Cracking the Cipher Challenge • Simon Singh • GOTO 2016

I will talk about the codebook but in case you haven't read of any of my books I thought I'd start by just telling you a little bit about what I do and why I do it my backgrounds in physics so I love science and I love technology and I love math but I now write about anything to do with science so I've written a book about alternative medicine very slightly offbeat topic for me but I'm worried about alternative medicine I think there's some risks and some dangers some are alternative therapies do work but potentially dangerous so this book I wrote with a doctor called ed Zod earnst I've written a book about pure mathematics about fair Mars Last Theorem I've written a book about The Simpsons and so on and I write about these subjects because I want to get other people as interested in science and technology as I am so this is the kind of stuff I do I mentioned this book do I mention this book I mentioned this were briefly one of the things when I write these books for kind of general the general public is I try and tell the stories of the scientists as well as the science so I tell the human stories as well as explaining the science and another of my books is the code book and then explain that I talked about how cryptography has evolved over the centuries you know suddenly makes a code somebody breaks the code somebody makes a better code somebody breaks that code and so on and so on but rather than looking at the whole history I thought I would look at the back of the book at the back of the book there was something called the cypher challenge and the cypher challenge was a competition there were ten coded messages from ten periods of history some of them were the early ones are very simple and very ancient and the later ones were very modern and very difficult and the idea was that children could break the early codes but if you were really serious and you broke all the codes then you could win ten thousand pounds okay and the competition was eventually won by some Swedish they were actually jugglers in London on a conference a juggling conference but one was a computer science this one was a number theorist one was a crypt analyst one was an electrical engineer one was a computer scientist they went back to Stockholm and they worked on these 10 codes and they won the money they won the competition and and when I wrote the check I tried to write it in code in the hope they wouldn't cash it but they they still will able to cash it so they got their money and these are the 10 codes they had to crack so this is a two thousand year old code this is a thousand year old code this is a 500 year old code 200 year old and so on through to the First World War Second World War right up to the 70s and 80s so this is the challenge that people had to crack and I'm just going to look at some of these codes and explain to you how how they were cracked and so on this was the first stage a very simple monoalphabetic substitution cipher you replace every letter with a different letter now that that code would have been unbreakable 2,000 years ago but it was broken the first document we have on crypt analysis the first code breaking document we have is this one here by an Arabic mathematician called al Kindi who was living and working in Baghdad and this document was only found about 20 years ago in Istanbul and in this document what al Kindi says is that every letter has a frequency so this is the frequency for English I think in German he is even more common and Zed's probably a bit more common the distributions change but for each language the distribution is is really distinct and so if E is the most common letter in English and X is the most common letter in the ciphertext then you kind of know that X must be e okay so today that's fairly obvious to us but when our kindy did it when al Kindi worked it out it was revolutionary and it gave gave him in his his his compactor it's a huge advantage in breaking the codes of their rivals so that was first stage one that was easy - even though that code was broken a thousand years ago by our kindy it was still being used by Mary Queen of Scots about 500 years ago she was a Catholic Queen of Scotland who wanted to become she was also Queen of France briefly and she wanted to become queen of England and she was a Catholic and Elizabeth the first at the time was a Protestant and Elizabeth was scared that Mary would overthrow her and become Queen so Elizabeth put Mary in prison to keep her safe and locked away but while she was in prison she sent out these coded messages to people in Spain and she was saying to the Spaniards come and invade England and let's get rid of Elizabeth you know make me Queen make me the rightful queen now these letters were were encrypted but they were intercepted they were given to Elizabeth's code breakers they pretty much follow a simple substitution cipher Elizabeth code breakers were able to break the codes it was clear that she was committing treason she was put on trial for treason she was found guilty and then executed so you can see how important the making or the breaking of a code can be it can be a matter of life and death in this situation let me jump forward in time stage so state one was easy stage two was easy three and four a bit tricky but but really most teenagers I think could do three and four five was the really tough one five was the first one that really stopped people in fact nobody could break this code for six months and Stage five is what's known as a book cipher and the way a book cipher works is you take a book and you number every letter in the book one right through to the end so it may be a million letters you may have a million numbers next