On the occasion of his new film Morten Tyldum, The Imitation Game (The Game of Imitation) based on the book by Andrew Hodges “Alan Turing, The Enigma” and was released in Greek cinemas on January 8, 2015, we will take a look back at a not so well known aspect of the second world war (WWII). This aspect is none other than deciphering the secret code of Nazi communications (Enigma) from the Poles initially who will be seen as "Part One" and the English in Bletchley ParkPart twoWhich, according to analysts, led to the early end of the war. Many say that the decryption of German secret communications by the British led to the end of the war, at least 2 years faster, saving the deaths of about 14 million people.
The beginning
The idea for the most impressive encryption and decryption engine was born 500 years ago. Arthur Scherbius (1878‑1929), patented a cryptographic machine that used disks similar to those of Alberti. It is no coincidence that the machine was named Enigma inspired by the Greek word, riddle.
Leon Battista Alberti
Cryptography scholar David Kahn in his book "The code breakers: The story of secret writing" published in New York in 1967, presents Leon Battista Alberti (1404 - 1472) as the "father of Western cryptography". He recognized in his face the rapid advancement of the West in cryptanalysis, the invention of multi-alphabetic substitution and the encrypted key, which largely determined the developments in cryptography. An Italian by origin and a talented architect, Alberti invented the cryptographic disk which, it seems, was to be essentially the first cryptographic machine. However, its construction, although very simple, could be used in a complex way and later in combination with technological maturity to be the heart of complex devices.
History of the Alberti album
When Leonardo Dato confided in Alberti that the Vatican had to send encrypted messages, Alberti offered to help. In 1467 he wrote an essay that laid the foundations for an entirely new way of cryptography. Alberti's essay included a clear interpretation of frequency analysis (ie, how many times a character will be encountered within the text depending on the language of the original text) and offered several ways to solve ciphers.
He also described the encryption system he used two concentric copper disks whose circumferences were divided into 24 equal parts.
To send an encrypted letter, the letters or numbers were read on the external disk and encrypted inside. The sender and recipient had identical disks and simply decided on the original position of the two disks.
Up to this point, the system was a mere single-alphabetical replacement, but what Alberti later wrote brought innovation. "After 3-4 words are written, we change the layout by rotating one disk". So the whole system changes, where in the original position the letter "k" corresponded to "f", now "k" corresponds to "t". Automatically with a simple setup, the work of the decoder became very difficult. Thus the usefulness of frequency analysis was greatly reduced. Alberti also used the numbers on the external disk as a kind of cryptographic code. That is, before encrypting the entire text, he replaced words with numbers with combinations of the numbers 1 - 4. Then these numbers were encrypted along with the text.
Code analysis
Let the text that was to be encrypted was as follows: "TELL THE POPE IMMEDIATELY ELEVEN SHIPS WILL LEAVE IN THE MORNING".
Initially it replaced some words as we said with numbers according to a predefined codebook. Let's say that 14 means "SHIPS WILL LEAVE IN THE MORNING" and 342 means "TO THE POPE".
Immediately the message from “TICK IN PAPA IMMEDIATELY EASTERN SHIPS WILL FALL ON THE MOON" done "TELL 342 IMMEDIATELY 14".
Then encrypting the entire phrase the final encrypted message would look something like this: THURSER FOX FROZBZ WEDNESDAY The recipient, with the appropriate disk settings and the codebook, could decrypt the message in a very short space of time. If the message was intercepted, it was virtually impossible to read, or if read, it might have been meaningless.
Arthur Scherbius and the Enigma machine
What happens when you complicate and reshape the idea of Leon Battista Alberti, a Renaissance genius who lived to 15ο century, with rules and techniques of 20th century?
On April 18, 1918, Serbius delivered the original military version to the German Navy but expectations of a supplier did not materialize and his company ran out of funds until 1923. In a show of perseverance, he co-founded with Richard, a close friend of his. company under the name Chiffriermaschinen AG which dealt with various constructions in addition to Enigma and proceeded to the implementation of its plans.
