeed strong contributing factors with much evidence to their support.

Perhaps the strongest evidence of all that Enigma was secure was there was little if any indication of the Royal Navy using Enigma decrypts in their own communications. The Germans had broken the Royal Navy codes during 1935 and continued to read Royal Navy messages though early 1944. Often times a British report of sinking a U-boat carried the ominous statement: “Radio Located” but this could and often did indicate radar (radio detection and ranging) and/or radio direction finding.

Nonetheless during June and July 1941 the British mysteriously located and destroyed the network of supply ships and tankers dispersed though out the Atlantic to support the Bismarck raiding operation. Alarm bells went off with in the Kriegsmarine High Command, or the OKM. It had to be that Enigma was compromised! A special investigation was launched headed by Admiral Fricke. When the Fricke Commission rendered its findings it found that either Enigma was breached or that it was coincidence. Coincidence was determined the likely cause because Enigma was though to be impossible to break. So strong was the German faith in Enigma that even when presented with overwhelming evidence of its failure that evidence was dismissed. To understand why the Germans thought Enigma was unbreakable we must understand the Enigma machine and how it worked.

[Dave Saxton]

The Enigma cipher machine resembled a typewriter. Each letter of the plain text or pre-coded message was typed in and a substitute letter was indicated by a lighted indicator. These substitute letters comprised the cipher text. The cipher text was complete gibberish with no rhyme or reason to it. Traditional code breaking procedures were useless. The cipher text was broadcast and the only way to de-cipher it upon reception was by typing the cipher text into an identical machine, set up identically. This is the difference between a code and cipher. A code is idea for idea, or word for word, or phrase for phrase, but a cipher is letter for letter, or number for number, substitutions. Sometimes a code may be ciphered called super-encipherment. Codes and even super enciphered codes are almost always eventually cracked because they must have some kind of a pattern or key in order to be de-coded on the other end. By comparing scores of messages, a process known as superimposition, patterns and duplications to the code will be detected. Machine ciphers were never the same from one day to the next or in the case of Enigma from one message to the next-mostly. The German military adopted machine encipherment in the late 1920s because it offered much higher security than codes. They were shocked to learn from a 1923 Churchill book that the British were reading their naval codes though out most of WW-I. They turned to the Enigma machine.

The basic Enigma machine utilized the concept of movable rotors. Each rotor had 52 terminals, 26 on the input side and 26 on the output side. Each terminal represented a letter of the alphabet. The signal from each input terminal ran through a maze of wiring to an output terminal. How each rotor was wired was a closely guarded secret and each rotor was wired differently. Each time a letter was typed into the machine the first rotor in series rotated ahead one position. If there was just one rotor then there would only be 26 possible substitutions or permutations. However, if there were two rotors then it became 676 permutations to work though, and 4 rotors yielded a period of 456,976, and 5 rotors 11,881,376 and so on…

Each time the first rotor completed a full rotation the next rotor in series would move ahead one position and then next rotor in series would do the same when the second rotor completed its cycle. The military Enigma machines utilized three movable rotors and a fourth unmovable ½ rotor called the reflector. The reflector turned the signal around and sent it back through the rotors again. This not only increased the period of permutations available, but made it possible to de-cipher the message by another machine on the other end by simply typing the cipher text into an identically set up machine. On the Enigma machine each input terminal on the rotors could be assigned any letter from the alphabet, by setting an alphabet ring concentric to the rotor, further scrambling the permutations.

Even if the enemy had a machine with the correctly wired rotors they still could not de-cipher messages unless they knew exactly what locations (1, 2, or 3) the rotors were positioned, and the start positions of the rotors and alphabet rings. These setting were intended to be changed daily. The solution to yesterday’s riddle was useless today, and today’s solution would be useless tomorrow. Thus Enigma had to be “broken” anew every single day. It wasn’t like they finally broke Enigma one day and from that day forward they could read Enigma ciphered messages.

Sorry Hollywood, it was not capturing a machine that mattered either, but the daily settings or the keys that were needed. The Allies had already built exact replica machines. To put it into modern parlance it wasn’t the computer but the software that mattered.

Today to solve the daily setting we would simply run various combinations through a computer until the correct combination of settings was found. However, when Enigma was invented in 1918 such a machine as the modern computer was inconceivable. Running the various calculations by hand would take a team of mathematicians an enormous amount of time. It was because of the need to solve the Enigma that the modern computer exists today as we know it, because a computer (even a primitive one) was really the only practical way it could be done.

