March 23, 2011

Polish-Hungarian Friendship Day

"Hungary and Poland are two eternal oaks.
Each of them shot up a separate and distinct trunk,
but their roots widely scattered in the ground
are intertwined and knitted invisibly. Hence the existence and vigor of one is the condition of the other's life and health."
Stanlislaw Worcell (1849)

Polish-Hungarian Brotherhood (00:06:45m)

On March 23, 2007 the Polish Sejm and the Parliament of the Republic of Hungary unanimously approved the adoption of the resolution establishing March 23rd as the Day of Polish-Hungarian Friendship. This Act reaffirms the unique relationship between the Polish and Hungarian peoples that has been in existence since the Middle Ages and which continues to forge the bonds of common ideals, mutual respect and affection, and shared political ambitions. Such a relationship is a veritable phenomenon that is unparalleled in any other two nations throughout history.

Polish-Hungarian Friendship Day is celebrated concurrently in Poland and Hungary. This year the honour of hosting festivities is bestowed upon the city of Poznan in which the richness of the Magyar heritage will be celebrated. Though the official Day is March 23rd, Polish-Hungarian Friendship Day has already begun (on the 17th of March) and will continue until March 28. Among the many events scheduled are theatrical performances, films, exhibitions, concerts, workshops, scientific exhibitions, and much more.

Polish and Hungarian Presidents, representatives from governments of both countries, and non-governmental organizations, academic institutions and associations all take part in a bi-national annual celebration of a common history and culture, past and present.

The "twin cities" of Györ and Poznan have demonstrated mutual co-operation and support for exhibitions and fairs; for example Györ representatives regularly attend the Poznan International Fair of Books for Children and Youth, Tour Salon, John's Market (Jarmark Świętojański). Conversely, last year Poznan representatives participated in Györ's festival of "The Magic of Baroque", the International Children's Olympiad and the International Exhibition of Books.

Moreover in the light of the Polish and Hungarian Presidency of the EU Council, theirs is a fervent commitment to consolidate the solidarity between their two nations, its cities and regions.

Good relations between Poland and Hungary date can be traced back to the Middle Ages. In fact in the 15th century the two countries shared a Polish king, Władysław III of Varna, who at barely twenty years of age, died in battle, fighting the Turks at Varna, Bulgaria. His name lives on today. There is a boulevard in Bulgaria and a district named after Vladislav Varnenchik and even a professional Bulgarian football team which in earlier years was named after him. There is also a symbolic cenotaph bearing his name in an ancient park at Varna.

  King of Poland and Hungary Władysław Warnenczy 

In the 16th century, Poland elected Stefan Batory, an Hungarian nobleman as their King. Batory came to be regarded as the greatest King in Polish history.

King of Poland Stephan Batory

During the Hungarian Revolution of 1848, Józef Bem, a Polish General became a national hero for both Hungary and Poland.

 General Jozef Bem

During the Polish–Soviet War, (1919-21), Hungary was prepared to dispatch 30,000 cavalry troops to Poland's aid. However the Czechoslovak government refused to allow their passage through the demilitarized zone. (The zone had been created just several months earlier at the end of the Czechoslovak-Hungarian war.) Nevertheless, some Hungarian munitions trains did manage to reach Polish troops.

Up until the 18th century, Poland and Hungary shared an historic common border between Poland and Carpathian Ruthenia (also referred to as "Carpathian Rus") and governed by Hungary. But after World War I, the Allies transferred Carpathian Ruthenia from defeated Hungary to Czechoslovakia. In the months leading up to World War II, the area became known as "Carpatho-Ukraine" because of its large population of Ukrainian nationalists.

On September 30, 1938, following the Munich Agreement, Czechoslovakia was slated for takeover by Nazi Germany. It set into motion diplomatic and paramilitary collaboration between Poland and Hungary in an effort to restore their historic common border. They realized their first goal, with the First Vienna Award on November 2, 1938.

A demonstration in favour of the common Polish-Hungarian border in Budapest, October 1938 (00:01:11min)

Polish - Hungarian border in March 1939 - chronicle (00:1:02min)

Na granicy Polsko Węgierskiej A Lengyel Magyar határon On the Polish Hungarian border (00:02:27min)

Germany was opposed to the existence of a common Polish Hungarian border but in March 1939 Hitler suddenly changed his stance and authorized Hungary to take control of the remainder of Carpatho-Rus (a territory which began to refer to itself as "Carpatho-Ukraine").  However the remainder of Slovakia was off limits despite Hungary's claim to its territory.

Hitler planned to strike Poland from a staging ground in Slovakia but changed his mind about the common Hungarian-Polish border. The Organization of Ukrainian Nationalists (OUN) were amassing ever-larger military troops along the southeastern border of Poland which placed Poland in imminent danger.  Though the OUN were allies of Germany, Hitler suspected that should they join German troops in the planned invasion of the Soviet Union, the OUN would surely demand their independence.  (Moreover, Hitler had designs on Ukrainian natural and agricultural resources.)

Carpathian Rus became a sore point for Hitler. He realized his error when his request to transport German forces across Carpathian Rus into southeastern Poland was denied by Admiral Horthy's government as a matter of "Hungarian honour". The common Polish-Hungarian border based on their long-standing friendship, presented itself as an obstacle.

Admiral Miklós Horthy de Nagybánya
Regent of Hungary 1920-1944

By refusing German passage, the Hungarian government allowed members of the Polish government and tens of thousands of Polish military troops and personnel to escape from Poland into neighboring Hungary and Romania. From there the Poles made their way to France and French-mandated Syria to continue their military operations. At that time, Poland was the third-strongest Allied nation, after Britain and France. For a period of time, many Polish and British intelligence agents and couriers, including Krystyna Skarbek, were able to access Hungary's Carpathorus as a route to cross the Carpathian Mountains to and from Poland.

Grave of a Hungarian Honved captain and six of his men who fell, fighting on the Polish side
in the 1944 Warsaw Uprising.

1956 - Hungarian Revolution (00:02:26min)

After World War II, during the Hungarian Revolution of 1956, the Polish people demonstrated their support for the Hungarians by donating blood for them. By November 12, 1956, over 11,000 Poles had donated blood. Massive shipments of medical supplies, totaling 44 tons were shipped by the Polish Red Cross to Hungary by air and even larger shipments by trucks and rail.

Lengyel, magyar — két jó barát,
együtt harcol s issza borát.

Polak, Węgier — dwa bratanki,
i do szabli, i do szklanki,
oba zuchy, oba żwawi,
niech im Pan Bóg błogosławi.

