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Alan Turing & Enigma
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0:00
a movie has just come out called the imitation game starring Benedict Cumberbatch as Alan churing and Kira knly as one of the uh team that worked with churing her name was Joan Clark 5 minutes and 34 seconds you said to do it an under six and I'm sure many of you know Alan churing worked at the government code and Cipher Center at Bletchley Park throughout the war right from when it broke out in 1939 right through until the end of War 1945 Alan Turing was at Princeton doing
0:36
research with another very famous mathematical logician called Alonzo church he returned from Princeton in 1938 but even in that year from 38 to 39 is very clear that he was contacted by GC and CS even though he wasn't employed by them and became a sort of consultant became acquainted with all of the difficulties that were going to hit the allies when war broke out has seemed inevitable in deciphering German ciphers that have been done on this Enigma machine now an awful lot of the material
1:11
that I'm going to be using today really uses as a reference book this one by Andrew Hodges it's called Allan touring the Enigma this has been reprinted republished I think in a slightly New Edition because the imitation game is based on this account of Ching's life now enigma goes back a long way prior to its use by the German Armed Forces it was just a simple commercial Cipher machine and it was a pretty reasonable system but I suppose you could say that the number of possibilities the the
1:44
degree to which it scrambled up the message was considerable but not Ultra Ultra safe I think it was a machine that as they say in the cryptological trade was designed to discourage casual snooping rather than to withstand serious attention from experts in the field and what I want to do is to go through with you in this video the components of the system and then in a later one summarize and say that's the pro the problem they were up against how do you make a machine that could help you
2:20
decipher that code if you didn't know the settings of the machine that have created it in the first place I'm going to cross refer you to some footage of on our sister channel number file James Grime has done a couple of videos on number file which actually use a real Live Enigma machine that belongs to Simon Singh the lucky James gets to use the real thing and I would strongly recommend if you're puzzled by all of this go and watch those two videos one of them is just a generalized
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introduction to the Enigma the other one explains precisely why the Enigma machine's big flaw was that it could never encipher a letter as itself believe it or not that is a big big security flaw and does provide a way in for people who want to crack that particular code the Enigma itself looks at First Sight it's a bit like an ordinary typewriter it's called a typewriter board layout there typewriter keys but you then notice that if you switch it on and it is battery powered
3:21
in the area just above the keys instead of having 26 further Keys you have 26 places where a lamp can light up a letter so you might press a t and it will light up as a g what else is there inside this machine how does the key press get through to illuminating a lamp well in the most amazing UNC convoluted way there's a set of rotors here these rotors have 26 alphabetic letters engraved around the circumference sometimes you don't get letters you get numbers 0 1 through to 26 but it comes
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down to the same thing in the end when the lid is closed on top top of them the letter as it were pointing upwards on the rotor anywhere between a to zed shows up in three identical looking Windows perhaps the easiest way to think of it even for those of you viewing who are relatively young can you remember back to your family's first ever car where it had an oldfashioned odometer you know a mileage indicator on the dashboard which wasn't all done in electronics it was actually driven off
4:26
the engine and you actually had little wheels moving in front of you and on the right hand side would be the tth of a mile or t of a kilometer and every time that had got up to nine it would nudge the dial to the left of it to move on one place and so on the principle is exactly the same on the Enigma the right hand rotor moves the fastest and at a certain stage will nudge the next one into moving on a notch the left hand rotor is the slowest moving of all and
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once the lid is closed on the Enigma all you see is the letter on the rotor that's uppermost showing through the windows at the top now complication upon complication within each rotor there is if you like on the two sides an input stud and an output stud and they are Crosswire if you could break open as it's shown here the rotor mechanism you would see a whole bunch of 26 wires in there which are cross-wiring an input stud to an output stud so you might get a cross-wired to J B Crosswire to q c
5:40
Crosswire to W something like that when Enigma first came out there were three sorts of rotor wheel numbered one two and three in Roman numerals typically in the German instruction manuals a rotor of type two would not be cross-wired in the same way as a rotor of type one and similarly a rotor of type three will be a completely different cross wirring I think many of you will know the number of ways you can arrange three things on a spindle like that is three factorial
6:10
