How Enigma was cracked
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- เผยแพร่เมื่อ 14 พ.ค. 2024
- 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 - วิทยาศาสตร์และเทคโนโลยี
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".
Thanks for the info!
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.
Now they struggle to deliver junk mail.
@@chrisst8922 who, the Poles lol.
Rejewski, Różycki and Zygalski polish mathematicians in 1939 gave all informations including their Enigma build in Poland to the British. Read XYZ by Desmond Turing.
A well put together and clear explanation. Many thanks for doing the work👍
Thank you! much needed motivation for the next video! :)
Very cool! Very accessible presentation!
What did you use to create the animations for this series if I may ask?
Hi, thanks for your comment! I used PowerPoint and Visual Studio for animations in this video.
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
Thank you for your feedback and kind words! :)
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).
Simplistic rubbish
Rejewski, Zygalski, and Rożycki. Read XYZ by Dermont Turing.
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.
You're all great at re explaining TH-cam videos.
"Only" is doing a hell of a lot of heavy lifting in that completely idiotic sentence.
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❤
It was NO(!) ‘’genius’’ of Alan Turing that cracked Enigma. It was Polish mathematical geniuses Marian Rejewski, Jerzy Rozycki and Henryk Zygalski who cracked Enigma. No American nor British did that. Get your history straight.
Dont forget the names of Marian Rejewski, Henryk Zygalski and Jerzy Różycki and that Bomba Rejewskiego was the device that Alan Turing built :)
@@TymexComputing Turing did not build anything. It was the Polish mathematicians.
Truly lovely video, but the AI voice kills me. Please, for the love of god, I don't care how bad you think your voice is just please voice it yourself or find someone.
Thanks for the feedback!
Question, how would one determine the position/pairings of the reflectors? Moreover, were all enigma machines built with the same reflector pairings? Or were they randomized with each machine built?? Obviously ridiculous considering the number of enigma machines built but im really curious
The Bombay machine
Now renamed the Mumbai machine. ;-)
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 ...
I don't want to downplay the work done by the Polish team, but their decoding system relied on a flaw in the German message protocol. Once the Germans had fixed that flaw, the Polish system no longer worked. Alan Turing essentially started from scratch and the bombe described in this video is nothing like the bombe designed by the Polish team. That's not to downplay their massive contribution, but to accuse the British of taking all the credit is unfair - particularly since the whole project remained a massive secret for decades afterwards, and no-one was in any position to make any claims.
Funny then that it took a team of hundreds of British workers over a year to build a machine capable of cracking intercepted messages.
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
Ok, i think i get it now. But there are other ways of completing the process that seems like it'd be more straightforward.
I taught myself c# and my first project to get to work was an enigma simulator!
Cool! 😎
An excellent first project. C# is a very cool language!
The correct pronunciation is Bombe. Sorry for the mistake. 🤕
I think it’s a computerised voice.
Correct pronunciation is ''BOBMA'', which is from Polish for a ''bomb''.
It was NO(!) ‘’genius’’ of Alan Turing that cracked Enigma. It was Polish mathematical geniuses Marian Rejewski, Jerzy Rozycki and Henryk Zygalski who cracked Enigma. No American nor British did that. Get your history straight.
The correct is Bomba. It is Polish word, and the name of the Polish machine cracking Enigma which was already in service in 1938 (when Turing was still doing his PhD). It was - a few years later - the inspiration for Turing's "Bomb(e)", and he even used the same name for his, much more advanced, device.
@@Edi_J Yes, it is Bomba. I should know; I am Polish. But Turing did not crack the Enigma. It was genius of Polish mathematicians. Turing is just a side effect of it.
@@Edi_J th-cam.com/video/jiRrjsYFdVo/w-d-xo.html
What percentage of TH-cam videos are voiced by computer?
Excellent!
a very simple improvement could be made on the Enigma Machine by simply re-designing the rotors so that they can sometimes give the same input letter as the output. In this case no bulb would glow if the output letter is the input letter but that's not a real issue. "If no bulb is glowing, the output is the letter you pressed."
Dankon pro via klare prononcita prezentado pri la deĉifrada teorio.
Dankon pro via komento!
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.
Thank you!
