Turing's Enigma Problem (Part 1) - Computerphile
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- Опубликовано: 28 май 2024
- The Enigma cipher machine, said to be unbreakable. Alan Turing had a pivotal role in cracking Enigma codes during WWII. Professor Brailsford takes us through just what Turing and his team were up against.
Engima Part 2: • Tackling Enigma (Turin...
Professor Brailsford's notes: bit.ly/enigmapart2
158,962,555,217,826,360,000 - Numberphile: • 158,962,555,217,826,36...
Flaw in the Enigma Code - Numberphile: • Flaw in the Enigma Cod...
Punch Card Programming: • Punch Card Programming...
Public Key Cryptography: • Public Key Cryptograph...
/ computerphile
/ computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: bit.ly/bradychannels
We can all agree this dude would be the best grandpa. So many interesting stories.
You are correct, He is my grandpa & he does have many interesting stories.
@@ApolloVIIIYouAreGoForTLI If he's your grandpa, CONGRATS to you. Seriously, I am jealous to hear his stories.
At last, a explanation that makes ring-settings clear. The various books are very ambiguous on this. This is the best explanation of the mechanism of Enigma I have seen
I want him to read a book to me... that voice is amazingly soothing
The military Enigma rotors had different internal wiring to the commercial version rotors. It was the miltary rotor wirings that Marian Rejewski was able to work out purely by applying mathematics, using permutation theory, from just having a body of enciphered messages available to him and code book settings for September and October 1932. It took him just a couple of weeks to do this.
Polskaaaaa, pozdrawiam wszystkich polaków oglądających ten film lub też czytających sekcję z komentarzamiii :D:D:D Polska mistrzem Polskiiiiii !!!!!@
Alan will never get enough recognition for his role in history. Highly recommend watching "The Imitation Game"
Damn, this guy is an excellent teacher. He can explain anything. I understand everything that he's saying.
Thank you for mentioning Polish matematicians.
yup, brits allways were trying to hide this information and took all the credit
Lol, not true at all. Go to Bletchley park, there is a memorial deicated to the Polish mathemeticians! Of course making a movie about such events has greater effect when you can attribute everything to one man but I believe that most people recognise the heroics of the Polish mathematicians as well.
respektek O yeah.. For how long the memorial has been there?
Afterall there's a reason for calling it a 'World' War lol, combined effort :)
@@Dziomolek Nope/ wrong - Its' never been any sort of secret that everything is based on Polish work and I've followed it for ? 40-50 years but deciphering needed the Bomb.
I could let this guy tell me a bedtime story.
Me neither, I'd never get to sleep waiting for the next bit
@@banama1758 Thanks for lowering the tone.
@@banama1758 hahaha ha ha
Isn't that what he's doing?
Once upon a time, in a land far away...
Three Polish matematicians: Marian Rejewski, Jerzy Różycki and Henryk Zygalski cracked the Enigma in the first place using the cryptologic bomb.
True, but it was an earlier version, as I understand it.
@@gh8447 The Poles cracked it, the Brits scaled up, and sped up, their process up to an industrial throughput.
But the Polish breakthrough was indispensable and inspirational and deeply non-obvious.
THE ENGLISH LIKE ALL THE CREDIT - JUST LIKE MONTGOMERY WAS THE GREATEST FELDHERR OF ALL TIME AND HOW SUCCESSFUL OPERATION " MARKET GARDEN WAS " AFTER THE LANDING IN 1944 ( IT WAS MONTY'S BRAIN CHILD )
Enigma code must have been cracked by Brits. Otherwise Poles made single most valuable contribution to war effort and they were left for idiots from east to run their country for 50 years - that's not acceptable. If you think this was early version of the enigma, so it was easy then think again, till the end of the war natzi were convinced that their code is unbreakable because mathematically it was impossible. Mathematics way how to do it was found by Polish mathematicians. Just before the war English officials were given working example of commerce version of enigma crypting machine.
The poles cracked the civilian version used for banking transactions. The military version was ALOT more complex
I love RUclips precisely because it gives me content like this. Thanks for the video!
❤❤😊
Trotz des cleveren Designs der Deutschen haben die polnischen und britischen Mathematiker herausgefunden, wie sie den Enigma-Code brechen können.
Danke, Professor und Team, für diese hervorragende Einführung!