Monument of Polish Hungarian Friendship in Gyor


From Polish to English
Pole and Hungarian cousins be,
good for fight and good for party.
Both are valiant, both are lively,
Upon them may God's blessings be.

From Hungarian to English
Pole and Hungarian — two good friends,
joint fight and drinking are their ends.


Suggested Links:

March 10, 2011

The Enigma Machine Part 4 Battle of Ciphers

WWll in Colour-Cracking the Enigma Code Machine (00:10:00m)

World War II was the greatest global catastrophe in the history of human civilization. No other war before or since had been as destructive on a global scale. Over 100 million personnel were mobilised from 1939 to 1945. It has been estimated that there were between 50 million to 70 million fatalities among civilians and military, including victims of the Holocaust. Belligerents included nations from around the world......the British Empire, Union of Soviet Socialist Republics, the United States, France (before invasion), China, Australia, Belgium, Brazil, Canada, Czechoslovakia, Ethiopia, Greece, Mexico, the Netherlands, New Zealand, Norway, Union of South Africa, and Yugoslavia......Germany, Italy, Japan, Hungary, Romania, Bulgaria, as well as Finland, Iraq,Thailand, and numerous puppet states established by the Japanese Empire.

The world had never before seen the likes of the Blitzkrieg as the German Wehrmacht, Luftwaffe, and Kriegsmarine carved paths of destruction and conquest until of all Europe was under its control. Allied troops were mobilised in massive numbers on land, in the air and at sea in a desperate attempt to fend off Hitlers advancing armies. Though British ambitions were high, they suffered enormous losses in men and materiel. Losing was not an option for the Allies however the fear of a humiliating defeat always hung in the balance.

Despite these uncertainties, Britain had a secret army - the largest ever assembled. They were the code breakers of Bletchley Park. Churchill code-named them "Ultra". A virtual army of men and women who labored tirelessly with one purpose in mind - to decipher the German codes, and thanks to the Poles, they were able to learn early on the secrets of deciphering the Enigma. In fact, just days before Poland was invaded by Germany, the team of mathematicians and cryptologists of the Polish Cipher Bureau met with British and French Intelligence, and presented them each with Polish-built replicas of the Enigma machine. Though the Poles were not part of the inner sanctum of Bletchley Park, they collaborated with the Polish Army Signals Corps, located in Boxmoor near London and subsequently cracked the German SS formations cipher.

Supreme Allied Commander, Dwight D. Eisenhower praised Ultra for having been "decisive" to Allied victory; Sir Harry Hinsley, historian of British Intelligence in WWII asserted that Ultra was singularly responsible for shortening the war by two years, perhaps even by four years. Without Ultra, there is no telling what end might have transpired.

Of major concern to Ultra was the danger of having their activities discovered by the enemy. Throughout the war the Germans never suspected that the Allies had broken the Enigma Code and had been routinely intercepting and reading their secret messages. Moreover, the Allies often used the Enigma machine to transmit misinformation directly to German troops. It was indeed a battle of ciphers, and one in which the Allies proved their superiority over and above the Nazi Germans.

The following is a random list, albeit a very brief one of just a few of the battles of World War II. It is meant only to illustrate the vital role played by Ultra that helped lead the way to an Allied Victory.

In the words of Churchill "it was thanks to Ultra that we won the war". However it should also be noted that it was thanks to the genius of Marian Rejewski and his colleagues, that Ultra was even able to get off the ground.

Battles of World War II

Invasion of the Low Countries

In April 1940 Ultra discovers information about the logistics of the German forces and of their subsequent orders to attack the Low Countries, before the Battle of France in May.

German Bombs

In June 1940, Ultra decrypts a message which reads "KNICKEBEIN KLEVE IST AUF PUNKT 53 GRAD 24 MINUTEN NORD UND EIN GRAD WEST EINGERICHTET". Translated it means: "The Cleves Knickebein is directed at position 53 degrees 24 minutes north and 1 degree west". The message clearly indicated that the Germans were developing a radio guidance system for their bombers. Ultra continued to play a vital role in the so-called Battle of the Beams.

Battle of Britain

Air Chief Marshall Sir Hugh Dowding, Commander-in-Chief of RAF Fighter Command was able to receive frequent reports from Ultra thanks to a teleprinter link from his headquarters at RAF Bentley Priory to Bletchley Park. He received vital information concerning German strategy, strength and location of Luftwaffe fleets, as well as advance warning of Nazi bombing raids, information which greatly contributed to the British victory.

Battle of the Atlantic

The contribution made by Ultra intelligence to the Battle of the Atlantic was crucial to the war effort and the very survival of the British Isles. It wasn't until June 1941 that Bletchley Park finally began to read U-boat messages. As a result, Allied Command, having advance information on the location of U-boat "wolf packs" could divert their transatlantic convoys to safety, and sink U-boat supply vessels. However, on February 1, 1942, the U-boat messages became once again unreadable and remained so until the end of the year. The reason was that the Germans had modified the Enigma machine so that it operated with four rotors instead of three.


Ultra contributed to Montgomery's victory at the Battle of Alam el Halfa by providing Allied troops with timely warning of Rommel's planned attack.

In the period between December 1940 to February 1941, Ultra intelligence provided invaluable information that helped the British army's victory over the much larger Italian army in Libya.

Battle of El Alamein

Ultra intelligence were instrumental in providing vital information to Wavell and Auchinleck which helped them to prevent Rommel's forces from reaching Cairo in the autumn of 1941. Moreover, Ultra intelligence deciphered Enigma messages transmitted by Hagelin, the Luftwaffe and the German navy which gave the Allies an enormous tactical advantage. As a result they were able to sink about half of the ships supplying the Axis in North Africa.

In an effort to disguise the source of Intelligence for these attacks, the Allies often sent "spotter" submarines and aircraft to search for Axis ships. The Allies intentionally maintained a visible presence and were observed by Axis forces who naturally assumed that their position was discovered by conventional Allied reconnaissance. The Germans believed that the Allied positions in the Mediterranean were reinforced by about 400 submarines and a huge fleet of reconnaissance aircraft on Malta. In reality, however, the Allies had only 25 submarines in the area, and as few as three aircraft. The ruse worked.

But the elaborate strategy also provided Allied Command with a high degree of security among their own personnel. As long as the crew was unaware of the intelligence source leading to the Axis ships, Allied missions would not be endangered in the event that the crew were to ever be captured and interrogated.
Quite often two or three additional search missions would be sent out to cover varying areas in addition to the one spotting the Axis ships.