The Enigma A version appeared on the market in 1923. Being large and heavy compared to the original, since with a built-in typewriter it weighed about fifty kilos, it was considered expensive for the time and was replaced by the Enigma B, without any of the two attract the interest of military services. Serbius promoted it for use by accounting firms, large companies and diplomats who needed to exchange confidential information without ever stopping to eye sales in the military. In the same year, he presented it at the World Postal Congress in Bern, but there was no particular buying interest. With sales down, the next Enigma C model follows, based on an idea from Willi Korn partner. It was much lighter and smaller but its commercial fortunes remained the same.
Finally in 1926 the German army, government agencies and organizations finally procured the Enigma in a variant of its commercial version. In 1927 he launched the Enigma D version with which he managed to find buyers, in military and diplomatic services in the rest of Europe. In the two decades that followed, the Serbius machine sold more than thirty thousand units to the military, making it the most secure encryption system in the world. In total, more than one hundred thousand machines with various variants were sold, even without the Enigma logo, from other manufacturers. Of course, the reputation that preceded the sales did not include the weaknesses of the seemingly impenetrable construction, which are worth noting that was not due to its own defect. What forced the Germans to reconsider their position on the Enigma were two events in England: a text by Winston Churchill, The Global Crisis, published in 1923 describing how the British had gained access to German cryptographic material that had helped Analysts in Room 40 read the German cryptograms and the official version of World War I history published by the British Royal Navy, which highlighted the Allied advantage of spying on and intercepting German communications.
It took the Germans almost ten years to realize their failure in this area. When the BPP broke out and they had the Enigma at their disposal, their victory seemed guaranteed. With such an unprecedented security system for their communications, they felt invulnerable, but in the end all that was secured was the fall of Hitler. Unfortunately, Serbius was not going to know the successes and failures of his achievement. He was killed in 1929 in an accident with his carriage.
The Enigma settings
The Enigma, as we have seen above, was a typewriter, the size of a modern computer, consisting of a 26 keypad on the front, at the top of 26 lamps that depicted letters and turned on when the user typed and depicted the replacement letter the user was typing. In the prototype version of the engine there were three revolving discs or reversers. Each reorder has a series of internal wiring with electrical contacts on its surface so that each different position of the reorder has different electrical contacts between the keys and the lamps.
As soon as one letter was struck, the right rearranger rotated by 1/6 of a full spin for a full 26-letter Latin alphabet. After 26 rotations, the middle rearranger would rotate accordingly and after 26 of its own rotations the left would rotate left. The complexity of encryption increased more than a table of plugs on the front of the machine, where special pairs of matched letters alternated with the insertion of the plugs.
It is estimated that there were about 1015 powerful ways of adjusting the camera. And the number of combinations produced is about 3 x 10114 combinations (3 followed by 114 zeros that is). These were the chances that the Poles and later the English had to eliminate in order to decipher the messages produced.
The role of the Poles in the decryption of Enigma.
Poland is a country that is geographically wedged between Germany and the then Soviet Union. After the GPA and in the mid-1920s, German leaders began to talk aggressively about annexing territories granted to Poles by post-war treaties. So it didn't take long for the Poles to understand that they had to gain access and knowledge of the Germans' communications. In 1928 they received mysterious coded messages that defied conventional decryption methods of the time. It is the first contact of Poles with Enigma.
1932 in Warsaw, three young Polish cryptographers and mathematicians, Marian Rezevski, Giersi Rozziski and Henrik Zigalsky, played a key role in breaking the codes used by the German Enigma machine. The machine was operated by letter retooling, the positions of which, as well as any changes, were described in a user manual. The user manual did not say anything about the rotor settings.
(Note that the fourth rotor was added much later by the Navy Navy, the machine we are talking about now consists of 3 rotors).
