The “Enigma” Secret

Some time ago, Dr. Elzbieta Ulanowska published an article in our “Forum” on the enormous contribution of Polish mathematicians in the victory over the Bolsheviks in 1920. Let me only remind readers that the Polish mathematicians deciphered the code used by the Red Army, so all the moves of the Red Army’s divisions were well known to the Polish leadership.

Many of us remember another, better known event in this history, when, again, Polish mathematicians played the main role. This is the Enigma Secret. And here’s how it all started. In 1927, or at the beginning of 1928, an innocent package has arrived from the German Reich at a customs office in Warsaw. According to the customs declaration, the package was supposed to be radio equipment. A representative of a German company demanded the return of the package prior to the customs inspection. This awakened a suspicion among the Polish customs officers who instantly contacted the Cipher Bureau of the II Department of the Main Headquarters. This institution was interested in new developments in the area of radio equipment. Since it was Saturday, the officers of the Cipher Office had enough time to examine the package in detail. The package contained a machine, which was subsequently dismantled and reassembled. Yes, it was a trade version of the Enigma ciphering machine patented by Arthur Scherbius. Its military analogue did not exist at that time. What is interesting is that this machine (a trade version) was available on the market.

The first ciphered dispatches were sent into the air space by military broadcasting stations on July 28, 1928. The efforts to decode these dispatches were fruitless. Major F. Pokorny, the head of the Cipher Bureau did not give up and in 1928-29, in Poznan, he organized cryptology lectures for students who spoke fluent German and had graduated in mathematics. Among these students were Marian Rejewski, Jerzy Rozycki, and Henryk Zygalski. After the completion of this course, a division of the Cipher Bureau in Poznan was organized. Starting September 1, 1932, the division was moved to the building of the Main Military Headquarters near Saski Square in Warsaw (since destroyed).

On cylinders, sheets and…beautiful women

As Mr. M. Rejewski recalls, “the military version of the Enigma had the shape of a portable typewriter. It had 26 keys marked with the letters of the Latin alphabet. Instead of individual characters it had a small board with 26 bulbs marked the same way as the keys. It was supplied by a normal battery. Enigma’s most important parts were ciphering cylinders mounted on one axis. A non-moving inverting cylinder was also installed. Each of the cylinders was equipped with a ring with 26 alphabet letters. From a distance it looked like a switch-over mechanism in a racing bicycle. When one was pattering the letters of the text, then the letters of consecutively lit bulbs were creating the coded text, or a cipher. Not going into the details of the construction of Enigma let us remark, that one could create 26! =403291461126605635564000000 different connections .The “Enigma” Secret between ciphering cylinders, adding to this also 7905853580025 possibilities of various invertible cylinders In this way the factory producing the Enigma could deliver to each recipient a machine with unique, non-repeating connections of the cylinders.

In this way the factory producing the Enigma could deliver to each recipient a machine with unique, non-repeating connections of the cylinders.

In contrast, all military versions of the Enigma had the same connections, so that the officers working on ciphers in various military units could easily communicate. This was possible provided these officers had the same key, along with the cylinder connection, the secret of Enigma.

It is estimated that during World War II between 100,000 and 200,000 Enigma machines like this were used.

In order to explain, even in general terms, the details pertaining to the role of the connections of the cylinders, and hence to understand what is happening inside the machine, one has to apply combinatorics, especially permutations. Rejewski and his colleagues were borrowing heavily from the theory of permutations , cycles, transpositions, etc.

Let me now explain the connection to Polish women. Well, our cryptologists noticed certain combinatorial regularities. For example in the following 9-letter long message, FDW KRM KSA, it happens that the fourth and the seventh letter is the same. When the fourth and the seventh letters, or the fifth and the eighth or the sixth and the ninth letters are the same – these situations were termed women. Apparently, 11 or 12 messages out of 100 are women. And why beautiful women? How could it be otherwise? One also has to mention Zygulski’s sheets, genius though time-consuming perforated sheets which were helpful in the determination of the sequence of rotors.

World War II and the Fate of our Cryptologists

With this complex situation, one has to be astonished at the arrogance of the German engineers who were certain that the Enigma codes were unbreakable. Remember, though, that cryptology was still in its infancy and as my colleague, Dr. Tom Korner of Cambridge University writes, even in 1996, Cambridge University Library stores its cryptology acquisitions in the paleography division, between stenography and ancient Greek. It turned out, as Marian Rejewski remarks, that in order to break the Enigma codes, one did not need to know the connections of the cylinders, nor the daily keys; what was needed was a certain number of these dispatches sent the given day – about 60 of them. With such a sample, one could recover the given password. In 1934, in Warsaw, the first (Polish) replica of the Enigma was built, by the company AVA. In July 1939, after a dinner in the restaurant of the Bristol Hotel, there was a secret meeting between French, British, and Polish cryptologists. The meeting took place in Kabackie Lasy, near the village Pyry, south of Warsaw. After a pleasant conversation in German (this was the language common to all the parties involved), the guests saw the Polish copies of the German Enigma. The French and the British could not believe that the Poles had prepared such gifts. Each of the cryptologists received one copy of the Enigma code along with the complete set of the related information.

On the 16th of August 1939, French General Gustave Bertrand carried one Enigma copy from Paris to London and personally delivered it to the head of British Intelligence, Commander Stewart Menzies. Less than two weeks later the German Army invaded Poland. The Polish Cipher Bureau and its employees were evacuated to Romania, whence they were transported to France, where they worked constantly to improve the German Enigma.

After the German invasion of France, our cryptologists tried to evacuate to Great Britain. However, while crossing the Spanish border, some of them fell into German captivity. Major Ciezki and engineer Palluth were arrested. Langner, Ciezki, and Palluth lectured at Adam Mickiewicz University to Rejewski, Zygalski, and Rozycki at the end of the 1920s. The engineer Palluth died on April 19, 1944, hit by a splinter of an Allied bomb during the air raid of the labor camp. Langner and Ciezki were placed in German camps as POWs and were released by the Allies. Jerzy Rozycki, the third of Wroclaw cryptologists was killed even earlier – on January 9th 1942 when the ship that he was on drowned in the Mediterranean Sea. Only Marian Rejewski and Henryk Zygalski made it to Great Britain. There they joined Polish military units. They were working on some German codes, but the British did not assign them to constantly improved Enigma codes. In light of Russian- British agreements even their unit was dismantled. After the war Marian Rejewski returned to Poland.

Before coming to the United States, as a young assistant professor at the Wroclaw University I took part in the meeting of the Polish Mathematical Society in Lodz. The honorary guest of that meeting was Mgr Marian Rejewski. The hall, filled with mathematicians, loudly applauded the modest Mr. Rejewski. He died in 1980. Dr. Zbigniew Piotrowski Translated by Sean Martin