to each letter and then what you do is let's say my book is A Tale of Two Cities it was the best of times it was the worst of time so I'm numbering every letter one two three four five six seven eight all the way up to a million then I take my message my message might be meet me at midnight so if I want to encrypt the M well here's an M here I repeat replace M with 17 e he's an e here I replace II with 8 I don't replace II with a number 8 because I keep with eight then it becomes obvious so I find another e here's an e that's number ten I put a 10 here T that's a two and so on okay so every time I come to a letter in my message I find a letter in the book and I replace it with that number and this code is almost unbreakable unless you can guess which book I've used you will have no hope at all now I could have made this code unbreakable I could have just gone to my library and picked a book at random and nobody would have been able to break this code but I picked a kind of a try I didn't want it to be unbreakable I wanted to give people a fair chance so I picked one of my own books okay I picked a book called fair miles last theorem which is my first book and but but but I didn't number it from the beginning okay because if I numbered it from the beginning if you have the Dutch edition of the book it starts differently it starts in Dutch if you have the Swedish edition it starts in Swedish so I couldn't number it from the beginning that would have been unfair so I identified a part of that book which is the same in every language whichever translation you have it's the same I picked a part of that book that must be at least 217 letters long and I picked a part of that book that's so famous that even if you don't have the book you can find this passage on the Internet and if you apply those criteria then you realize that the story of Fermat's Last Theorem is a French mathematician called pierre de firma who solved a mathematical problem but he never told us the answer and he wrote in the margin of his book a message that was about 217 letters long it's a message that's so famous that it's on the internet everywhere and it's a message that was written in Latin so which which ever Edition you have you will have that Latin quote if you don't have my book than you it's on the Internet in a million places so it's a very very famous Latin note ferma says I can solve this problem but I'm not gonna write down the answer and if you take that piece of text and you number it up and you you you reverse the encryption then the message just falls out very easily okay but nobody could figure that out it took six months of work before one person in Cambridge figured out that that that decipherment his name was Andrew Plato and if somebody broke one of the stages they would email me and I would have a bulletin board and I would have whoever was leading at that stage would be top of the board and so Andrew Plata emailed me he was right so he went to the top and other people I would drop into other discussion forums and other people were saying well how come Andrew plate is so smart how come Andrew plate is ahead of all of us how come he knows something we don't know and this conspiracy theory began to develop and the conspiracy theory was that Andrew Plato was in Cambridge and I was in Cambridge for a while Andrew Plato did his PhD in Cambridge I did my PhD in Cambridge and people began to figure out then what's the connection how I know what did Andrew play to have access to and as a result of this conspiracy for the first time ever people went to the library in Cambridge and read my PhD thesis they've never read it before or afterwards so for anyway so that was a five stage six was seven was was again six or seven were his trickiest age five actually it turns out but stage eight is the one I was going to concentrate on which is the enigma cipher so the enigma cipher is famous for lots of reasons but one of the reasons it's important in the history of cryptography is because here it is being used by the Germans in the Second World War I think that's general Guderian and here is a close-up of the machine you can see it here and the reason why it's so important in the history of encryption is that in the First World War you have a revolution in communication you have Ray for the first time people can send large amounts of traffic instantaneously over vast distances but on the other hand other people could tune in their radio sets and listen to everything you're sending so you have this technological revolution in being able to send data but you need something to be able to protect that data and so the Enigma was developed as soon as the first world war ended really in the years after not just the Enigma there was a Swedish encryption device there was an American encryption device have a feeling that may even have been a Dutch one and people trying to develop these technologies but all of these companies went bankrupt apart from the Enigma company started by arthur scherbius he was just about to go out of business but then the German military machine began to gear up and they wanted his machines in large numbers and so every railway station every army battalion every u-boat every airbase had to have one of these machines okay and the way it worked was a three-person operation so you can see here you have somebody has the message in their hand and he reads out the message this person types it into the machine here's a keyboard their lights light up here so you might type in hello and the lights bvz QA might light up he writes down B vqz a he gives it to the radio operator and then the radio operator sends bvq z-day at the other end the radio operator takes down BV Keys la somebody reads that bvq said