I absolutely agree,. I visited the Bletchley Park museum and saw the replica bombes. If a video such as this was included in the AV (audio visual) presentations it would be of enormous help to understand the concepts.
thank you
Welcome!
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
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.
Indeed!
The "Bombay Machine"?
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.
The Polish method was a complete tour-de-force, but it relied on the rotor starting positions being transmitted twice at the start of each message. These starting positions were set at the discretion of the Enigma operator. However, the Germans abruptly changed the protocol so that the starting positions were only sent once. This meant Polish system no longer worked and Alan Turing had to develop a completely new system to break the machine. Fortunately, by the time this happened there was a massive catalogue of stored messages to provide a rich variety of possible cribs.
So, to characterise the whole development of an entire new coding system as improving the Polish system "a bit" is both unfair and completely incorrect.
Furthermore, the whole existence of the project was kept entirely secret for many decades after the war and no-one was making any claims at all. Anyone who knows even a little bit of the history of Bletchley Park is well aware of the massive Polish contribution - without their ground-breaking work, the war would have gone on for much longer.
They actually cracked it before the war began, and realizing that they were about to be invaded, they gave their findings to the British. In fact, the Poles invented the “cryptologic bombe” machine later made famous by Alan Turing and his compatriots. His version was more complicated, because the Germans kept adding features to the Enigma machine. Turings machine cracked a much more advanced encryption, so I think it only fair to complement the British for their achievements. The Bombe machine was indeed named in recognition of polish efforts, after all.
One thing you probably needed to clarify was the blue wires not in sequence alphabetically. While watching the video, that was the main question I had. Why were the blue wires not in sequence alphabetically? Is that just how the Germans did it for an extra layer of security or is there a more significant reason?
Not going to listen for almost 20 minutes to bad computer narration. I turned this video off when it said letteree instead of Letter E.
Thanks for the feedback. Next one will not be computerized voice! :)
@@IngeniousideasThe animation and the script are excellent and deserve a proper human voice.
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?
I'm afraid bombe required a guess (/crib) to work. No other way as far as we know.
The germans were bad about using lieh reltih(backwards to avoid censorship), berlin, and other common words. His use of weather report was probably very common. I believe the rotor settings on all enigma machines were the same for every machine each day. So, any transmission that was decoded gave the settings for all the rest.
Bombay. How funny.
0:07 Not the "Bombay machine" but "Bombe," in which the "e" is silent. That's right, it's pronounced "bomb." For some reason, Turing gave it a French name.
Couldn't listen to the voice for very long
Thanks for the feedback. Next one will not be computerized voice! :)
Можно сделать русскую озвучку?
Turing Bombe Pronunciation: The word "Bombe" is not pronounced "Bombay" is pronounced "Bomb" the e is silent
Great video, great graphics, nice explaination! But....Wouldn´t it be only fair to give credit to the polish mathematicians around Marian Rejewski, who cracked the enigma already in the 1930s and invented the bombe machine as well? Poland handed both their own (rebuild) enigma machines as well as first-generation bombe machines to France and UK in summer 1939. Alan Turing learnt all these basics from the polish people, and was very instrumental when, during the war, next-generation enigma machies with more rotors were introduced by German submarine command.
If you think Alan Turing couldn't have worked out a way to do it then you don't know much about Turing. The important part of what the Poles handed over was the physical setup of the Enigma machines - How many rotos, how many plugs on the plugboard etc.The Men and women at Bletchley Park weren't sitting around drinking tea you know, Enigma had several variations and being able to crakc the code is one thing but being able to do it quickly quite another.
@@richardevans560 sorry but you have no idea what are you talking about .. Poles did all the mathematics using permutation theory… they also created the “bomba” and give that all information to Brits .. on the silver platter. Without Poles Turing wouldn’t know where to start .. sorry . Just read any cryptography book or something.
And I don’t want to discredit Turing as he was a brilliant man … but let’s stick with the facts .. Polish mathematicians been decrypting messages for years where at bletchley park they thought of using linguistic for that which is impossible. Even head of bletchley park admit that the poles have broken the code .
@@Dycdom Wrong. You even got the name of the "Bombe" wrong en.wikipedia.org/wiki/Polish_Enigma_double
en.wikipedia.org/wiki/Bombe
@@richardevans560 dude you just showed that you don’t know much about the history of the enigma … „Bomba” is the original device designed and built by Polish mathematicians… which was then copied by Brits.