Ultra also contributed to the success of Montgomery's offensive in the Second Battle of El Alamein, by having provided him with a detailed list of Axis positions and strength. In addition Ultra reported among other details, Rommel's own reports to Germany during the course of battle.

Invasion of Sicily

The Allied forces depended on Ultra for information on positions and strength of German troops, whose input was of immense importance to the Allied mission. Ultra even planned elaborate strategic deceptions that fooled Hitler and the German High Command.

Allied Advance to Germany

As the Allies were advancing towards Germany, Ultra frequently provided detailed tactical information, and insight to Hitler's failing judgement, that is, he often ignored the advice of his own generals and commanded German troops to fight 'to the last man'.

Operation Sea Lion

Ultra intelligence provided vital information about the Germany's plans to invade England in 1940. Had it been carried out, Britain would have been well prepared.

Battle of Normandy (Falaise Pocket)

Ultra warned Allied troops of a major German counterattack at Mortain, and provided the Allies the advantage of surrounding the forces at Falaise.

German Rockets

Ultra contributed to the monitoring of German developments at Peenemünde and the collection of V-1 and V-2 Intelligence from 1942 onwards. The major intelligence reports came from the Polish Underground members who managed to salvage one of the V-1 rockets after it had crashed into the Bug River in Poland. Detailed information and diagrams were provided to Allied Command in Britain.

World War II Mind of a Code Breaker 1/12 (00:10:01m)

World War II Mind of a Code Breaker 7/12 (00:10:01m)


World War II Mind of a Code Breaker 8/12 (00:10:01m)

World War II Mind of a Code Breaker 9/12 (00:10:00m)


World War II Mind of a Code Breaker 10/12 (00:10:00m)


World War II Mind of a Code Breaker 11/12 (00:10:01m)

World War II Mind of a Code Breaker 12/12 (00:03:34m)

Editors Note: Much gratitude is owed to the code-breakers of Bletchley Park for continuing the work that the Poles started.  It is disappointing that this last video in particular made no mention whatsoever of the Polish contribution to breaking the code. This honour has been misattributed to Bletchley Park.

In the words of Gordon Welchman, a former Bletchley Park cryptologist,

"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... Enigma machine, and of the operating procedures that were in use."

L-R: Henryk Zygalski, Jerzy Rozycki, Marian Rejewski

This concludes the special series on The Enigma Machine. I do hope that you enjoyed reading this series and I thank you for visiting Polish Greatness (Blog). For further reading and research please click on the following link:

Flag of Polish Home Army (Armia Krajowa)

The Enigma Machine A Compendium of Resources for the Enigma Enthusiast

Most of the information gathered for this special series on The Enigma Machine has been collected from  Wikipedia articles under various titles, as well as the following sources. Rather than post lists after each blog, I have collected them in one place so that they are more readily accessible.

In addition I have also included a section of Recommended Websites that I hope might be of interest to those seeking more information on the subject of the Enigma.

And as a special treat for Enigma fans everywhere, I have provided a selection of links to online
Enigma simulators that prove to be as fascinating, amusing and educational.

A. Sources
B. Recommended Websites
C. Articles written by Marian Rejewski (pdf files, in Polish only)
D. For Enigma Machine Enthusiasts

A. Sources

Biography of Marian Adam Rejewski  by J.J. O'Connor and E.F. Robertson

B. Articles written by Marian Rejewski

Marian Rejewski: 'How Polish Mathematicians Deciphered the Enigma'.
From  Annals of the History of Computing. Arlington, Vol. 3, No. 3, July

M Rejewski, Mathematical solution of the Enigma cipher, Cryptologia 6 (1) (1982), 1-18. 

Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to Wladyslaw Kozaczuk, Enigma, 1984, pp. 241–45. 

Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to Władysław Kozaczuk, Enigma, 1984, p. 290.

ENIGMA: 1930-1940, Metoda i historia rozwiazania niemieckiego szyfru maszynowego (w zarysie); Rejewski's report of 1940

Rejewski o japo?skiej "Purpurowej Maszynie"; Rejewski on Purple Machine

Rejewski o j?zyku kryptologicznym; Rejewski on codebreaking language

Uwagi Rejewskiego do Aneksu 1 w historii wywiadu brytyjskiego w II wojnie ?wiatowej prof. F.H. Hinsleya; Rejewski's comments to Appendix 1 to Hinsley's British Intelligence in the Second World War

Porównanie wojskowej Enigmy z innymi maszynami szyfruj?cymi II wojny ?wiatowej; Military Enigma and other rotor cipher machines of the II WW

Rejewski o niemieckich instrukcjach szyfrowania Enigm?: Rejewski's on German Enigma manuals.

Many of these articles can be downloaded from the website
(however, the articles are available only in Polish.)

C. Recommended Websites

Polish Contributions Before and During the Second World War (Bletchley Park National Codes Centre)

Enigma's Secrets Finally Revealed (BBC News, April 20, 2001)

How Poles Cracked Nazi Enigma Secret by Laurence Peter (BBC News July 20, 2009) 

The Enigma Code Breach by Jan Bury 

Enigma and Other Cipher Machines (Closeup photos of approximately 280 machines and components.) 

The Commercial Enigma: Beginnings of Machine Cryptography (Pdf file) by Louis Kruh and Cipher Deavours 

How the Enigma Works by Alan Stripp (NOVA Online PBS Network) 

Marian Rejewski and the First Break into Enigma (American Mathematical Society)

Virtual Tour of Bletchley Musuem by original curator Tony Sale.

The Origins of the Enigma by Dr.Wladyslaw Kozaczuk 

March 9, 2011

The Enigma Machine Part 3 The Science of Secrets How the Poles Cracked the Enigma Code


Enigma Codebreakers (00:03:39m)

The Enigma was a complex electro-mechanical device used by the German Army and Navy during World War II to encrypt messages. Their encryptions were so elaborate that German Command was convinced that nobody could ever break their ciphers. They were wrong.

German soldiers encrypting/decrypting message on Enigma

A team of Polish mathematicians and cryptanalysts Marian Rejewski, Jerzy Rozycki, and Henryk Zygalski were the first to uncover the secrets of the Enigma. They laboriously studied the Enigma and developed solutions, techniques, and specialized instruments to crack the codes. Meanwhile French and British Intelligence remained clueless never suspecting that the Poles had already cracked the Enigma code. In fact the Poles had been deciphering and reading secret German messages for years, right up to the eve of the Invasion of Poland.

The French and British were astonished when the Poles presented them with fully functional replicas of the Enigma machine.