(Danke auch an Google und RUclips)
I don't know if this was of much help for deciphering, but since Enigma lacks umlauts you could probably expect a lot of the combinations "AE" "OE", "UE", in places where you'd expect to find vowels.
Great to see David Brailsford back on the channel.
Absolutely fascinating stuff, I could listen to this all day - I can't wait for a further installment!
I want to fix his collar
+ximbabwe0228 lol
i can't watch it :( :'(
*O.C.D* (Obvious : Collar DISLODGEMENT!!) : and - *P.T.S.D* (Protruding _Turned-back-cuffs_ _of_ Shirt DIFFER !! ) *_R > G_*
Leave it be, and listen.
He is a preppie!
It so interesting how all the "security measures" the germans had actually made enigma easier to crack.
By adding rules (like dont put the same wheels in the same spot two days in a row, the wheels spin at different points and other i don't remember) they gave cryptographers outside constraints. If they had not done it then there would be no apparent system or logic. But the settings list had rules and the wheels were different.
This is the video I wanted to see from you guys from a loooong long time... love this!
Great repertoire. Love your simplistic account of all issues. Thank you.
aaaand above all of that they were speaking german. That is harsh.
The Enigma Machine: From the people who brought you the word "Rechtsschutzversicherungsgesellschaften"!
This is brilliant and massively interesting. Thank you for this fantastic video.
😊❤
Is there any imformation about the guy or gal that invented enigma ?? Seems that person must have been years ahead of their time
Yeh that guy must be crazy
Cyphers are far, far easier to make than they are to break.
@@tommothedog it's also far easier to crack when you have the information about the settings of the machine.
The clearest explanation I've seen - especially that part about the ring settings vs. the rotor settings which is not explained elsewhere. Thanks!
It's as muddy an explanation as possible.
Hugely entertaining! Can't wait for the next EP!
It would be very interesting to see some explanation of how the cryptoanalytic process of deciphering such a contraption looked like in a bit more detail. Did the people at Bletchley Park use some specific mathematical approach helping understand the code ? Did any other electrical tools were used ? Can't wait for the next video!
Simon Singh wrote a book where he along other things explained how the enigma worked, the polish intelligence did the dirty work in first place to then hand it over to the British when they ran out of time. If the polish had the resources they would've cracked it earlier.
But anyway the book provides many graphical explanation to understand the matter. I recommend reading the youth edited version caused there are just more explanations :D
Why mentioning Simon Singh only as the owner of Enigma machine, but not the author of "The Code Book", the best introduction to cryptography ever written, and - what's important - very well researched, unlike some error-laden movies ? Singh's account of Enigma history and techniques is both complete and simple to comprehend.
Amen. I love The Code Book.
Agree
Welp, my brain is jello. It's amazing that Bletchley Park ever figured this out. Truly speaks volumes to the intelligence of the folks that broke Enigma.
I've seen that movie (As I expect many have); But the way you have described it, makes it obvious now, why Turing proposed the computer. This looks/sounds like a perfect problem for a computer. Many factorials, and simple bit/binary math. Nicely done. |Thanks.
I've watched this entire series 3 times now but I still find it really interesting.
❤😊me too
This is the coolest video you guys have done in a while I'm really looking forward to the next one!
The enigma machine has already been broken (in early 1930) before the war even started.
So who played a major role Alan Turing OR Marian Rejewski OR Tommy Flowers?
Rejewski use mathematics to show what makes the Enigma ticked and demonstrated some of the ways to decipher it and Turing mechanised it while Flowers digitised it (well using punch tapes).
All. Also, it was never "broken", you're entirely wrong with that. Except Turing played a major role and is likely not replaceable like the others mentioned.
There were versions of the enigma. The Polish broke the 3 wheel version. Germany then redesigned the thumb wheels (not even aware of Polish break) and two more scrambling thumb wheels were added in series.
There was even a plaque in Bletchley park honouring the 3 main Polish mathematician / cryptologist.
Which is why Turing's machine called the' Bombe' as it originated from Marian design.
But the Polish teams where mostly under resourced and against the clock, while the Germans upgraded to 4th wheel before the Polish invasion.
Some of the Polish cipher teams died smuggling out of the country, 1 died by drowning and 2 where captured and sent to concentration camps.
Never Forget their contribution.