E.g. on the 4th of the month the rearrangements had to be A, X, N at the top. The user then sent the message: AXNAXN before continuing with the content of the message. It was not long before the Poles realized that this repetition every day in specific messages was not just accidental. It was the settings of the machine's rotors to start the encryption, they were essentially the "keys" of that day. (Repetition in cryptography is a huge mistake). The Poles also realized that they could use theoretical mathematics "group theory" in order to break the cryptogram. They realized that for each given machine setting, each incoming letter would be encrypted as a different letter. Because the machine was reversible, that is, it encrypted and decrypted, the encrypted letter would then be encrypted as originally used. This awareness paved the way for them to Enigma.
We can record how a machine setting shifts characters using group theory.
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
| J | R | U | X | A | W | N | S | F | Q | Y | T | B | H | M | D | E | V | G | I | L | P | K | Z | C | O |
In the first row are the letters of the alphabet and in the second the letters that light up (with the help of light bulbs) when the user types. E.g. When the user presses "A" once, the machine depending on its setting gives "J" and so on.
Note, however, that "A" shifts to "J", "J" to "Q", "Q" to "E" and "E" to "A". (AJQE). There are three other letter cycles:
(GNHS), (BRVPDXZOM), (CULTIFWKY).
That is, two groups of four letters and two groups of nine. This awareness reduced the volume of manual effort required to crack the encryption. They also found that the arrangement of letter pairs did not affect the theory of the groups they applied.
So basically the problem was with the initial machine settings that changed every 12 hours and which were shipped between German cryptographers, months earlier.
The role of Marian Rezevski
Marian Rezevski was one of the three Polish mathematicians chosen by Major Maximilian Chianski to work on decrypting the Enigma machine. Resevski was a mathematician, and when he chose what career to follow, that was mathematics. Fortunately, however, he did so to work on decrypting the Enigma machine.
As we said above, the Polish euthanasians (ie those who obstructed the transmission of the Morse code) suffered many messages everyday, Rezevski was slow to observe that every day at 12 at midnight, the Germans sent a specific message twice, settings of the Enigma engine. For example, user A was typing TIM TIM, the machine produced something random, that is, HUW WYT which, for sure, the Germans sent it through Morse signals twice. Rezevski, by analyzing thousands of such messages, manages to make paintings, with every possible shift of letters through 6 powerful algebraic equations.
Rezevski was the one who introduced the solution of variables by permutation, until then no theory had been formulated, he developed it. Using these boards, the Poles managed to decrypt the Enigma machine for some time, but it did not last long. In 1932 in Germany the Nazis achieved significant political victories and finally in 1933 Hitler came to power. And then the decryption of the Enigma machine becomes a major issue in Poland.
The role of Hans - Thilo Schmidt
It could not exist in a history of war, secret, crypto-cryptography, and a person with an air of espionage (or rather betrayal).
This is none other than the depicted Hans - Thilo Schmidt. Rezewski would not have made the progress he had made with his equations and tables if he did not have more data in his hands to be able to completely decipher the Enigma machine.
In November 1931, a year before Rezewski completed the six equations of variation, a meeting took place at a Grand Hotel Vervier in Belgium, where French counterintelligence officer Gustave Bertrand met with Hans-Thil. Schmidt.
There Schmidt sold him copies of the machine settings Enigma. The reason Schmidt did this was financial, he lived a very rich life, although he was a business owner, yet the money was not enough for him for the way of life he used to do. His brother found a job in a ministry that strangely came in contact with the specific documents, so he was tempted to sell them. He sells them to the French officer for ten thousand Reichmarks, about twenty thousand pounds today (about twenty-eight thousand euros).
Bertrand soon realized that he could not use them and informed the British, who found them very expensive. In an act of despair, Bertrand informs the head of the Enigma decryption team in Poland, Lt. Col. Guido Langer, who, of course, saw them as the mother from heaven and buys them. Later he gives them to Rezevski who draws a lot of information from the specific documents and makes the tables we said above.
This is the end of the first part of the dedication of the Enigma machine. In the next part we will deal with the English side who later enters the game by decrypting the Enigma specifically in the German navy and the Atlantic front, where the war in Europe was finally judged and ended with the allied forces in Normandy.
Very interesting article! Well done! We are waiting for the sequel!
https://iguru.gr/2015/03/15/enigma-enigma-hitler-...