The Inner Workings of an Enigma Machine

so let's have a look at this machine so i open up the lid there you go and there it is and it's a beautiful thing there it is it's a beautiful machine it's 1930s styling it's all black and silver highlights it's all wooden steel very nice very mechanical but let's see how it works so let's say let's say i send you a message i'm going to send you a messaging code and it should be something in german really should be something about braatfirst or schnitzel or something like that or chardon freud but uh i'll keep you i'll just say hello to you i'm going to say hello to you right so i'm going to type in hello in the machine let's see how it works so when i type in hello i'll do the h first and then i'll press h there we go now if you can see that the letter c lights up the code lights up that's h becomes c let's do the eve hello e there you go becomes an i so this is the code l is an m the second l in hello becomes a queue and you finish it after you do the o and oh look you get an m again that's interesting so that's the code the machine doesn't transmit it never did it doesn't send anything someone has to stand next to it and write down the letters that light up there is a reason it lights up if you built it with a carriage like a typewriter with paper it made it heavier it made it eight times heavier so that was the reason why it lights up to make it portable but you may have seen something odd about that so the two ls in hello were two different letters so old-fashioned codes if you had double letters they become double letters in your code and for code breaker you can use that as a clue helps you work it out but this is different no a double letter might not be a double letter if i do this again if i press a oh my god i've got e there if i press a again i've got l and it will keep changing and there's no pattern to this there's no way to know what it's going to be next so you can see why the germans thought they had an unbreakable code i'll show you how this works i'll open up the lid and i'll show you the inside so you might see these in museums uh there are a few i did check there's two in the in canada uh but now there's three there you go now if i open up the lid here we can have a look at the inside so not quite a typewriter anymore at the top here let me let me point some things out first of all i hope you can see there are 26 little light bulbs here in rows and then we've got these three big wheels at the top as well so those wheels are called rotors and inside these rotors it's full of wires right and all the wires inside are crisscrossed it's all like spaghetti inside all mixed up wires now let's have a look at what happens when i press a letter if i press the letter if you can see that the rotors turn or they rotate which is why they're called rotors so this one on the right hand side moves every time every time i press it clicks when this one on the right when it does a full turn when it does a full revolution it will kick the middle rotor one place you may have seen that happen a little bit earlier let me see if i can do it again i don't know when this is going to happen so if i keep pressing when it does a full turn it will kick the middle rotor one there we go and then it will keep going when the middle rotor does a full turn eventually it kicks the left hand rotor one place so you've got a fast rotor which is going all the time a middle rotor and a slow moving rotor and it's kind of like you've got hands on a clock it's like a minute hand and an hour hand and a second hand kind of like that now it's a very clever machine but all it is well all it is it's just a circuit it does a battery connected to a bulb it's almost the most simple thing you can make what i've got in this top right corner is the battery this is a conversion there with the wires coming out of it that's the battery that's a modern battery we've got in there now but when i press a letter this battery connects to this bulb and it lights up all the wires for the circuit are inside the rotors there but the clever bit is the wires move so when the wires turn the battery gets connected to a different bulb so you get a different bulb lighting up let me do that for you i'm going to turn these wires and now the battery will connect to a different bulb and it will do each time because you're moving the wires i might give you a better idea of that in a second i might show you something else just to say before i do that these rotors actually come out they can swap order so you can swap the order of the rotors each rotor has 26 starting places and i'll show you this as well at the front of the machine we have even more wires there's more wires for the circuit if i pull one of these out it's called the plug board you can see that on my hand there it's like an old-fashioned telephone switchboard it's like an old plug board or a patch board and these wires connect letters up together in pairs now let me try and show you this what i've got over here is great a enigma machine simulator and you can find these on the internet you can google this and you can find these enigma machine simulators and you can use them and they work just like my enigma machine down here but if i do this for you let's try one out uh i'll press a letter here i'll press g for no reason and g becomes j so g becomes j now if i click this button here i'm going to show you all the wires inside the enigma machine now if you remember what i said inside it's full of criss-cross wiring so it might look complicated don't be put off by this this is the insides of the enigma machine and it is it's just full of crisscross wiring but if you can see what i did if you can follow that yellow line i press g so when i press g the path of that yellow line it goes through the enigma machine goes through the rotors one two and three it actually loops back and then goes through the machine again backwards it actually goes through it twice goes through it again and it connects to the letter j and so j would light up but if i keep doing this let's see if i press g repeatedly let's see what happens so here i've got g becomes a what was that an s g becomes an s g becomes an l if i keep doing that it will keep changing because those wires turn and the path of that yellow line changes each time the rotor moves and that's why the letter changes each time but you might be thinking how do you get the message back how does this work how do you get the message back in right this is a good bit right let's try this i'm going to show you how to get the message back again so let's do one more message then uh if i switch