How Enigma was cracked

Welcome to Enigma Series. We have built from scratch a complete Enigma machine and a Bombe machine (the machine which Alan turning built) in software to be able to see them working inside out and understand every aspect of these incredible machines.

In this video:
0:00 Introduction
0:53 Enigma's weakness no.1
1:52 Finding a Crib
4:04 Objectives of Bombe Machine
5:07 Crude way of breaking Enigma
8:22 The Bombe rotors
10:37 Equivalent circuit of rotors
12:09 Making of the Bombe circuit
14:43 Working of the Bombe circuit
17:42 Enigma's weakness no.1
18:34 Summary of cracking the Enigma

#enigma #ww2 #cryptography #technology #history

[krzysztofpoczatek]

Main facts (in short);

Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra.
The Enigma machines were a family of portable cipher machines with rotor scramblers.
Good operating procedures, properly enforced, would have made the plugboard Enigma machine unbreakable.
The German plugboard-equipped Enigma became the principal crypto-system of the German Reich and later of other Axis powers. In December 1932 it was "broken" by mathematician Marian Rejewski at the Polish General Staff's Cipher Bureau, using mathematical permutation group theory combined with French-supplied intelligence material obtained from a German spy. By 1938 Rejewski had invented a device, the cryptologic bomb, and Henryk Zygalski had devised his sheets, to make the cipher-breaking more efficient. Five weeks before the outbreak of World War II, in late July 1939, at a conference just south of Warsaw, the Polish Cipher Bureau shared its Enigma-breaking techniques and technology with the French and British.
During the German invasion of Poland, core Polish Cipher Bureau personnel were evacuated via Romania to France, where they established the PC Bruno signals intelligence station with French facilities support. Successful cooperation among the Poles, the French, and the British at Bletchley Park continued until June 1940, when France surrendered to the Germans.
From this beginning, the British Government Code and Cypher School (GC&CS) at Bletchley Park built up an extensive cryptanalytic capability. Initially the decryption was mainly of Luftwaffe (German air force) and a few Heer (German army) messages, as the Kriegsmarine (German navy) employed much more secure procedures for using Enigma. Alan Turing, a Cambridge University mathematician and logician, provided much of the original thinking that led to upgrading of the Polish cryptologic bomb used in decrypting German Enigma ciphers. However, the Kriegsmarine introduced an Enigma version with a fourth rotor for its U-boats, resulting in a prolonged period when these messages could not be decrypted. With the capture of cipher keys and the use of much faster US Navy bombes, regular, rapid reading of U-boat messages resumed.

In the 1920s the German military began using a 3-rotor Enigma, whose security was increased in 1930 by the addition of a plugboard. The Polish Cipher Bureau sought to break it due to the threat that Poland faced from Germany, but its early attempts did not succeed. Near the beginning of 1929, the Polish Cipher Bureau realized that mathematicians may make good codebreakers; the bureau invited math students at Poznań University to take a class on cryptology. After the class, the Bureau recruited some students to work part-time at a Bureau branch set up in Poznań for the students. The branch operated for some time. On 1 September 1932, 27-year-old Polish mathematician Marian Rejewski and two fellow Poznań University mathematics graduates,  Henryk Zygalski and Jerzy Różycki, joined the Bureau full-time and moved to Warsaw.
 Their first task was to reconstruct a four-letter German naval cipher.
Near the end of 1932 Rejewski was asked to work a couple of hours a day on breaking the Enigma.

Rejewski's characteristics method.

Marian Rejewski quickly spotted the Germans' major procedural weaknesses of specifying a single indicator setting (Grundstellung) for all messages on a network for a day, and repeating the operator's chosen message key in the enciphered 6-letter indicator. Those procedural mistakes allowed Rejewski to decipher the message keys without knowing any of the machine's wirings. In the above example of DQYQQT being the enciphered indicator, it is known that the first letter D and the fourth letter Q represent the same letter, enciphered three positions apart in the scrambler sequence. Similarly with Q and Q in the second and fifth positions, and Y and T in the third and sixth. Rejewski exploited this fact by collecting a sufficient set of messages enciphered with the same indicator setting, and assembling three tables for the 1, 4, the 2, 5, and the 3, 6 pairings. Each of these tables might look something like the following:

First letter

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Fourth letter

NSYQTICHAFEXJPULWRZKGOVMDB.

A path from one first letter to the corresponding fourth letter, then from that letter as the first letter to its corresponding fourth letter, and so on until the first letter recurs, traces out a cycle group.

The following table contains six cycle groups.

Cycle group starting at A (9 links)
(A, N, P, L, X, M, J, F, I, A)
Cycle group starting at B (3 links)
(B, S, Z, B)
Cycle group starting at C (9 links)
(C, Y, D, Q, W, V, O, U, G, C)
Cycle group starting at E (3 links)
(E, T, K, E)
Cycle group starting at H (1 link)
(H, H)
Cycle group starting at R (1 link)
(R, R).