For those who are interested:
Factorial (!) of 4 for example is 4 x 3 x 2 x 1 = 24 so 4 items of any kind can be arranged in 24 different combinations. Most calculators can only calculate 69! modern ones can go a bit further by having 3 digits in the exponent.
My tablet calculator app just managed to get me an approximate result for 205000! 1.68924757542880496668254080814683170840294519*10^999882 in less than a second.
You could have mentioned his collar to him at some point.
Did not notice until i read this comment
Jake Harrison word
Jake Harrison That was a British style at the time they made this.
shows you're not paying attention if you have the time to look at his collar
Jake Harrison His collar is simply sprezzatura!
I made a vb module for ASCII encryption. It can be "set" with any number of one-to-one character mapping arrays (tumblers), but it goes a step further with additional settings to programmatically determine which tumblers to use based on an ASCII sum of the character being encrypted along with its previous character which is already encrypted. Also, the process can be coded to happen any number of times for completely sloppy results. It remains the code of which I am most proud.
The process of making a device as complex as Enigma boggles my mind, though.
ABSOLUTELY FASCINATING!!!
The collar?
You know, I don't understand half the stuff this guy talks about, but his voice is so engaging.
Great teacher, great energy, great voice!
Truly magnificent fellow that Professor Alan Turing.
Second part please! Im loving this
Agreed! What's not to Love..
The Polish Cipher Bureau doesn't get nearly enough credit for its early work on Enigma.
Very very true
Awesome video! I did a school project on Bletchley Park!
Personally, this isn’t Turings work that I find most fascinating, his paper “The chemical basis of Morphogenesis” is truly original and brilliant.
Thanks Professor!
Good video professor, thanks for uploading! :)
He is making my head spin , I am seeing stars in the middle of the afternoon
I also love the raspberry pi teddy bear on the desk, so cute and iconic!
I'm so glad that someone's finally addressed the rings on the rotors. So many books, documentaries, and RUclipsrs seem to shy away from them.
I'm still a little bit confused though.
Does changing the ring position on a rotor effectively, and rather crudely, create a "new" rotor (i.e. one that has different wiring)?
In a way, yes it does "create a new rotor"
No, the way the wires are laid out remain the same. Changing the ring positions simply changed each wire's start position and end positions, but not the individual wire's position. Changing the ring by +1 would then turn A into B, B into C, C into D and so on. A wire could not be changed individually, independent of the other wires.
You could say that changing the ring position encrypted the rotor with a caesar (shift) cipher.
@@dellitsni6466 No, that's not true, and it is explained incorrectly in the video itself. The wiring or the connection of the contacts in the rotors are absolutely fixed. There are no moveable parts whatsoever that could change anything of that. The ring just moves itself - and since it contains the little recess that causes the next rotor to move, as well, setting the ring to a different position changes the point, when the rotor kicks the next one. That's it, what the ring does. It definitely does *not* change anything about the wiring or the way the contacts are connected with each other. They are hardwired, not moveable parts.
Amazing explanation sir.
I'm unclear on two points: 1 - The alphabet ring on the rotors could be set to any one of 26 positions but did not interfere with the wiring, this was fixed inside the rotor. This was an offset was provided although no alterations were made to the wiring. 2 - I was led to understand in the past that the commercial Enigma's 3 rotors had different wiring from the military version, even with only 3 rotors. This was one of the breakthroughs Hans-Thilo Schmidt's information gave to the Poles, who had access to the commercial Enigma.
*C.S.E* (Casual : Snooper's Enigma) : I admire - the woodwork *_R > G_*
Love these videos!
looked at some photos of the paperwork that accompanied these machine, almost looked like a predecessor to ASM. Hearing it had a vuln though, useful. Suppose thats like an system built by people though..... perfect way to begin the morning.
Nicely done. Would like to know the specifics of the battery as power source. Also, the lighting mechanism for the buttons in the days before LEDs.
incandescent bulbs, no?
There's one thing that doesn't seem correct: The Ringstellung (positioning of the ring) does *not* change the wiring of the contacts. It did *not* make an 'offset' there or alike.
There was *no way* to change the wiring or which contact connects with what other contact, at all. This was just impossible, because they were fixed parts that could *not* move or rotate in any way.