a he types it in and the left lights hello light up okay that's how the Machine worked now I'm fortunate enough that I own an Enigma machine and I fortunate enough that I managed to get it through airport security today and it's here and so yella if we can switch to this camera oh great so it's this is a genuine enigma cipher machine it was captured in northern France at the end of the war by an American soldier he was also cryptographers so when he saw it he knew exactly what it was and he just picked it up and took it back to America and it lived in Texas for about 60 years and this one was built before the war started it was built in 1936 and some 80 years later it's still working pretty well so we can type in a letter if I type in the letter O the letter D lights up can you see a deal I tap great okay you can see pretty much where I can see so I type an O a d lights up if I type again a lights up if I type again our lights up and then age so it is a pseudo-random letter generator I'm typing in the same input but I'm getting a different output each time so why is that happening well if we lived if if we lift this lid here you can see the lamps here but more importantly behind the lamps you can see three rotors three drums and I can take those out if I take the first one off here you can see it's got 26 contacts and on the other side it's about twenty-six contacts so when I type in the letter A it goes in at the top contact does ABCD efg background to Zed type in a it goes in at the top but doesn't come out at the top in the middle of these discs the wiring is like spaghetti so it goes in as an A it might come out at B it might go to the second one is B it might come out as M goes into the third one is M and it might come out as a J okay so the scrambled wiring inside these rotors is what changes the letter but on its own that doesn't explain why the output keeps changing because if I keep typing a it would follow the same electrical path and you have the same output I think I said the output was an M but the reason the output keeps changing is every time you type a letter this moves one step so you type a it goes in at the top but that's a different contact so it's a completely different electrical pathway type A again it moves goes in at the top different contact different electrical pathway different output so it is the dynamic nature and when that does a full revolution it kicks the middle one okay so it's a dynamic nature of the wheels that really causes the changing output in fact if I operate it with the lid open then you'll see you'll see that happening so I type O again and you can see the first roaster move sometimes you might see the second rotor kick over as well every so often that will happen but I won't wait for that to happen but you can see that that rotor is moving and that's the reason why the output keeps on changing so that's how the encryption works essentially but how does decryption work well if you want to decipher a message sent with the Enigma machine you need to have the Enigma machine but you also need to have it set up in the same way now there are lots of ways to set up the Enigma machine this wrote this wheel has got this roughness axle sorry this axle has got three rotors so I could move the rotors around to different permutations so in this case I have three objects and three positions that gives me just six permutations but then I can put them at different orientations 26 26 26 26 cubed is about 17,000 times the six permutations is a hundred thousand now where this wheel kicks the next one I can change where this wheel kicks the next one I can change this one doesn't have a wheel to kick but that's still a factor of 26 and another factor of 26 that's a hundred thousand times 26 is two and a half million times 26 is 50 million so this little thing here has 50 million different settings okay and then on top of that I don't think you can see it very well but just in here there are some plugs and what the plugs do is they swap letters around so if I plug a with B it means every time I type a it follows a path of B and every time I type B it follows the path of a and I can change the way those plugs are set up and I think there are 20 plugs so I could swap 10 pairs of letters and that has a hundred million million different settings okay so this the permutations here the combinations here are much much bigger than the combinations here but these don't change once you've plugged it that's it it's fixed for the day whereas this is continually changing so it's really that the large number of permutations here and the the dynamism of the of what's going on up here coupled together is what gives you the security but if you have an Enigma machine and you have it set up in the same way then encryption and decryption is pretty simple let's try and send and decipher a message let me close the lid I just pick a simple setting to pick this one two three maybe two three okay now if I type the message okay Oh gives me a s and K gives me L so okay is SL okay so you get SL you think well what is SL mean well your machine has to be in the same position so I'm going to move that back two spaces one two now if I type in SL I should get okay s gives me o and L gives me you get the idea yeah yeah so so it's pretty reliable too sometimes the contacts get a bit damp and they don't they don't work and we one of the nice things if something goes wrong like like now the wheels are moving the keys are pressing down the plugboard might not be connecting so one things you can do is you if you keep your finger down you can do a walk-through test now that wheels are not moving over so nothing's changing so that gives me an opportunity so by typing the letter T I know there's