Rejewski recognized that a cycle group must pair with another group of the same length. Even though Rejewski did not know the rotor wirings or the plugboard permutation, the German mistake allowed him to reduce the number of possible substitution ciphers to a small number. For the 1, 4 pairing above, there are only 1×3×9=27 possibilities for the substitution ciphers at positions 1 and 4.
Rejewski also exploited cipher clerk laziness. Scores of messages would be enciphered by several cipher clerks, but some of those messages would have the same encrypted indicator. That meant that both clerks happened to choose the same three letter starting position. Such a collision should be rare with randomly selected starting positions, but lazy cipher clerks often chose starting positions such as "AAA", "BBB", or "CCC". Those security mistakes allowed Rejewski to solve each of the six permutations used to encipher the indicator.
That solution was an extraordinary feat. Rejewski did it without knowing the plugboard permutation or the rotor wirings. Even after solving for the six permutations, Rejewski did not know how the plugboard was set or the positions of the rotors. Knowing the six permutations also did not allow Rejewski to read any messages.

Before Rejewski started work on the Enigma, the French had a spy,  Hans-Thilo Schmidt, who worked at Germany's Cipher Office in Berlin and had access to some Enigma documents. Even with the help of those documents, the French did not make progress on breaking the Enigma. The French decided to share the material with their British and Polish allies. In a December 1931 meeting, the French provided Gwido Langer, head of the Polish Cipher Bureau, with copies of some Enigma material. Langer asked the French for more material, and Gustave Bertrand of French Military Intelligence quickly obliged; Bertrand provided additional material in May and September 1932.
The documents included two German manuals and two pages of Enigma daily keys.

In December 1932, the Bureau provided Rejewski with some German manuals and monthly keys. The material enabled Rejewski to achieve "one of the most important breakthroughs in cryptologic history" by using the theory of permutations and groups to work out the Enigma scrambler wiring.
Rejewski could look at a day's cipher traffic and solve for the permutations at the six sequential positions used to encipher the indicator. Since Rejewski had the cipher key for the day, he knew and could factor out the plugboard permutation. He assumed the keyboard permutation was the same as the commercial Enigma, so he factored that out. He knew the rotor order, the ring settings, and the starting position. He developed a set of equations that would allow him to solve for the rightmost rotor wiring assuming the two rotors to the left did not move.
He attempted to solve the equations, but failed with inconsistent results. After some thought, he realized one of his assumptions must be wrong.
Rejewski found that the connections between the military Enigma's keyboard and the entry ring were not, as in the commercial Enigma, in the order of the keys on a German typewriter. He made an inspired correct guess that it was in alphabetical order.

Britain's Dilly Knox was astonished when he learned, in July 1939, that the arrangement was so simple.
With the new assumption, Rejewski succeeded in solving the wiring of the rightmost rotor. The next month's cipher traffic used a different rotor in the rightmost position, so Rejewski used the same equations to solve for its wiring. With those rotors known, the remaining third rotor and the reflector wiring were determined. Without capturing a single rotor to reverse engineer, Rejewski had determined the logical structure of the machine.

The Polish Cipher Bureau then had some Enigma machine replicas made; the replicas were called "Enigma doubles".

[DaffyDaffyDaffy]

The text to speech voice was initially offputting, but the presentation was so nice and i've never understood the bombe machine more. This is great

[united]

In 1932 a team of young mathematicians from the University of Poznań POLAND was set up. Among them were the main code breakers Marian Rejewski, Jerzy Różycki and Henryk Zygalski. It was Rejewski who first cracked the Enigma code, in only ten weeks... during the war, the Poles gave the French and the British a copy of the Enigma Machine built by them, ... after the war, the English took all the credit for themselves ...

[johntruman]

My instructor in wireless communications was helping Alan Turning in ww2 when they were locked out when the fourth wheel was used, he told Alan that if I was on a German submarine the first three wheels would have to be on the weather code as he would not have time to keep changing the wheels, we already knew the weather code so we were only 26 turns from knowing what they were saying, it was that simple and it worked.
Great brain but common sense solved the problem.

[philipdurling]

Credit also to Tommy Flowers and his team of GPO engineers. This was a team effort by all the allies in WW2. Credit also to our brave Polish allies.

[Olivier_the_Dilettante]

Alan Turning only expanded on plans supplied by Polish mathematicians who supplied the full working enigma machine and plans of how the bombe was to be build (there was no time for Poles to developed as the country was overrun by Germans).

[Ingeniousideas]

The correct pronunciation is Bombe. Sorry for the mistake. 🤕

[noiricha]

After watching this video I recognize I could have been very valuable in cracking the Enigma machine ... by fetching tea or coffee for the scientists working on this problem.