So, what did the changing of the Stellring actually do then? It changed the point, were this special rotor caused the rotor next to it, to move a step, as well. The Stellring is the only part of the rotor that could be rotated - all other parts are fixed. And only the Stellring itself moved (no contacts, wirings, whatsoever). But the Stellring had a little recess on it. (In the case of some rotors, it had two, as you mentioned.) So, if you moved the Stellring and fixed it in a different spot, you could determine, when exactly the rotor next to the first one would move, as well.
Say, you start with the rotor in position "A" (shown in the little window), and it's Stellring is set to position "B", then this rotor would move ONE step alone, but when it moves again, it would cause the rotor next to it, to move, as well. And, if you changed the Ringstellung to position "E" (but again begin with the rotor in position "A"), the first rotor would move FIVE times alone, before it would cause the next rotor to move, as well. That's what the Ringstellung does.
There was a door at the front of the machine that allowed for rewiring, by switching plugs.
idk why but hearing his story makes me both heartbroken and happy
What about the number 12 is significant to Turing's implementation of the Enigma problem? Is there a mathematical principle which explains why he needed 12 machines and not 10? Thanks for any suggestions.
Both "The imitation game" and the movie " enigma" weren't actually filmed at bletchley Park. I live 6miles away from it and my grandfather was stationed there during the war
this guy is amazing at explaining
Jessica C. Solomon I wish he was my professor!
amazing, I am loving it!
12:09 Some modems use the same concept to enable wires to connect without having a "plug"
James Grime explains this much better. Very clear understanding of the machine after watching the numberphile video.
It is so cool to see how some engineers invented and evolved an encryption-machine on the one side. Meanwhile their enemys found the weak point with very smart ideas.
So what role did the first British computer by the name of Colossus, and the first American computer by the name of ENIAC play in breaking the Enigma codes? I've watched the Numberphile videos on the Enigma, but these machines weren't mentioned at all, while here in Germany it's always written and told that the Enigma code breaking was done by using these computers?
And eniac I believe was used for ballistic calculations...
Colossus was used to increase the speed with which Lorenz ciphers were broken.
David Attenborough bit at the end :)
Loved it, great video.
Well done!
Bletchley park is well worth a visit to see a running Bombe!
i keep hearing voices in my head repeating everything i read but i have no idea who it could possibly belong to
Computerphile exists? Is this the -phile series ?
At 10:58 he says choose 3 from 8 and arrange them in any order is 336. And 8*7*6 = 336, but that's just the picking of the wheels, with the 6 ways to arrange them you'd get 2016 possibilities.
nope! 336 is correct. number of ways to choose 3 from 8 is 8C6 = 56 then multiplied by 6 which gives 336
@@temuandrew Duh, I had a brain fart there apparently. 8*7*6 of course also gives an order for the wheels already.
Happy birthday, Turing!
(He’d be 109 years old today, June 23, 2021)
Enigma was not "ultra, ultra safe." Now there's some inside humor for you! 1:45
1:48 "Not Ultra safe".
Indeed.
The Polish army was the first to decypher enigma but it was quickly changed. The British army was able to do it because the Luftwaffe was very unprofessional in the use of the machine and they didn't take precautions.
The good professor should have been a computer historian. The guy has a way of putting computing history in a dichotomy of the atmosphere of J.R.R. Tolkien. Guy is bloody brilliant.
Another video about the evolution of ciphers after Enigma would be interesting.
Enigma now tuning into complex computer encryption .. with billions posibilities.. if you learn computer encryption now, enigma is your third meeting..
Left handed computer scientist using line printer paper, classic ! Thanks for the introduction.
I still had trouble seeing how the message was recreated, until I realized (I think) that the character map "pairs" letters. If E was mapped to Y, then Y maps to E. Without this the plain text wouldn't be recoverable if Y had mapped to some other character.
It's not so much random mapping as random pairing, many times.
14:40 Yes. Adding complexity from a superficial perspective (let's make to wheels engage the next ones at different points) doesn't necessarily add up to the mathematical or reverse engineering complexity, quite the opposite sometimes.
I got 99 problems but a cipher aint one.
did the ring setting add a Caesars code per rotor?
Surely it would be possible in theory for the Enigma machine to encode to the same output letter or is that simply unfeasible?
Where can I get hold of the document at 7:34? It's not in the links.
Amazing! :]
Heer's a qwestion: Coold intenshunal typos maek an endoced massage harderer to brake?
its like 5 am why the f am i watching this?
Why not? I hope that you enjoyed it.