Enigma Machine
Marian Rejewski was a genious. He applied pure mathematical analysis of group theory as the means to discovering the internal wiring configuration of the rotors. His work was well under way when secret documents were given to him by Captain Gustave Bertrand, chief of French radio intelligence. The documents were procured from a spy in the German Cryptographic Service, Hans-Thilo Schmidt, and included information about the Enigma settings for the months of September and October 1932. French Intelligence presented the documents to Rejewski in December 1932 thus enabling him to reduce the number of unknowns and reconstruct the wiring system and nonrotating reflector.

In the words of historian, David Kahn, "The solution was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time". The mathematical theorem that Rejewski used was hailed by one mathematics professor as "the theorem that won World War II."

Rejewski studied the ciphertexts, intrigued by its permutations, particularly the first six letters of each message. He discovered that Enigma operators were using a six-letter indicator to ensure security, that is, the message key setting consisted of three letters which was typed twice. This was the ground setting shared by all German operators for global settings for that day and through which the Germans unwittingly introduced a weakness in their cipher. Rejewski detected that the indicator, in plaintext followed specific patterns: for example, the first and fourth letters were the same, the second and fifth were the same, and the third and sixth were the same. Other patterns might be the second and fifth letters, the third and sixth letters, This new insight gave the Poles the means to break the Enigma codes.

Rejewski knew that certain pairs of letters were related. For example, assume that there were four messages with the following indicators: BJGTDN, LIFBAB, ETULZR, TFREI. B was related to T: L was related to B; E was related to L; T was related to E; and I was related to E; This was defined as a "cycle of 4" as it required four jumps until it returned to the starting letter. With enough messages on any given day, all the letters of the alphabet would be covered by; different cycles of various sizes, changing to different cycles the next day.

It became apparent to Rejewski that despite the unpredictability of the Enigma machine itself, the Enigma operators had a tendency to choose predictable letter combinations as indicators, say, for example, a girlfriends initials. Rejewski's insight, in addition to the data received, made it possible for him to deduce the six permutations which corresponded to the encryption at six consecutive positions of the Enigma machine. These permutations were then described by six equations which represented the internal wiring of the entry drum, rotors, reflector and plugboard. Because of the large number of unknowns in the set of his equations Rejewski began to encounter difficulties. (In 1980, he commented that without further data it could not be determined whether the six equations were soluble.)

Rejewski solved another obstacle that had been puzzling British cryptologists. In the commercial model of the Enigma, the keys were connected to the entry drum following the sequence of letters according to the German keyboard, that is QWERTZU. However, the military version of the Enigma had been modiified so that this was no longer the case. Instead. the letters followed in alphabetical order, ABCDE and so on. Rejewski understood the German penchant for orderliness, was thus able to resolve the problem. He later commented that "from my pencil, as by magic, began to issue numbers designating the connections in rotor N. Thus the connections in one rotor, the right-hand rotor, were finally known."

German Enigma Keyboard and Lamp Panel
The secret documents obtained from French Intelligence provided information regarding rotor settings for a two month period. In the second month, German operators had inserted a different rotor in the right-hand position. This made it possible for Rejewski to discover the wiring of the two rotors using the same method of calculation.

Rejewski later recalled: "Finding the [wiring] in the third [rotor], and especially... in the [reflector], now presented no great difficulties. Likewise there were no difficulties with determining the correct torsion of the [rotors'] side walls with respect to each other, or the moments when the left and middle drums turned."

By the end of 1932, Rejewski uncovered the secret of the wiring for all three rotors and reflector. The final details were resolved using sample messages from an Enigma manual, which provided both plaintext and corresponding ciphertext along with daily key and message key.

In 1980, Rejewski affirmed that there was indeed another method that could have been used to resolve the matter, but that the technique was "imperfect and tedious" and dependent on a certain degree of chance. He acknowledged that the intelligence material in his possession led him to resolve the mystery of the Enigma machine. The British could not accomplish this until the Poles showed them how to do it.

The following is a summary of inventions created by the remarkable Polish code-breakers. Though some British sources acknowledge and give credit to the Poles for having broken the Enigma Code, they have not done enough to reveal the true extent of the Polish contribution. Far too often British documentaries and periodicals mention the Polish contribution only very briefly and casually, if at all.

What the Poles did for Britain, and for the Allied war effort
merits our deepest respect.





The Grill Method was used by the Polish mathematicians, before the advent of the Cyclometer, in decrypting Enigma messages. It had been described by Marian Rejewski as being "manual and tedious" and, like the later Cryptologic Bomb, as being "based... on the fact that the plug connections [in the Enigma's commutator, or "plugboard"] did not change all the letters." Unlike the bomb, however, "the grill method required unchanged pairs of letters [rather than] only unchanged letters."

However in December 1938 the Grill Method proved quite successful in working out the internal wiring of two Enigma rotors that had just been introduced by the Germans. ( Even though the Germans had introduced the new drums, version IV and V, they continued to use the old system for encrypting the individual message keys.)


The Cyclometer was designed,by Rejewski "probably in 1934 or 1935," to facilitate decryption of German Enigma ciphertext. It was used to prepare a catalog listing the length and number of cycles in the "characteristics" for all 17,576 positions of the rotors for a given sequence of rotors.

Since there were six such possible sequences,the resulting "catalog of characteristics," or "card catalog," comprised a total of (6) (17,576) = 105,456 entries.

Diagram of Rejewski's Cyclometer

In Rejewski's articles he noted that the utility of the card catalog was independent of the number of plug connections being used on the Enigma machines (and of the reconstruction of message keys).

Preparation of the catalog "was laborious and took over a year, but when it was ready... daily keys [could be obtained] within about fifteen minutes."

But on November 1, 1937 the Germans changed the "reversing drum," or "reflector" which meant that the Cipher Bureau had to start all over again and produce a new card catalogue but the second time around was somewhat easier, taking less than a year to complete.

On September 15, 1938, the Germans implemented a drastic change to the entire procedure for enciphering message keys. As a result, the card-catalog method became completely useless. It did however spur the inventions of Rejewski's Cryptologic Bomb and Zygalski's Perforated Sheets.


Each Enigma machine was reset by its operator every day using a different trigram key, for example, FED, which determined the way the machine was to be set up before use: the rotor order, which rotors to install, which ring setting for each rotor, the initial setting for each rotor and the settings on the stecker plugboard. The operator would then select a trigram for each message, say, "BGK" which would be typed twice and encrypted using the daily key. Then the message would be typed using the same key.