[Dave Saxton]

The German Navy adopted the Enigma during 1927. The early naval machines differed from the machines used by the German Army by using rotors with 29 input terminals for additional letters. However, by 1932 the Navy was calling into question the long term security of Enigma and was considering dumping it for something else. The Army suggested they instead adopt the Army version of Enigma.

The German Army used 26 terminal rotors, but it differed from the naval Enigma in two other significant ways. One, it used a plug board or switchboard which by -passed the rotors and substituted 6 different letters (everyday) via cables. This essentially increased the number of keys, greatly increasing the problem of solving the settings from the interception of cipher texts by machine. Secondly, the start position of the first rotor varied from each message to another. The cipher clerk selected a start position letter at random for each message. In order for the intended receiver to de-cipher the message he had to know what start position letter the transmitting clerk had randomly selected for the main text. Therefore, at the start of each message was a six digit code that indicated the start position, called the message key. It was actually three digits (the start letter and two meaningless ones) repeated in case the transmission was garbled. The receiving clerk then reset up his machine to match (in addition to the daily rotor, ring, and plug board settings), before going on to de-cipher the main message.

The German Navy adopted a similar Enigma system, but not exactly the same, to the Army’s Enigma during 1933.

[Dave Saxton]

As soon as the German military adopted the Enigma during the late 1920s German messages became completely blacked out to outside intelligence agencies world wide, and stayed blacked out for years. Intelligence agencies were not used to not being able to break the enemy’s (and allies) codes and ciphers. Everybody was reading most of everybody’s codes but everybody thought their own codes and ciphers were safe. In Paris, London, Warsaw, and Washington frustration mounted into the 1930s. Nothing could be found to break the Enigma. They bought commercial Enigma machines, but the military machines were obviously different.

Then during 1932 a low level Intel officer in the German Army approached French Intelligence offering to trade Enigma secrets for money. The French received some instruction manuals and the ring/rotor keys for a few months of 1932 as well as plain text message transcriptions in the first “drop”. The French gave the data to their code breakers but they found without the random message key and how the rotors were wired it was useless to them. The British code breakers rendered the same verdict. In frustration the French gave the information to the Poles. The Poles could do something with it.

The Poles understood that traditional code breaking approaches were mostly useless to solve machine enciphers. It would take a mathematical approach if it could be done at all. They had recruited a mathematical expert for this purpose and set him at work.

[Dave Saxton]

Marian Rejewski had attended the University of Posazn (Before Versailles the German border town of Posan) and then Goettingen University in Germany. Rejewski had actually left the employ of Polish Intelligence to take on post graduate studies at Goettingen. After a year he returned home to work in the family business, but returned to Polish Intelligence because he became bored. The year spent at Goettingen would prove to be very important.

Rejewski realized that the final permutation created by the Enigma machine was a function of a complex type of advanced algebra for number groups’ theorem he had studied at Goettingen known as PN(inverse)P Theorem. The P and inverse P represented the permutations of the plug board, and N represented the total permutations of the rotors. The various elements could be broken up and solved for separately. The plug board settings for a particular day could be solved for by using a test cipher text that was the inverse of a plain text message utilizing the likely letters (as indicated by the message type or time sent every day, such as “nothing to report” or “spare parts needed” or a crib of the message from another known message) connected by the cables.

When Rejewski super imposed the cipher texts from about 60 different messages from a given day he began to see a pattern for the first 6 letters of the messages. This was of course the enciphered message key repeated. This pattern had to be a product of the fast rotor combination for that day before the other rotors were triggered to move forward and provided a way to determine how the rotors were wired and set up. Rejewski later commented that it would have been better if the message key was left un-enciphered.

Based on the encipherment patterns of the message key (which was itself a product of PN-P number group theory) Rejewski constructed six huge and very complex algebra equations which he expected would yield the fast rotor’s wiring pattern. This failed to yield any solutions, however. Then Rejewski thought he may have made an incorrect assumption. He had assumed that connections from the key board to the rotor transfer terminals would be in numerical order. That is to say the first key, Q, would go to the number 1 terminal and 2nd letter W to the 2nd terminal and so forth. What if the Germans wired it letter to letter (Q to Q..) instead? This worked and within a day Rejewski had determined the wiring for the fast rotor then in use. Determining the wiring of the other rotors came by the same method because the German Army was at that time rather lax about scrambling the rotor locations. They only changed rotor locations every three months and then the second rotor replaced the third rotor and the first rotor replaced the second rotor and the third became the first in the order. After two of the rotor’s wiring was determined the wiring for the remaining rotor and the reflector’s wiring came in due course.

http://chc60.fgcu.edu/Images/articles/Rejewski.pdf

[Dave Saxton]

The Poles then constructed replica Enigma machines to de-cipher intercepted messages. Each day they had to determine the daily, rotor locations, the rotor settings, the concentric ring settings, the plug board settings, and finally the message key to each message. Every single day this had to be done all over again. The first step was to obtain 60 to 100 intercepts to determine the pattern of the message keys. From this a menu was developed to test the most likely combinations of ring and rotor setting to match the pattern and then test them manually by setting the rotors on a machine to those combinations. Without this it would be an astronomical number of combinations to work through! The rotor locations were determined from 52 different cardboard templates with slots cut in them over laid on the replica machine. After awhile the Poles built a machine consisting of two rotors cycled mechanically to speed up the process. This machine was called a cyclometer.