The odometer was not driven by the car's engine like you stated. If it was it would be continuously moving while the engine was running whether or not the car was moving. It was driven by a wheel of the car.
What drives the wheel of the car then?
@@patbutete1722 Man I wish I was chatting with you live to ask you if you really do not know what the purpose of the odometer is. I am by no means a car expert myself having never learned to drive myself but even I know its purpose in the car! And knowing that purpose it makes no sense whatsoever for it to be turned by the engine.
As I can not ask you live I will assume you do not know. The odometer measures the distance the car has travelled in its lifetime. As I stated in my OP, if you run it from the engine then the odometer will still turn while the engine is running but the car is in neutral, not exactly the best way to measure the distance a car has travelled if it's value is rising while the car is not moving!
Yes, the engine turns the wheels as you are eluding, BUT it it not required to turn the wheels! For example you can have the car facing down a long hill with the engine off. Release the brakes and let the car roll. Now gravity is turning the wheels, the car is travelling and the odometer needs to measure the distance. How can it do that if its turned by the engine? It can't! Yet it will still turn because it's turned by the wheels!
Fascinating
4:56 , what happens when the third rotor reaches its turn over point, does it do nothing or does it move on the middle or right hand rotor ?
If the slow rotor ever reaches this point at all (most messages were just to short to make this happen), it wouldn't do anything special. It just turns itself without moving other rotors.
BRAVO!
10:27 I feel Doenitz' face was too small for his head.
~ 8:30 5! over 3! is 10 ? or 20? 5! / 2! I'm rusty on maths, but am I wrong? or does he mean [ 5! / (3!)(2!) ] where 2! represents the 2 unused rotors.... I would assume its already used in determining 3! .
Awesome
Couldn't one put a voltage monitor on the wires and track which ones are transmitting when which buttons are pressed?
Nice vid, but why would you do the multiplying by 6 and stuff? Surely you could just do 8!/(8-5)! which is a lot simpler...
So how hard would it be to crack a scaled-up digital version of the enigma machine today if you remove the flaw of not being able to reflect onto itself (which is trivial to do digitally)? Say, compared to modern cryptographic methods.
As an amateur cryptographer, familiar with modern encryption algorithms, I would guess that this "Enigma v2.0" still wouldn't hold up very well. Engima did a very job securing communications in the late 30's/early 40's because the work needed to break the code had to be done by manually. The were no computers that could automate a brute force attack, such as there are today. Which is why it wouldn't succeed now because with a relatively small number of finite initial settings (
Daniel Rogness
Well said dude.
Daniel Rogness
That's why I said "scaled up" because it's obvious that you'd have to use more wheels and stuff. My _guess_ is that rotor machines in general are still subpar in terms of both key length per security and encryption time per security (where security is the time needed to crack the code without having the key). I can't say why that is exactly though. Obviously the rotor machine principle isn't used anymore in software (although it apparently was in Seventh Edition UNIX's crypt) so it's clear there has to be at least one deal breaker with these algorithms but what is it exactly? What makes them that much more vulnerable to brute force attacks than say Blowfish or 3DES?
BTW, I don't think I'd say Enigma has less than 10000 settings since I'd consider the internal setup part of the symmetric key. If you do this digitally, it would be as easy to change the internal setup as it would be to change the wheel and patch settings.
It might work better than you think against casual snooping from the average person. There's not alot of people today that would recognize morse code let alone an encrypted code sent in morse. Also you have to remember the message that was encrypted was in german not english. That alone would probably put alot of people off. taking all that time and care to crack a code would be useless unless you could actually understand/translate german.
Penny Lane Winter Break is coming up soon for University students here in the USA and it might be an interesting way to pass the time by actually making this digital Enigma machine. If I happen to complete it, I can send it to you and if you happen to be as bored as I am, you can examine more closely yourself and see if you can spot how you might be able to break it, if you (a) knew something about the initial settings of the machine or (b) knew nothing about the initial settings of the machine.
exquisite!
4:31 wow that car goes fast jeezus how fast is that thing going mach 11?
What was the name of the similar mechanism that the Japanese used during the war?
I want more videos on algorithms!!!
Once the button is pressed to produce a number, there is no path, right at the switch, for a signal to come back to light up its own light. Independent of reflector or anything else.
@4:07 odometers are driven off a gear in the transmission, not the engine. Engine RPM is not directly related to miles driven.