British Intelligence considered it virtually impossible to decrypt Enigma messages because its configuration changed each time a key was pressed -  the letters "BGKBGK" could be encrypted in endless number of ways, such as "NITUPV", or perhaps "XBLEWZ", and so on.

Though the Germans considered their encryption procedure invincible, it was prone to errors. When Marian Rejewski discovered that the first letters of a message were actually the same as the second three, he was able to determine the internal wirings of the Enigma machine and thus reconstruct the device. It was easy to determine the general traits of the machine from examining the commercial model of the Enigma however the military versions were markedly different and presented an entirely new set of problems to resolve. It was becoming an increasingly difficult task decrypt Enigma messages due to the increasing frequency with which changes were made to the complexity of the machine, its keying procedures and more particularly the existence of thousands of keys to choose from.

In order to mechanize and speed up the process of decryption, Rejewski invented the "Bomba Kryptologiczna" (Cryptologic Bomb), in October 1938. Each Bomb constituted an electrically-powered aggregate of six Enigmas and took the place of some one hundred workers. Six of the units had been built in Warsaw for the Cipher Bureau before the outbreak of World War II.

Bomba Device decrypted Enigma messages: Invented by Marian Rejewski

The Bomb Method was based on the fact that the plug connections did not change all the letters. (much like the Poles' earlier "grill" method). While the Grill Method required unchanged pairs of letters, the Bomb Method required only unchanged letters therefore it could be applied even though the number of plug connections in this period was between five and eight. By mid-November 1938 the Bombs were ready, and the reconstruction of daily keys now took only about two hours.

However, on January 1st, 1939, the Germans increased the number of plug connections from seven to ten, thereby drastically reducing the effectiveness of Rejewskis Bombs. Just weeks earlier, the Germans had increased the number of rotors from three to five. This resulted in a tenfold increase in the Bomb's workload. It may have been possible to build an additional 54 Bombs thereby increasing their output to 60 from the initial, however, the prospect would have overwhelmed the budgetary confines of the Polish Cipher Bureau.

Diagram of a few possible Enigma connections using three rotors and reflector

For the duration of the War, the British Bombe became the main tool that would be used to break Enigma messages.  It was named after and indeed inspired by the Polish Bombe, invented by Marian Rejewskiwould be named after, and likely inspired by, the Polish bomb, though according to Gordon Welchman the cryptanalytic methods embodied by the two machines were different.

Up until July 25, 1939, the Poles had been successfully breaking Enigma messages for over six and a half years without telling their French and British allies. But on December 15, 1938, the Germans added two new rotors, IV and V which greatly increased the complexity of their encryptions. Many years after the end of WWII Rejewski wrote about it: (Remarks on Appendix 1, volume 1 (1979) British Intelligence in the Second World War" by F.H. Hinsley, page 80)

"we quickly found the [wirings] within the [new rotors], but [their] introduction [...] raised the number of possible sequences of drums from 6 to 60 [...] and hence also raised tenfold the work of finding the keys. 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 (60 series of 26 sheets each were now needed, whereas up to the meeting on July 25, 1939, we had only two such series ready) and to manipulate the sheets."

Hinsley, of British Intelligence, had speculated "that the Poles decided to share their Enigma-breaking techniques and equipment with the French and British in July 1939 because they had encountered insuperable technical difficulties". This was a preposterous notion on his part and  to which Rejewski responded:

"No, it was not [cryptologic] difficulties [...] that prompted us to work with the British and French, but only the deteriorating political situation. 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."

Barely a month after having given Polish Enigmas to the French and British, Germany invaded Poland on September 1, 1939.

World War II Mind of a Code Breaker 3/12 (00:10:01m)


Editors Note:  Reference was made in this video about "Jeffrey's Sheets" (4:47) however the narrator makes no mention that years earlier, Polish mathematician, Henryk Zygalski had already invented these perforated sheets which had been used to decrypt Enigma messages long before the "so-called"  Jeffrey Sheets.


This method was invented by Henryk Zygalski in October 1938 and used to decrypt messages enciphered on the Enigma. The device was comprised of 26 perforated sheets for each of the six possible sequences for inserting the three rotors into the Enigma machine's scrambler. (Later the sequence increased due to the implementation of additional rotors.)

Each sheet related to the starting position of the left (slowest-moving) rotor. The 26 × 26 matrix represented the 676 possible starting positions of the middle and left rotors and was duplicated horizontally and vertically: a–z, a–y. The sheets were punched with holes in the positions that would allow a "female" to occur.


Rejewski wrote about how these perforated-sheets were utilized:
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.
Like Rejewski's "card-catalog" method, developed using his "Cyclometer," the Zygalski-Sheet procedure was independent of the number of plugboard plug connections in the Enigma Machine.


The "Clock" was a method devised by Polish mathematician-cryptologist Jerzy Rozycki at the Polish General Staff's Cipher Bureau, to facilitate decrypting German Enigma ciphers. His method made it possible to determine which of the Enigma machine's rotors was at the far right - in other words, to identify which rotor always revolved at every depression of a key.

Polish Mathematicians-Cryptologists
L-R: Henryk Zygalski, Jerzy Rozycki, Marian Rejewski
(Cadix, between September 1940 and July 1941)

After the invasion of Poland in September 1939, the work of Enigma decryption became the exclusive domain of British and American Intelligence.  Rejewski and Zygalski were now excluded from the inner sanctum of Bletchley Park. According to British code-breaker Alan Stripp, very few people were aware of the Polish contribution because British Intelligence operations were held to a strict secrecy and "need to know" basis.

Stripp commented that "setting them to work on the Doppelkassetten system was like using the racehorses to pull wagons".

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.
Welchman, Gordon (1984) [1982], The Hut Six story: Breaking the Enigma codes, Harmondsworth, England: Penguin Books, ISBN 0 14 00.5305 0  page 71

Marian Rejewski, Jerzy Rozycki and Henryk Zygalski have been celebrated throughout the world.  Rejewski had been decorated with numerous Polish medals before and after World War II. In 2000, they were posthumously awarded the Grand Cross of the Order of the Rebirth of Poland.

And on July 4, 2005,  the 1939-1945 War Medal was awarded posthumously by the British Chief of Defense Staff,, and received by Rejewski's daughter.

In 2002, a plaque was unveiled at Bletchley Park. The English side reads as follows:

This plaque commemorates the work of Marian Rejewski, 
Jerzy Różycki and Henryk Żygalski, mathematicians of the
Polish intelligence service, in first breaking the Enigma code. Their work greatly assisted the Bletchley Park code breakers
and contributed to the 
Allied victory in World War II

Bletchley Park - Plaque honoring the Polish Code-Breakers

After half a century of silence, the British have finally
honoured the Polish Code Breakers
for their contributions to the Allied war effort.