to the camera let's see um i'll see i'll keep it short i'll say hi to you i'll go hi how you doing so i'm going to say hi i'm going to send you that message in code so let's do that first let's do the hi so h first so that's a t and i for high is a w t w is your k so someone would write that down they would then transmit that message by radio that would travel by morse code by radio and then miles away maybe on a ship somewhere miles away you've got a second german officer and they're listening to this radio signal and they're writing down the code and it's tw they're writing that down now the second officer has an enigma machine as well they've got one of these machines and their machine is exactly the same as the first one it's set up exactly the same there is something i have to do now when i typed in high this rotor on the right it moved it moved two places so i'm gonna have to reset this machine back to where it started i'm gonna move this rotor back two places so that just resets through back to where it started now i'm gonna type in the code instead i'm gonna type in tw so if i type in the code t t becomes h and if i type in w w comes out and you get the message back again it's very clever it's absolutely brilliant yeah a very clever machine brilliant piece of engineering so it's a code and decode machine if you type in your message you get a code and if you type your code in you get your message back again now like i said you've got these two people here each with an enigma machine they're miles apart and they have to be set the same how did they know how to set their machines the same so that was written down for you if i switch back again the settings were written down for you on a big piece of paper it was actually a big monthly sheet of paper and the settings changed every day of the month so it changed for each day i'll show you what it looked like big code sheet looks like this and on the left hand side if you can see that that's just the date we've got 31 30 29 and so on that's just the day of the month let me run through how this code sheet works so you've got the date on the left that first column with the roman numerals is your rotors i said there were three rotors and they can swap order uh they were just called rotor one rotor two and rotor three and there are six ways that you could arrange those three rotors so let me do that so there are six ways that you can arrange those three rotors this second column here this ring sterling this ring setting it's called this is something i've not talked about on the outside of the rotor they are labeled with one two three four or maybe a b c d so they've got labels on the outside of the rotors those labels actually turn you can shift those labels they rotate as well so each rotor has 26 ways to adjust its labels if you change that it's going to change your setup so you need to know where those labels need to be so each one has 26 places to arrange it 26 for the first one 26 for the second one 26 for the third one you multiply that together the total number of ways you can set those ring labels is 1576. now this third column here these pairs of letters uh what we've got here at the front then that's the plug board and that makes pairs so this pairs of letters here this column with pairs of letters are the instructions for setting up the plug board so those are you putting your pairs together you actually had six pairs of letters at this point you would make six pairs and the total number of ways that you can make six pairs of letters out of the alphabet this is the biggest number they were quite pleased about this when they added this it is this number which i think is a hundred billion yes a hundred billion ways that you can set the plug board at the front of the machine the final column it's called the ground setting that's pretty much the rotor starting position so each rotor has 26 starting places 26 for the first one 26 for the second one 26 for the third one so total number of starting positions is again 17 576. if you want to know the total number of ways to set up this machine you would multiply that together and the total number of ways is about 10 000 trillion there are 10 000 trillion ways that you can set up the enigma machine they were quite pleased about that so you can't check them all it's not possible now if you've understood most of that i hope then fantastic few there is one more thing i need to tell you because it's there is one more thing you see there would be dozens or hundreds of these enigma messages being sent every day and if they were all being sent using the same key the same setting then that would be bad security that would be a very bad idea so they didn't do that each message actually had its own secret starting position for the three rotors they all had a secret starting position for each message let me show you how they sent that secret starting position so first of all they would set the enigma machine to the ground setting that was written down for you on that sheet of paper so you would set that so let's say the ground setting is xyz you'd set your machine to xyz the operator could then pick his own secret starting position and maybe the operator chooses to pick abc it can be different for every message but let's say he picked abc he's got to send that secret in code and that's what he would do he would send it to the other guy in code at the beginning of the message and he would use the enigma machine itself to encode those three letters abc so he would type that into the machine in fact he would do it twice actually do it twice so abc abc and it would turn into six letters of code in this example i've got jte qgl he's got six letters of code and he puts that at the beginning of his message at the other end the other guy with the enigma machine will then use his enigma machine to decode those six letters and he would get abc abc and then he would know that that's the secret setting for the rest of the message and so each message had its own secret starting place you

Channel: Perimeter Institute for Theoretical Physics

Views: 392,828

Keywords: Alan Turing (Computer Scientist), History Of Science (Field Of Study), History, Mathematics (Field Of Study), Enigma Machine, Bletchley Park (House), Physics (Field Of Study), WW2, England (Country), United Kingdom (Country)

Id: mcX7iO_XCFA

Length: 14min 4sec (844 seconds)

Published: Mon Jun 23 2014

Reddit Comments

[u/BrotherSeamus]

Full lecture here

Related Numberphile videos previously posted here.

[u/Mr_Calvy]

The inner machinations of my mind are an enigma.

[u/themcgician]

Nice video, that was really interesting!