@@richardevans560 everything I have said earlier are just facts .
;)
Stop being so intellectually lazy and do some reading.
Even in your link it said that the original one was “BOMBA” ..
Dude seriously??? 😂😂😂
en.m.wikipedia.org/wiki/Bomba_(cryptography)
Text to speech voice used
.:DING:.
The speaker audio is like a robot! Please let a real person speak or don't affect the sound. Thank you for the great video
Thanks for the feedback. Next one will not be computerized voice! :)
"Bombay machine" !!!! WTF
The audio cadence is just HORRIBLE - I assume it's being read by a computer. It's entirely obvious and it completely undermines what likely would have been a good video otherwise. Did you actually LISTEN to it before you posted it???
This is the first I've heard of "The Bombay Machine"... it's consistent mispronunciation tainted the whole thing for me...
Yes. Sorry for the mistake. :( It is Bombe Machine.
I would have loved to watch this video, but the AI voice is unbearable ... Too sad everyone starts using those today ...
Why is the narration done by a robot voice? I could not listen to it for more than 2 minutes.
Will do better for the next one!
I heard it was mathematicians from central Africa.
Nahhhh...that does not sound right.
🤣.
Potentially interesting topic, however the "AI" voicing was intolerable.
will do better in the next one!
Screw this automated voice.
It's Bomb, NOT bombay.
You tackle the subject well but sound ridiculous with the miss pronunciation!
Just go to any other video about Enigma to hear it spoken correctly.
Funny how American[ actor]s in the 1971 bond film Diamonds are forever can get the pronunciation of "bombe surprise" correct....
(Even if the script shows them not knowing their clarets.)
Correct pronunciation is ''BOBMA'', which is from Polish for a ''bomb''.
It was NO(!) ‘’genius’’ of Alan Turing that cracked Enigma. It was Polish mathematical geniuses Marian Rejewski, Jerzy Rozycki and Henryk Zygalski who cracked Enigma. No American nor British did that. Get your history straight.
@@cigmorfil4101 Correct pronunciation is ''BOBMA'', which is from Polish for a ''bomb''.
It was NO(!) ‘’genius’’ of Alan Turing that cracked Enigma. It was Polish mathematical geniuses Marian Rejewski, Jerzy Rozycki and Henryk Zygalski who cracked Enigma. No American nor British did that. Get your history straight.
@@user-ky5dy5hl4d
I never said the Poles didn't crack enigma
They had a Bomba machine.
According to an addendum in "The hut six story" by Gordon Welchman (of BP) the Polish Bomba and the British Bombe are not derived from the Bomba. Further the Polish methods of cracking were not particularly useful after the Germans changed keying system in May 1940.
The name for the BP machines, according to Gordon Welchman in his book comes from the French for bomb[1][2], and as such would be pronounced as bom-b.
[1]"The name "bombe" seems to have been attached by the Poles to an earlier concept, but it was also applied to the machines that we actually used. The term "bombe" is simply French for "bomb"; the connection with our machine is not clear to me, but it may have had to do with the idea of a mechanism that will go on ticking until it reaches an output..." [The hut six story, Gordon Welchman, M&M Baldwin, 1997, pg 77]
[2]it is also the name of an ice cream dessert which I seem to remember possibly being a favourite of Turning's, but that may be apocryphal; that is the "dessert" at the end of Diamonds are forever: it was a bomb inside a fake ice cream bombe dessert, hence "bombe surprise"...
@@cigmorfil4101 Your answer is explosive. Thank you.
Synthetic voices are boooooooring listen to.
Thanks for the feedback. Next one will not be computerized voice! :)
Ai voice kills this video thumb down
Turing was a genius. Wow.
Watched 15 seconds and gave up because of the incredibly irritating robot voiceover.
I hate robot narration.
oh pleeze stop with the "auto-voice". If you can't have a real human narrator, the video is just crap. Boo!
Bombe .NE. "Bombay"
I don't care for TH-cam channels that use artificial voices for the narration of the videos. It is actually creepy
Terrible , Historically inaccurate and that voice is so bad