something wrong so I can begin to investigate T a bit further without anything changing if I think a bulb is broken there's a nice feature these bulbs are all originally these bulbs 80 years old and the spare bulbs at the top are all original as well but if I think a bulb is broken then I've got a battery tester here if I think a cable is broken I can test the cables as well there's just nice contacts for testing cables if if I think the battery's flat I don't need to change the whole battery completely I just have an external power connections here so I can just put externally connected to power and see whether that's the problem so it's it's well-designed in terms of troubleshooting and trying to figure out what what what's gone wrong as the machines open and as we've got it on camera now might be a time if people have questions I'm happy to take them now if people have one or two questions you can just shout them out if yes how do they share the key so every month there would be a piece of paper and every line would be a different day so today is the 15th so let's say 15 pick rotors I've only got three rotors here but there may be five or eight that you could choose from so it's a might pick say pick rotors 1 4 and 2 in that order put them in orientations C F and K make the kick over points m and W and this is the plugboard settings and if we're in the same network we might be north atlantic or we might be north africa everyone in our communications network would have that piece of paper and every month somebody had to deliver that piece of paper so you can imagine there were motor bytes going across a Sahara and that's a huge risk you know that person may be hijacked they may be a double agent they may be just incompetent but you know the security relies on that bit of paper not falling into the wrong hands and there were times when those bits of paper were captured and we then put to good use and if you do capture it you kind of want to capture it at the beginning of the month not at the end of the month although that's still very useful yep so why is it why is it symmetric okay so one of the things I didn't mention is it actually goes through the wheels twice so I've missed out a few different things but but but that's a very good point this thick wheel at the end it actually sends the wire back down a different path that's called a reflector so let's say it comes out the three wheels as an M it will send it back as a P and it follows the electrical wiring back again it might come out as a as a Q but that means if you type Q it goes through to a P gets reflected as an M and goes back as an A so that is what and that's a really crucial thing I'll come to that a bit later so thank you for that point maybe one last question or I'll I'll push on I'll be around afterwards if people have other questions and do come and catch me but I just mention one other quick thing while we've got the camera here if you're working at night the risk was that the lights the board might give away your position so a sharp-eyed sniper might be able to to spot where you are so at night they would often use if they're working outside they would often use this piece of just green plastic so the idea is you just place it over the over the lamp board and now if I type L ya V has just faintly lit up so this is a there are a few of these machines around but what's really nice about this one is that it's kind of got everything that it had when it was built and all the serial numbers match and so on so as I say I at the end of the talk I'll just need about five minutes to put it away but if people have questions after that I'll be at the back of the room but let me carry on with the story quickly so the story of the enigma here here this is it may be just a useful graphic for showing you how it well if we can switch back to the PowerPoint that would be great yella if yellows there are great some ones look great yeah this graphic might help if I haven't explained it very well here is a six-letter keyboard that's what the rotor looks like I type a B the B goes in here it goes up there up there and it lights up as an A then then this wheel rotates so now I type B again the wiring looks different so it comes out differently comes out as a C and in this one you can see the reflector that I talked about a second ago so you type in an A there's the plugboard as well here the a is swapped was a B and this comes through here through here through here through here through here through here through here gets reflected back down a different path and comes out or it comes out as a C so that gives you an idea of what the wiring that's going on inside the machine now when the Germans first started using these kinds of machines people thought they were unbreakable then the shin numbers involved made it look like an impossible task to try and break the Enigma and the French and the British and the Americans and everybody's just just didn't even bother trying the only people who did I am break the enigma before the war with the poles because Poland you know because of its geographical location with Russia on one side in Germany on the other it knew that it was going to be in trouble sooner or later so faced with such a desperate situation the poles tried to break the Enigma and they made a very important decision which was to bring mathematicians into code breaking prior to this code breaking was all about linguistics and and and and you didn't see mathematicians or engineers or scientists involved at all although Charles Babbage worked secretly on code breaking that wasn't known until about 30 years ago because if you're a code breaker you don't tell people yeah so there were scientists involved in it but but it wasn't very common