The message key was theoretically over 17,000 combinations (26 cubed) but in practice only about 30-to 40 keys were likely to be selected at “random” and the Poles soon knew which ones were the most likely to be selected. Duplications by different cipher clerks almost always occurred as well. It was just the human element.

After about a year of cyclometer solutions, repeatable settings began to turn up. All cyclometer solutions had been recorded and cataloged on card stock so usually once the daily menu was developed it only took about ten minutes to find the daily settings from the card catalog.

In 1935, however, the German Army upped their game. They began to change up the rotor locations daily, made the message key more complex, and changed the number of letters connected on the plug board from 6 to a variable of 5 to 8. The cyclometer could no longer keep up, and the card catalog was rendered useless (it still worked for Nazi Party communications for sometime).

To replace the cyclometer, the Poles designed what was in essence a primitive computer consisting of three pairs of Enigma machines driven by electric motors through various combinations until each pair hit upon the settings for one of the three rotors matching the daily menu that had been developed. This machine was called a Bomba. It usually took the Bomba from two to four hours to find a solution to each day’s settings. The daily plug board setting was now found through using multiple cardboard templates, with slots, process called the Zygalski sheets.

The Bombas worked up until December 15th 1938 when the German Army increased the number of rotors from 3 to 5. It was not five at one time but any three of the five at a time with the other two sitting on the sidelines so to speak. The number of plug board letters substituted was also increased to 10.

The Poles calculated it would take a 60 fold increase in Bomba capacity to figure out the new complexities and this was simply beyond their means. It was time to come clean with the British and the French.

Several times the British and French had inquired of the Poles to see if they had found any success regarding the Enigma. Each time the Poles had lied.

[Dave Saxton]

When the British code breaking establishment, now located at Bletchley Park, learned of the Polish success and how they were now stymied they sought the expertise of Alan Turing. Turing was the greatest mathematician of his generation. He had for his doctrinal dissertation at Princeton solved one the great mathematical riddles of mathematical theory, known as the Entscheidungsproblem. (The correct solution was no solution.) Turing’s task was to design better bombas, which the British now called Bombes, up to the tasks of dealing with determining the daily Enigma keys of the more complex types.


Turing not only designed bombes of greater capacity but they represented a great advancement into the field we now know as computing. Turing’s bombes utilized electrical circuits that essentially asked the question: does this combination of settings complete a circuit? Yes or no? It was a type of primitive binary language. The bombes could be connected together into a network and talk to each other.

Turing not only designed these machines, but the first few he hand built himself saving an enormous amount of time, and certainly helping to win the war in time.

The way the machines were used was essentially the same as the way the Poles used their more primitive bombes. First a menu of likely daily keys was developed from super imposing 60 to 100 cipher messages from that day, or from cribs (known portions of text from another code or cipher). Remember each day’s keys had to be solved all over again. The bombes were set up to run through the menu. It usually took several hours. Any “hits” were data logged and then those settings were tested to see if they transformed cipher text from that day’s intercepts to portions of plain text on replica Enigma machines set to those settings and rotor locations. The daily plug board setting and the message keys were solved separately. It all might come together and allow messages from one day to be de-ciphered, or it might not. With the Army and Luftwaffe Enigmas it succeeded most days. With the naval Enigma ciphers the process did not work at all. Months and months went by and the naval Enigma remained, well an enigma.

[Dave Saxton]

To understand why the naval enigma was so difficult to solve we must understand the differences between the regular das Heer and Luftwaffe (called the Red Enigma) enigmas and the naval enigmas. The naval Enigma did not use the same system to relay the message key. Instead the cipher clerk selected a start position at random from a daily list. He also selected a code for which key net the message was to be on. From these the correct bi-gram to be sent was determined from a daily chart. This bi-gram replaced the message key and was called instead the Indicator Key. The use of the indicator key blocked the normal pathways to developing a likely menu to run through bombes and usually kept the start position hidden even if by chance the correct rotor settings had been obtained. The indicator key indicated which key net the message was on as well.