[DrMerle-gwwj]

The fundamental work on cracking Enigma was done by Polish mathematicians. Just days before the 1 September, 1939 invasion they were successful in getting all their notes and an Enigma machine out of Poland and sent to the Brits. The latter then took the basic work by the Polish, improved on it a bit, and took full credit for cracking the Enigma code.

[Jaggerbush]

This series should have way more views. This is so well explained. This is the definitive explanation of Enigma. I just wish the narration wasn't so dry. Should've used a real person.

[abhishekshukla]

Your way of teaching was so admirable, even my professor was unable to teach this topic in the way you taught us!
Thank you so much for this❤

[mikemordkovich]

1:54 It seems to me that all the following is based on the assumption, which could be quite wrong, that you have the encrypted string and the original string (massage). Will this approach work IF you do not have the original (not encrypted) massage to start with?
The other question I have: why the encrypted massage is LONGER? It seems to me that the Enigma is supposed to produce one-to-one letter, isn't it?
And the last one: if the operator on the receive side, by mistake, misses the punch or makes extra punch, all the rest of the decoding on the receive side is screwed. Both machines, on the transmit and receive sides must be reset to their original state.

[mircob-]

To help people as me that were stuck to understand the passage at 14:27, they connect the outputs to the inputs because the letter was equal in the sense that the signal was the same so they can automatize the machine I think that this process was manually done base on the encrypted phrase and the crib guess

[happybear]

The enigma wasn’t the only cipher machine that the Germans were using either, nor was it the strongest. They had at least 2 other cipher machines that were much stronger such as the Lorenz and the t52 sturgeon. Both of which had nothing to do with Alan Turing or the poles. Then there were also the Japanese cipher machines such as the red and purple machines with the naval code (jn-25) being the most prominent one. Both of which had nothing to do with Turing or the poles. Then you had the cipher machines the allies were using like the us sigba and british type x which again, both Turing and the poles had nothing to do with. There was a lot going on for ww2 codebreaking.

[Redspider]

this is a common misconception for evrybody 1:49 it's not possible for E to become E bc the enigma works on wires, and they can't go into eachother. has nothing to do with the buttons.

edit:
for the bombe machine it's still not possible.

[gustavvogels]

This is undoubtedly a very good, interesting and complex animated lecture.. But the question for the audience is, do they want to be entertained or do they want to see a lecture after which they understand this decryption process from start to finish?
To do this, you need to know the following. The ENIGMA-decryption-process according to Alan Turing and Gordon Welchman consists of several steps. Some of these steps require the use of a machine so that the decryption process can take place in an acceptable time.The TURING-WELCHMAN-BOMB is just one of the machines in this decryption process, but it is also the most impressive machine.
I show all of this in my lecture here on YOUTUBE called "TURING WELCHMAN BOMB decrypts Enigma" (Gustav Vogels". I show and explain the complete decryption process step by step. (English language).
I prove each of my statements with the help of my microprocessor-controlled "TURING WELCHMAN BOMB that I developed. This microprocessor decryption bomb works in exactly the same way as the mechanical bomb of Alan Turing and Gordon Welchman.
My lecture is long and complex, but that is also the way Alan Turing's and Gordon Welchman's decryption method is.

I would like to remind you that in January 1941 a delegation of high-ranking American cryptologists visited Blechtley Park and stayed there for five weeks. After their five-weeks stay, theses American cryptologists still did not know how the British were able to decrypt the ENIGMA radio messages. This gives an idea of the overwhelmingly, great inventive achievements of Alan Turing and Gordon Welchman.

[jollyrogererVF]

A well put together and clear explanation. Many thanks for doing the work👍

[LittleCoud]

Throughout the comments I see people talking of the other machines that people created during the war that were also used to crack the code or other methods that were used and trying to put down the Bombre. However, the machine that Alan Turing invented was still very impressive. Its a lot of work that goes into making the machine, figuring out how to crack the cribs and what settings the letters have everyday. It was still a major help in the war for the British Allies. Plus the Imitation game, now called the Turing Test, is still a very fascinating concept and one we are facing today.
I watched The Imitation Game and found myself extremely intrigued on how the machine actually worked and this video helped a lot. Although some of it is still a little confusing, as it's a lot to take in and I'm not studying maths at Harvard, both this video and the one explaining the Enigma machine are really good and explain things well. Thank you

[purrdiggle]

The German army Enigma had 5 possible rotors. 3 of the 5 were chosen to be used each day. The process being described here is how the order for the 3 chosen rotors were formed. But, how were the 3 of 5 rotors chosen?

[sadidrahimi]

But how then would you know what the guess is? What if you have no information on a guess, and you just intercept a random set of letters?