and it wasn't very public and the poles were the first they say right we need mathematicians we need lots of them and we're going to try and break the Enigma and they made significant breakthroughs before the war even started and just before they were invaded they smuggled out their their ideas to the French the French passed them on to the British and before the war started the British set up a code-breaking center called Bletchley Park and they started well they had a great head start thanks to what the Polish code breakers had given them and you can visit Bletchley Park it's about a 40-minute train ride outside of London and right next to Bletchley Park is the National Center or the National Museum of computing which is also really really worth visiting they've got some terrific stuff there and there's some silly rivalry between Bletchley Park and the National Museum of computing and they should really patch up their differences and be friends but you have to visit them separately unfortunately but yeah this is the code-breaking center of Bletchley Park and this was the very first visit to Bletchley this photo shows the very first visit by government officials who went there to bless you to see is this place quiet is it secluded is it private does it have good communication links does it have space for adding new buildings and after their visit they were convinced this was a good place to build a code-breaking Center and as the months and years passed this became home to hundreds and hundreds of people who were dedicating their their lives are trying to break not just the enigma code but other German codes and Japanese codes and so on and I'll just speak briefly about how they broke the Enigma so there was a message one day a message was intercepted by a woman called Mavis Beatty and she looked at this message she was a codebreaker and she looked at the message and the message was 200 random letters because the output is kind of pseudo random but it wasn't quite pseudo-random because in the 200 letters there were no w's which is weird because you would expect at least five or six or ten or fifteen w's but no the W's at all and then she realized the only way you can have an output ciphertext which is devoid of any double use is if the input is all double use because if you remember from the question we had earlier know if no letter can ever be encrypted as itself because it goes through the fruit three rotors gets reflected back down a different path it goes back down a different path it can't get back to itself so no letter can be encrypted as itself so if I type in W 300 times my output will be everything except double use so she'd cracked the code she knew what the message was 300 double use not the most interesting message in the world but once you have the message 300 double use and once you have the output which is what you have in your hand to start with with it with once you know the input and the output then you can work out the exact setting of the machine okay because you normally you don't know the input and you don't know the setting all you have is the output and you have two big unknowns once you know the input and the output then you can work out the only unknown which is the the machine machine setting and she figured that out she could then go back and decipher other messages that were sent that day and one of the messages that she deciphered was about an attack on the British fleet at Alexandria the British fleet were warned and as a result it was the first allied victory in the Mediterranean all because of this message being deciphered now that one so the first question is why would somebody send w 300 times now the reason for that is if you if you think if I've got an unbreakable code and I'm sending it across a battlefield and you you just can't break my code you've got no hope but what you can do is you can count the messages and if you see I'm sending one message on a Monday one on a Tuesday one on a Wednesday but ten on a Thursday then you know something big is going to happen on Friday and that's called traffic analysis and just just by traffic analysis you can begin to know what's going on in my head or what we're planning so i combat that by sending ten messages every day and if my traffic is flat you can't your traffic analysis is no good so when somebody sent 300 w's they were probably just maintaining their quota for the day yeah if they sent a random message it would have been fine but they didn't they sent something that was utterly predictable or deductible deducible so that that worked once but it wasn't something that you could rely on and what Alan cheering did what his great contribution was was to say that with a lot of messages you can't guess what the whole message is you can't guess it's 300 W so you can't guess the whole message but even if you can guess part of the message maybe that's enough and you can often guess the part of the message you know the way the message starts may follow a certain format if the message arrives at midnight it might begin with 0 0 0 0 if the message comes from over there we know the Germans have a weather ship over there then we may be able to guess what terms they're using to describe the weather in that part of the ocean Sochi Riis great breakthrough was to say even if we can guess a bit of the input and match it with a bit of the output that will help us work out the settings of the machine and he built machines called bombs to help sort this out and as a result of his work and many other works and many other breakthroughs it came to the point where the Bletchley Park code breakers were deciphering messages almost as quickly as they were being read but by the German military and I think it's almost