The Kreigsmarine did not use one Enigma but several Enigmas. Each had its own set of daily keys. Solving one did not mean another could be solved. There were key nets for different levels of officers, for home waters, and for distant waters, one for U-boats, and one for surface ships, one for weather ships, and hilfe cruisers, and one for shore facilities. For example the U-boat key net was known as Triton and surface ship key net was known as Neptune. The key net for the Med was Medusa.

Each of these key nets required the use of its own rotors to be used as one of the three from a set of seven rotors. Moreover the secondary rotors could move ahead at irregular intervals when triggered by the input of certain letters instead of waiting until the proceeding rotor had completed its cycle, essentially changing the key during mid message.

Through 1940 little if any progress was made at decrypting naval enigma. From cribs such as from the non-enigma Dock Yard Cipher a bit or piece could be determined once in a great while. The Dock Yard Cipher was used to transmit the locations of mine fields to non Enigma using naval traffic. However, this information also had to be transmitted on the Enigma nets so that warships and U-boats would not run into new mines. The Dock Yard Cipher was easily broken. This made possible setting up a bombe menu for the same Enigma messages based on comparing commonalities between the two cipher texts. It usually took ten days to two weeks to yield a de-crypt that was usually the exact same information already obtained from the Dock Yard Cipher.

Sometimes they got lucky if a cipher clerk made a mistake somewhere or did something foolish like transmit a fake message (used all the time to change up traffic analysis) with all the same letter comprising the plain text message. Such a mistake by an Italian cipher clerk resulted in the British getting the drop on the Italian fleet off Cape Matapan. But the naval enigmas could not be broken into reliably even with Turing’s computers. The British realized they would need the daily keys.

[Dave Saxton]

Getting the keys was no easy feat. The daily keys were printed in water soluble ink on water soluble paper. The keys were kept under lock and key in an officer’s cabin and distributed to the cipher clerks on a need to use basis by the signals officer. This way the cipher clerks could not reveal keys to the enemy under torture or hypnosis, or by bribery. But this also meant that the keys could be recovered from the officer’s cabin even if the cipher clerks had disposed of the daily keys and the Enigma hard ware properly in the case of the ship being boarded. Once the British learned this they sought to capture keys from the German weather ships. The weather ships were at sea for months at a time and so must have the daily Enigma keys extending for several months on board.

During May 11, 1941 a British destroyer forced U-110 to the surface and managed to capture it before it could be scuttled. They also captured all of the Enigma keys and hardware intact!

During May the British captured a weather ship in a raid lead by Admiral Lancelot Holland. The cipher clerks threw the Enigma machine overboard and the keys for that day. But the keys under lock and key and the extra rotors were captured intact. This was followed by further weather ship capture in June with the keys extending to Oct 1st 1941.

Thus during late May through September 1941 Bletchley Park was able to de-cipher Naval Enigma with out much delay, but only because they had stolen the daily keys, not because they had really “broken” the naval Enigma. Once the captured keys expired it was right back to bits and pieces here and there with long delays. Then on Feb 1st 1942 it all went completely black again.

[Dave Saxton]

On Feb 1st 1942 the German Navy began using Enigma with 4 rotors at a time instead of three rotors at a time. The new M4 Enigma system was also accompanied by new key nets. For example, Triton was replaced by Shark. BP knew that something big was coming up in Feb 1942 but the extent of the black out was shocking in both its completeness and effectiveness. M4 Enigma was completely secure until December of 1942.

During a late November night in 1942 a Royal Navy officer named Antony Fasson boarded the sinking U-559 off the coast of Palestine and managed to pass the keys up for the new short weather cipher before the U-boat sank, tragically taking Fasson and an assistant, Collin Grazier, down with it. But Fasson’s and Grazier’s sacrifice paid off.

Analysis of the short weather cipher at Bletchley Park on December 12th indicated that it used only three rotors so the 4th rotor must be put in the neutral position during short weather enigma broadcasts. Borrowing six bombes from Hut-2 it took 12 hours of running programs to determine the wiring pattern of the fourth rotor. Now that the 4th rotors (there were two) or thin rotors wiring was known, Shark could now possibly be broke into by developing a daily menu based on cribs from intercepts of the short weather cipher.

[Dave Saxton]

Shark could now possibly be broke into by developing a daily menu based on cribs from intercepts of the short weather cipher.