which is six six possible orderings of the rotors on the spindle so you can begin to see the multiplication of the number of combinations about how this thing could be set up in the first place you've got different orderings on the spindle you've got different cross wirings within different sorts of rotors so the very basic machine then that was just about it you fed the signal through the rightmost rotor through the middle rotor with a different cross wirring and
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mapping through the left hand rotor and then there was what the Germans called a reverser sometimes in English called a reflector what it would do was to return the signal back via a different stud on the left hand rotor so it would take a different Journey back through the machine to the way it came in now here is the secret of why it never mapped a letter to itself it couldn't because to make that effect happen you'd have had in the reflector drum here to say ah
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it's coming out of the a slot I'm going to return it back through the a slot it wasn't electrically set up to enable you to do that you effectively had to decide to cross Crosswire in that reflector to something different and I think here if you look carefully a is actually cross-wired to something like w now in the early three rotor Enigma that reflector had fixed cross wirings uh which was the same on all Enigma machines so your current goes back through a different route and then
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finally lights up a lamp on the lamp array just ahead of the keyboard over here so that's the way it was up until about the mid-30s but then as the German armed forces were taking more and more interest in these things and saying oh if we could beef them up these could be made into military grade security devices they did two things first thing they said we're not just going to have three rotors in six combinations we're going to do the following we're going to
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invent two more rotors called four and five amazingly here's what you now do we will choose any three out of those five rotors well the ways of picking three from five is 5 * 4 over 1 * 2 5 factorial over 3 factorial the answer is 10 but for each of those 10 ways you can still jumble them up in six ways on the spindle 10 * 6 is 60 so classic Army Air Force Enigma use this pretty well throughout the war you chose three from five and the three you chose could be put in the spindle in a certain way
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now comes the real killer if that wasn't bad enough the Armed Forces decided that on the input to the machine and on the output they would have another cross wiring board called the plug board now this one's simple to understand it's basically got sockets numbered from a to zed and you given chunks of wire if the instructions say cross link a to J that's what you did cross link B to R you did that as well usual operating practi ice 10 out of 13 of those plugs would be cross wide and wired up you
9:35
could wire up in pairs but you didn't absolutely have to wire up everything if you left something unwired or un stered as they would say in German then that's fine I mean the letter Q might have no plug in it going absolutely nowhere fine so Q maps to Q it's not not altered to anything else at all but like I said typically 10 of 13 will be wired up so this is getting to be a pretty complex machine now and you would think by golly surely this is enough security for
10:10
anybody well what's good enough for the Army and the Air Force in almost any armed forces in the world is never good enough for the Navy I think it's that case in the UK it's certainly that way in the US and it certainly was that way in Germany Admiral Carl dunit who was the head of the German Navy was a very smart guy some people theorize and maybe they're right that he strongly suspected as the war went on that maybe Army and Air Force Enigma was being decrypted
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successfully sometimes by the allies and he was determined to make the the German Navy version of enigma far harder so first thing he did was say all right we'll stick with three rotors for the moment but it doesn't choose three from five it choose three from eight and by the time you worked out how many ways to pick three from eight and then multiply by six for the number of ways you can arrange the three you've chosen on the spindle the answer is 336 and that's daunting one of the
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things that I think does need a bit of careful explanation it's not very well done in the various books about Bletchley Park and Enigma and how it worked is to explain what these so-called ring settings were now the straightforward internal wiring is simple you just look at the top row and for every letter you follow vertically downwards and you say okay in a tip one rotor a on one side gets mapped to e on the opposite side b gets mapped to K C gets mapped to M all the way through to
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zed gets mapped to J but to complicate matters just a little bit further every one of these rotor Rings had a little blob of paint pain associated with it showing which was the proper setting with a at the top and a against the dot of paint but it had the ability to be able to turn the thing in such a way that instead of a being against the canonical blob something else was so you could set a little Notch that held it in position but in a place that actually
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was not the standard position if you put your button your ring setting button against the letter B it had the effect of making a map across to what B would normally have turned into B would normally have turned into k b goes to m c goes to f d goes to L and so on it's just an offsetting mechanism it's just moving as it were the bunch of wires inside the rotor so that is what a ring setting is it's basically an initial offset that changes the mapping ever subtly makes things even more