Flag of Polish Home Army (Armia Krajowa)


N.B. Sources and References will be provided at the completion of this special series.

March 8, 2011

The Enigma Machine Part 2 The Science of Secrets

World War II Mind of a Code Breaker 2/12 (00:10:01m)

Cryptology is the science of secrets. Throughout history there has been an endless array of techniques devised and used by the military, government, and business to encrypt important information. It's as old as ancient history. We have come a long way since Herodotus in the fifth century B.C. when he tattooed a secret message on the shaven head of a slave, under regrown hair. Or Julius Caesar who was reported to have used cryptography in his communications during the course of his battles, and often relied on what we consider to be its most simplest form -  substitution cyphers; the systematic substitution of letters of the alphabet or groups of letters, with other letters or groups of letters. Even the Kama Sutra recommended cryptography to lovers, which allowed them to communicate with each other without the danger of having their relationship discovered. It wasn't until the ninth century and the discovery of frequency analysis by an Arab mathematician, Al-Kindi, that such classical cyphers could easily be broken.

The creation of the polyalphabetic cipher lay the groundwork for the eventual development of the famous Enigma Machine. The polyalphabetic system was first described by Giovan Battista Bellaso in his 1553 book about ciphers, however, through misattribution, it was called the Vigenere cipher, after the  French diplomat and cryptographer, Blaise de Vigenere. The "Vigenere" cipher was the first one of its kind to employ multiple substitution alphabets, albeit in a simplistic form. The Enigma, though also based on the same principle, is far more complex.

A Dutchman by the name of Hugo Koch invented a rotor machine for the purposes of encryption, though it was meant for commercial purposes only. It was patented on October 7, 1919 (Netherlands patent# 10700).   Another inventor by the name of Arthur Scherbius, a German electrical engineer also applied for a patent on February 23, 1919 for his cipher machine based on rotating wired wheels. In the same year his company, Scherbius & Ritter purchased the rights of the patent for the rotor machine invented by Hugo Koch, thereafter naming it the Enigma. Scherbius tried to market it to the Imperial German Navy but initial reactions were lukewarm. In 1923 the patent rights were bought by a firm Chiffriermaschinen AG, who commercialized the Enigma. The first Enigma - Model A came on the market that year.

The early models of the Enigma were very heavy and bulky and attracted little, if any, interest from the German military.By 1926 however the Enigma design had improved considerably, and being lighter and more compact found favour with military and diplomatic services across Europe. The German Navy purchased the Enigma and adapted it for its own use. It became the standard cipher machine of the German military forces and was used at all levels throughout the chain of command, from top echelons to front-line tactical units as well as airplanes, tanks and ships.

By the end of the war over 100,000 Enigmas had been produced.

Enigma Machine

Like those of other rotor machines that preceded its inception, the Enigma also featured a complex mechanical and electrical system. It included elements of a keyboard, a set of rotors (rotating disks attached along a spindle, and components that turned one or more of the rotors one full stop which each press of the keys. While one rotor may turn with every key press, another rotor may turn with less frequency which resulted in a far more complex encryption process.

Rotor Assembly of the Wehrmacht Enigma

The Enigma was designed so that whenever a key is pressed, the electrical current flows through the wiring and illuminates one of the display lamps to indicate the output letter. For example, let's say you were to encrypt a message beginning with the letters "FED" - pressing "F" would light up a lamp indicating the substitution perhaps "M", then pressing "E" followed by "D" which would result in substitution letters for each. Considering that there are 26 lamps and 26 keys, several plugs and rotors, the combinations were virtually infinite.

A typical three-rotor Enigma with reflector and six plug connections could generate the following number of theoretical coding combinations.

006,433,616,627,409,666,933,182,371,154,802,769,920,000, 000,000

That is roughly the same as 3.283 x 10114

Enigma in use (1943)
Whenever a key is pressed an electrical current flows from the battery (1) through a depressed bi-directional letter-switch (2) to the plugboard (3). The plugboard gives the operator the flexibility to rewire some letter connections between the keyboard (2) and the fixed entry wheel (4).  Subsequently, the current travels through the plug (3) (unused in this example, so shown closed) via the entry wheel (4) through the wiring of the three installed rotors (5) (as in the Wehrmacht Enigma, or in the case of Kriegsmarine M4 and Abwehr variants there were four rotors) and enters the reflector (6). The reflector returns the current through a completely different route, through the rotors (5) and entry wheel (4), proceeding through plug 'S' connected with a cable (8) to plug 'D', and another bi-directional switch (9) to light the appropriate lamp.

Enigma Illustration of Current Flow

A very high level of security was attained by repeated changes in the electrical paths through the Enigma's scrambler, implemented by a polyalphabetic substitution encryption. The diagram below illustrates the changes to the electrical pathway caused by each key depression, which in turn causes rotation of at least the right hand rotor. The electrical current passes into the set of rotors, into and back out of the reflector, and out through the rotors again. Note that the faded lines of the illustration indicate just a few of the other possible paths within each rotor. These are hard-wired from one side of each rotor to the other.

Diagram of scrambling action of the Engima Rotors

For example, when the letter A is pressed, it will encrypt differently with each consecutive key press, first to G, and then to C, etc. The reason is that the right hand rotor has stopped moving and has sent the signal on a completely different route.

Subsequently the other rotors will also respond to each key press resulting in varied routes of the electrical currents.

The rotors are the core of an Enigma machine. Each rotor is a disc measuring approximately 10cm (3.9 in) in diameter and made from hard rubber or bakelite. It features brass spring-loaded pins on one side arranged in a circle while the other side has a corresponding number of circular electrical contacts.
Rotor contact detail  (E-bay photo)

The pins and contacts represent the 26 letters of the alphabet, that is letters A–Z. When the rotors are mounted side-by-side on the spindle, the pins of one rotor rest against the contacts of the adjacent rotor thus establishing an electrical connection. Inside the mechanism of the rotor the 26 wires connects each pin on one side to a contact on the other side in a complex pattern.

The rotor itself can only perform a simple substitution cipher.For example the pin corresponding to the letter E might be wired to the contact for letter T on the opposite face, and so on. However, when the Enigma machine uses several concurrent rotors (usually three or four) and implementing its regular stepping movements, it thus creates a highly secure poly-alphabetic substitution cipher.