The computing power at Bletchley Park was now much greater. They now had 60 bombes of greater capability at their disposal. The bombes could also be connected via cable to the American bombes on the other side of the pond. The American bombes were designed and built by National Cash Register Corporation of Dayton Ohio. Each had 6 times the computing power of the British bombes. By obtaining cribs from the short weather ciphers and developing menus, the combined computing power of British and American bombes could obtain the daily keys to the Shark key net on most days. It took the efforts of both the Americans and Bletchley Park to solve the 4 rotor Enigma from day to day.

In Feb 1943 the Germans changed the short weather cipher and it became useless for a bridge into the 4 rotor Shark key net.. However, the short signal cipher now being used by German U-boats with great frequency proved to be a handy substitute. To prevent their radio broadcasted from being D/F’ed the German U-boats were using a short cipher transmission method that lasted only a few seconds. They were unwittingly compromising the Enigma key net Shark by this practice. The traffic levels of both the Shark key net and the short signals net gave Bletchley Park, and the American organization known as OP-20-GI-2 (A), plenty of material to work up bombe menus on. During the climax of the Battle of the Atlantic during the spring of 1943 Shark messages were de-ciphered on about 80% of the days.

The surface ship key net for distant waters remained secure mainly because the traffic level was so low that there was little material for BP or the Americans to develop menus with.

[Paul L]

Very good work Dave!

Can you please tell us the source you used on this work?

[Mostlyharmless]

One of the puzzles is why the Germans kept on improving their codes through the Thirties and WW2 whilst at the same time believing that there was no way that the Allies could make a long lasting break into the codes (i.e. beyond capturing a month's settings). Bauer's “Decrypted Secrets” mentions on page 194 that “Already in 1930, Lieutenant Henno Lucan, Second Signals Officer of the battleship Elsaß, pointed out in a study a weakness of the ENIGMA. With the introduction of the plugboard, the worries seemed to be banished.”

There is an interesting book by Rebecca A. Ratcliff called “Delusions of Intelligence: Enigma, Ultra, and the End of Secure Ciphers” (see a review at http://www.h-net.org/reviews/showrev.php?id=13210 as I cannot see anything via Google Books). She argues that the Germans could believe in the superiority of Allied production and equipment much more easily than believing in superior Allied cleverness. An article called “Der Fall Wicher” by Joseph A. Meyer at https://www.nsa.gov/public_info/_files/ ... Wicher.pdf shows that some of the Polish work was discovered but then ignored.

Turning to the British work, one might also mention Gordon Welchman. There is a good site at http://www.ellsbury.com/enigmabombe.htm explaining the mechanics. “Enigma: The Battle for the Code” by Hugh Sebag-Montefiore gives quite a lot of details on the Allied attacks on German naval Enigmas.

[Dave Saxton]

Thanks guys but my purpose is only to provide a general survey of the Enigma storey to the online naval history community. If your more interested then by all means go to some better, more detailed works such as the excellent Seizing The Enigma by David Kahn, which in addition to the Rejewski paper (linked to above) was a major contributor in my study of this topic. BTW.. I'm sure I have made mistakes and left things out in the above, so please point such out, so that correction can be made.

Turning to the British work, one might also mention Gordon Welchman.

Yes this man must be recognized. He turned Hut 8 around after the demoralizing failures. The amount of hard work put in by the Anglo/Americans and Poles to this problem is amazing. That might help explain why the Germans thought that solving the Enigma was beyond reach. Normally with out this much work extending for more than a decade it would have been unsolvable. I don't think that anybody concieved of the invention of the bombes or the embronic modern computer going in. It was German policy regarding Enigma (drawn up by the Reichsmarine) to assume that the enemy could break it. So on going improvements were always rolling forward based on this policy despite the conventional wisdom that it was unbreakable.

In some ways the Naval Enigma must be considered in some part unbroken. It was really hit and miss at any given time during the war. It could never be taken for granted that naval Enigma could be de-ciphered on any given day. Only during the period of a few months during 1941 when the Allies had the keys, and during the climax of the U-boat battle in spring 1943 (due to the extensive use of the short signal procedure and the amount of traffic on the Shark net) could naval enigma be reliabley de-cpihered on most days. For almost all of 1942 naval Enigma was secure.

One thing that strikes me now that I have a better undrestanding of when the naval Enigma was vulnerable and when it was not is that we can really see how vital Ultra was. The Allies won victories during those periods of Enigma vulnerability, and the Germans won more victories (particularly during the U-boat offensives) during the other periods. Or is that coincidence?

I'm also interested in the breaking of the Japanese codes and ciphers but I need to study that more.

[Paul L]

I some times wonder how much more difficult the war would have been if the Naval Enigma had become the standard for the whole Wehrmacht from the start of the war?

It does look like pure luck In the first year or two of the war and then hit-miss until mid 1943 ; with only delayed decoding when it worked.