13:03
complicated final bit of complication now just so that we're completely mind blown and think how on Earth could this ever be decrypted by anybody that you might think that just as a car's odometer would go all the way up to nine on the right hand side and the moment it turns over at nine it would nudge the next one on on the left some bright spark had the idea that it might give more security if you made different wheel types have different turnover points and theit's extra rotors 6 s and
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8 even worse they turn over twice once at Zed and once at M in the middle of the alphabet actually it's not a good idea if you think about it and I'll tell you why imagine you know because you've done a lot of work on this you're pretty sure that at the moment the machine has got a type one Rotor at the right and you also pretty sure from the Crypt analytical work you've done that but it's currently on the letter N you then type in three more of the received
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Cipher text letters and you suddenly see you suddenly find things going completely weird this isn't just the same wheel turning something's happening it shouldn't have come out looking like this this sequence oh it's turned over the middle rotor so if I think it was on n and it's turned over the middle rotor on a Q then it follows that that rightand rotor must have be of type one and I wanted to know that all along so these turnover points because they weren't all at Zed to a
14:42
which would have made it all look uniform you know whenever anything turns over it that's the way it does it has this little signature that if you're very careful in your crypto analysis gives the game away how is this all gathered together if you were very lucky in the very early days of the war you didn't even have to try and crypt Analyze This incoming cyhex traffic either by hand or by Machine if you could do what Bletchley Park called a pinch you could actually get a secret
15:12
agent or an army officer to just accidentally be able to get hold of the code tables issued to the German Armed Forces you didn't have to do any Crypt analysis at all either by hand or by using this very expensive Machinery that we'll be talking about next time electromechanical bomb you didn't have to use those it's all here but as James makes very clear in his videos if you did get that bit of luck it never lasted long you maybe got a month's worth and then it ran out or somebody back at
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headquarters said I'm not happy one of our code books seems to been stolen and disappeared tell you what even though there's 6 months to go on it we're throwing it away and we're resuing another one just to be on the safe side we've assumed and it's quite right that but the good thing about Enigma from the Crypt analysis point of view it started off Life as a commercially available totally open machine so you might think well the wiring inside those rotors then
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three of the rotors at least one two and three will be known yes but of course the moment the uh lft buffer and the Army start introducing two more rotors you've then got the problem of can we steal these things or do we have to work out from first principles and with rather a lot of advanced group Theory and Mathematics and a lot of known Cipher text and plain text and all sorts can we work out what the wiring is in those rotors without actually having them and the answer is eventually yes
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but it's very very nice if somebody helped you on this front what did you need to know in order to decrypt a cipher stream done with Enigma that your listening stations had picked up it was transmitted in Morse single letters sent to Blackley Park what do you need to know to make any sense of this number one which rotor wheels are in use number two what is the ordering left to right of those rotor Wheels number three for each of those rotor Wheels where has that stud been located that does the
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ring setting against which letter fourth thing which we haven't mentioned very much but which in the next video we'll say a lot about the operator himself usually himself not herself had to also do what was called a message setting for this particular message every separate message had to have a different message setting it wouldn't have been safe just to keep using the ring settings alone without any alteration to those so that had to be worked out as well and finally last
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but not least the plug bard board cross connections had to be worked out now that's a lot of stuff in the very early days of simple Enigma whether we only three rotors not chosen from anything else just three we'll find out next time that the Polish Cipher Bureau had a lot of success by hand and with a very simple machine in getting things decrypted but the moment you start adding more rotors plugboard and all the complications you rapidly find that you just don't have enough time in the day
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to decrypt all that you'd like to do the sheer weight of Cipher traffic takes over you have to
18:39
mechanize the wires of the circuit are inside the rotors so when the wires turn the battery will connect to a different bulb let's try and see that happen six options are wrong that means your rotor position is wrong and what you do is you go click you check the next rotor position and you go through all that again
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