Each rotor can be set to one of 26 possible positions. Once inserted it can be adjusted manually, merely by turning the grooved finger-wheel (which protrudes when the lid is closed over the Enigma machine.) The operator was able to know the position of each rotor by the letter of the alphabet visible through a small window. (In earlier Enigma models the alphabet ring was fixed to the rotor disk however subsequent models made it possible to adjust the alphabet ring relative to the rotor disk)

The setting of the rotor was the preliminary process in every operating session, and whose settings were referred to as the "key".


Stepping Motion of Enigma Machine
The movement of the rotors is controlled by a mechanism of the ratchet and pawl. Every time an operator pressed a key, each of the pawls, corresponding to a particular rotor, would move forward one step in unison in the attempt to engage with a ratchet.  However, the movement was varied due to the insertion of a thin metal ring to each rotor (upon which the pawl rode).  As this metal ring rotated with its adjacent rotor, its notch would would eventually align itself with the pawl permitting it to drop into position, engage with the ratchet thus advancing the rotor.

While the first rotor always stepped or advanced with every key press, the movement of the adjacent rotors were variable dependent on the position of the notches - which could be adjusted by changing the letter ring. (Some of the rotors used by the Kriegsmarine had two notches instead of one.)

Consequently, Rotor 1 would step 26 times for every step of Rotor 2, and Rotor 2 would step 26 times for every step of Rotor 3. As simple as that sounds, there is much more to the Enigma machine.

In a feature known as double stepping, the rotors deviate from odometer-style regular motion. This is due to each pawl being aligned with both the ratchet of its rotor and the rotating notched ring of the neighbouring rotor.

When a pawl finally engaged with a ratchet by aligning itself with a notch, it moved forward and pushed both the ratchet and the notch, thus advancing both rotors at the same time. But in the case of a three-rotor machine, the double-stepping would affect only Rotor 2.

Rotor 2, if in moving forward allowed the ratchet of Rotor 3 to be engaged, would move again on the subsequent keystroke, thus resulting in two consecutive steps. Rotor 2 also pushes Rotor 1 forward - after 26 of its steps, but as rotor one moves forward with every keystroke anyway, there is no double-stepping.

With three wheels and only single notches in the first and second wheels, the machine had a period of 26 × 25 × 26 = 16,900 (not 26 × 26 × 26 because of the double stepping of the second rotor).

Historically, messages were typically limited to a few hundred letters thus eliminating any chances of repeating the exact combination of rotor positions from a specific encrypting session. Hence cryptanalysts were denied a valuable clue to the substitution used.

In 1942 a fourth rotor was added, which made it necessary for the reflectors to be much thinner. No other changes were made to the machine. With only three pawls, the fourth rotor never stepped, but could be manually set into one of its 26 possible positions.

Before the end of the war a device was designed but never implemented: the Lückenfüllerwalze(gap-fill wheel) which created irregular stepping. It featured notches in all 26 positions. If the number of notches was a relative prime of 26 and the number of notches were different for each wheel, the stepping would be more unpredictable. In addition it permitted Its internal wiring to be reconfigured, like that of Umkehrwalze-D.


The current entry wheel or entry stator, connects the plugboard to the rotor assembly.(However in models without a plugboard, the entry stator would connect directly to the keyboard and lampboard.)
Its configuration proved to be an obstacle to Allied cryptologists during WWII. While British Intelligence remained baffled as to the alphabetic configuration, the problem was easily resolved by Marian Rejewski in a flash of inspiration.

In the commercial model of the Enigma, the keys were connected in the same sequence as the German keyboard, that Q to A, W to B, E to C and so forth whereas, in the military version connected the letters followed in logical sequence, that is: A to A, B to B, C to C, etc. (Typical of German ordnung!)


The reflector connected outputs of the last rotor in pairs, and redirected the current back to the rotors through by a different route. In doing so, the reflector ensured that the process would be self-reciprocal: that is, decryption would be the same as encryption. The only flaw in the system was that no letter was ever encrypted to itself, a factor which was exploited by the Allied code-breakers.

A distinctive feature of the early models of Enigma placed the last rotor before a reflector. However, In the commercial Enigma (Model C) the reflector could be inserted in all 26 positions, (though stationary) or, as in case of the Abwehr Enigma, the reflector stepped during encryption in the same way as did the other wheels.

In the Enigma models used by the  German Army and Air Force, reflector was fixed and did not rotate. There were four versions:  The original version "A" was replaced by Umkehrwalze "B" (translated "reverse roll") November 1, 1937. Umkehrwalze C was used only briefly in 1940 until it was solved by
Hut 6 (of Bletchley Park).  Umkehrwalze D was first encountered on January 2, 1944, and had a rewireable reflector which allowed the Enigma operator to change the connections as part of the key settings.


Each cable inserted into plugboard connected letters up in pairs; thatis, E and Q might be a steckered pair. The effect was to switch those letters before and after the main rotor scrambling unit. For example, when an operator presses "E", the signal is diverted to the letter "Q" before entering the rotors. Up to thirteen pairs of steckered pairs might be used at one session, though normally it did not exceed 10 pairs at any one time.

Enigma Plugboard

Electrical current flowed from the keyboard through the plugboard, and proceeded to the entry-rotor. Each letter on the plugboard had two jacks: the insertion of a plug disconnected the upper jack (from the keyboard) and the lower jack (to the entry-rotor) of that letter. The plug at the other end of the crosswired cable was inserted into another letter's jacks, thereby switching the connections of the two letters!

The plugboard permitted the operator to easily change the wiring making a stronger encryption - even stronger than could have been achieved by adding an extra rotor.

Without a plugboard (unsteckered). Enigma encryptions could easily be resolved manually. However, the addition of a plugboard meant that Allied cryptanalysts had to use special machines to solve it.

The steckered plugboard raised the number of possible enciphers by a factor of 2 to 3 billion, to a staggering 10 quadrillion. To better illustrate the virtual infinite number of possiblities try to imagine If 1000 operators with captured machines were to tested four keys a minute 24 hours a day, it would take them 900 million years to try them all. It is no wonder then that the Germans were convinced that their codes were quite unbreakable.

Schreibmax, printer accessory for the Enigma Machine

The Schreibmax was a feature used on some M4 Enigmas. It was a small printer which could print the 26 letters on a narrow strip of paper ribbon. It was placed on top of the Enigma machine and was connected the lamp panel, however, its installation required that the lamp cover and light bulbs all be removed.  The printer eliminated the necessity of having a second operator present to write down each letter.  Moreover, it provided operational security as the printer could be installed remotely so that the signal officer no longer had to see the decrypted plaintext information.

The remote lamp panel was another accessory, which made it possible for a person to read the decrypted plaintext without the operator seeing it. 

Uhr attachment for Enigma 
In 1944 the Luftwaffe introduced a variation of the plugboard switch called the Uhr ( or clock) which replaced the standard plugs. It consisted of a little box containing a switch with 40 positions.  After connecting the plugs, according to the daily "key" sheet, the operator turned the switch into one of the 40 positions. Each position produced a different combination of plug wiring which unlike the default plugs, were not pair-wise. In one switch position,  the Uhr did not switch any letters, but simply emulated the 13 stecker wires with plugs.


The encryption of messages on the Enigma were based on a vast network of settings, called keys. Each session was assigned a specific key for its Enigma and changed constantly. For messages to be correctly and quickly decrypted, both sender and receiver had to adjust their Enigma machines using identical settings in rotor selection and order, starting position, and plugboard connections. German Command distributed the codebooks which provided the daily keys to be used.

The "key" determines the setting of the following elements of the Enigma machine:

Wheel order: the choice of rotors and the order in which they are fitted.
Initial position of the rotors: chosen by the operator, and changed for each message.
Ring settings: the position of the alphabet ring relative to the rotor wiring.
Plug settings: the connections of the plugs in the plugboard.
In very late versions, the wiring of the reconfigurable reflector.

NB: Although the ring settings were a required part of the setup process, they did not affect the message encryption because the rotors were positioned independently of the rings. The ring settings were useful only to the extent of determining the initial rotor position. Once the receiver had set his rotors to the indicated positions, the ring settings no longer played any role in the encryption.

Enigma was secure so long as the wiring was secret: if the wiring was secret, the total number of possible configurations could have been calculated to be around 10114 (approximately 380 bits). With the discovery of the wiring, and other operational obstacles, this is reduced to around 10²³ (76 bits).

Navy Codebook for German Enigma

Procedures used by the Kriegsmarine were more elaborate than those used by other services of the German military. Navy codebooks were printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were at risk of being seized by the enemy.This codebook was taken from the captured U-505.


Typically a key was kept constant for a pre-determined period of time, usually a day.However, in a process similar to initialisation vector in modern cryptography, a different initial rotor position was used for each message.

The reason is that, messages encrypted using identical settings could easily be attacked using a statistical formula such as Friedman's Index of coincidence. To prevent that possibility, an enciphered message would be transmitted indicating the starting position for the rotors, just prior to transmitting the ciphertext. The exact method used was termed the indicator procedure. Ultimately, the Enigma messages were broken due to the design weakness of the Enigma as well as operator sloppiness in applying these indicator procedures.


The operator would set up his machine according to his settings list, which included a global initial position for the rotors. In this example, AOH is the key. The operator turns the rotors until AOH is visible through the rotor windows then chooses his own arbitrary starting position for a message. He  may select, EIN, which is typed into the machine twice. The resulting encryption might show up as XHTLOA, which is transmitted before the actual message. The operator would turn the rotors to the same message settings, EIN and typed the plaintext of the message.

The operation was reversed at the receiving end where the operator would set his machine to the initial settings and type the first six letters of the message XHTLOA. The lamps on his Enigma would indicate the letters EINEIN, thereby indicating how the rotors are to be set. At this point the operator can decipher the message by typing in the ciphertext.

Polish cryptologists were able to break Enigma messages using such indicator procedures.

Despite its ingenious design, the procedure was seriously flawed and rendered weak due to two factors: the use of a global ground setting, and the repetition of the indicator. The global ground setting was later changed to allow the operator to select his initial position to encrypt the indicator.  However the repetition made it possible to discover the relationship of letters, that is the first and fourth, second and fifth and third and sixth characters. Hence the Polish Cipher Bureau was able to break into the pre-war Enigma as early as 1932.  However, from 1940 onward, the Germans changed procedures to improve security.

Codebooks were used daily to set up the rotors,ring settings and the plugboard. For each message, the operator selected a random start position, let's say WZA, and a random message key, perhaps SXT, as follows:

1. He set the rotors to the WZA start position and encoded the message key SXT. (Assume the result was UHL.)

2. He then set up the message key, SXT, as the start position and encrypted the message. 

3. He transmitted the start position,WZA, the encoded message key, UHL, and then the ciphertext.

4. The receiver set up the start position according to the first trigram, WZA, and decoded the second trigram, UHL, to obtain the SXT message setting. 

5. Next, he used this SXT message setting as the start position to decrypt the message.

This new procedure, used exclusively by the Wehrmacht and Luftwaffe, was an improvement over the previous method. It avoided the security flaws of double-encoded message settings because each ground setting was different. To complicate matters, they transmitted messages into five-letter groups, while the Kriegsmarine converted messages into four-letter groups.


Since the World War II, information about the Enigma had been carefully safeguarded and it wasn't until the mid-1970s that the secrets of the Enigma became known to the public. Original Enigma machines are on display in museums around the world. Some machines under private ownership have been sold at auction garnering $20,000 (US).

The world has been fascinated by the Enigma, and its allure continues to grow. It has been dramatized in many fictional productions, the most controversial being the 2001 British film called "Enigma" (based on Robert Harris' 1995 novel of the same title). The screenplay for the film was written by Tom Stoppard, produced by Mick Jagger and Lorne Michaels, directed by Michael Apted and starred Kate Winslet and Dougray Scott. (Incidentally, Mick Jagger owns one of the Enigma machines.)

The screenplay made drastic changes to the plot, and as a result has been widely lambasted for its historical inaccuracies. It completely ignores the role of the Polish Cipher Bureau (Biuro Szyfrow) in breaking the Enigma code and worse - portrays the Polish as villains!!

Marian Rejewski wrote several articles on how it was possible to break the Enigma code through mathematical applications. The following are just a few of his publications are as follows:
Marian Rejewski: 'An Application of the Theory of Permutations in Breaking the Enigma Cipher'; in: Applicaciones Mathematicae. 16, No. 4, Warsaw 1980.  In the above-mentioned publication 
Rejewski wrote,
" It should be mentioned that the present paper is the first publication on the mathematical background on the Enigma cipher breaking. There exist, however, several reports related to this topic by the same author: one - written in 1942 - can be found in the General Wladyslaw Sikorski Historical Institute in London, and the other - written in 1967 - is deposited in the Military Historical Institute in Warsaw.

Flag of the Polish Home Army (Armia Krajowa)

The Enigma Machine Part 3 The Science of Secrets 
How the Poles Cracked the Enigma Code

N.B.  Sources and references will be provided at the end of this special series.