gosh 10 - let me just wrap this up fairly quickly I'll just make two or three points before I finish as I said it was Alan Turing who broke the Enigma working with many many other people and Alan Turing never got any credit for his work and he took his own life in the 1950s because their sexuality he was being handed by the police and by the government security forces as well to some extent but he never got the credit for his work and neither did many many other people and people often wonder why why didn't you know enigma the breaking of the Enigma was kept secret not just during the war not during the 1950s not just the 1960s but it wasn't until 1973 that the story of Bletchley Park began to emerge so people often wonder why was this kept so secret for so long and the reason for the secrecy was that as the war ended the Allies captured lots of these machines this machine was captured and many many others were captured and they were brought back to London and they were kept in the government offices in central London and the government civil servants the government workers would would ring up other countries such as Australia and Canada and they would say to these friendly countries they would say look you know you're our friends and we've captured lots of these German machines and the Germans say they're absolutely unbreakable why don't you have some so the British were giving machines to their friends because the British knew they could crack these codes okay and so the British could spy on their friends in the 50s and in the 60s and that's why this was so top secret for so long I just ran out I'll just wrap up the story of the cipher challenge quite quickly start stage 10 of the of the V of the challenge was an RSA cipher and these are the Swedish code breakers who cracked the code cracked all 10 codes and stage 10 was obviously the hardest one and it involved RSA so you had to factor a very very large prime number and it was pretty much the biggest number that had ever been factored it wasn't much bigger than the record so I knew that people could factor this number if they tried but it would be really tough and they came up with some new ways of implementing factorizing software and did some really clever things and they factored the the the the the large number and they could break the RSA actually if you decipher the RSA that gave you two keys and with those two keys you could undo another code called Triple DES okay so let me just tell you what Triple DES is so so des was a the data encryption standard it was a form of encryption that was developed in the 1970s in America and it was kind of the standard form of encryption that was kind of shared around the world but then des became weak by by the mid 80s probably and so des was replaced by Triple DES so with Triple DES you apply des once with one key and then you you decrypt but you decrypt with the wrong key you have a second key so you decrypt with the wrong key so you're making even more encrypt it and then you re encrypt with the first key just to get it in the right format okay and that's Triple DES and this is unbreakable you will never break Triple DES or nobody at the moment can break through all days but you didn't have to break triple des what you're supposed to do is factor this not number under the RSA the RSA would give you these two keys key one and key two and then you could undo this very easily okay but but the factoring was a mammoth task okay but this was impossible unless you did the factoring but when I went to Stockholm when they won the prize I went to Stockholm to give a talk on how I made the codes and they gave a talk and how they break the codes and I gave him the check for ten thousand pounds but during their lecture they revealed that I'd made a mistake okay and my mistake was that when I did the triple des okay triple des remember you encrypt with one key you decrypt with the wrong key to make it even worse Yuri encrypt with the right key to get it in the right format what I did was I encrypted with the first key and then I decrypted with the first key and then I encrypted with the second key and that's only single des and that could be broken in about two hours okay now luckily they didn't think I could be that stupid so they didn't try this approach until they done the factoring which took them about three months and then when they did the factory and they realized that I've got this completely wrong and and I suppose that that's a really important message is that you know the encryption systems that were used today and Sven mentioned it today that will act them you know a lot of the the technology that we use today a lot of the companies that are successful today would just fall apart and we rely on this effectively unbreakable form of encryption that's often used in so many places but if it's not implemented properly and if human error like like the 300 double use with the Enigma the Enigma was actually a very strong machine and often the way Bletchley broke it was by people doing regimented starts or predictable ends or predictable time checks and so on so whether it's him nigma or whether it's Triple DES or whether it's me and my cipher challenge and often it's the human error that leads to the undoing of these codes if people I think we're probably we took questions during the talk so we probably don't have time for questions now I guess but but if if people if people do have questions or want to come and chat then please just give me about six or seven minutes to put this away and then I'll be at the back of the auditorium but but thank you very much for inviting me to speak thank you

Channel: GOTO Conferences

Views: 12,659

Rating: 4.8857141 out of 5

Keywords: GOTO, GOTOcon, GOTO Conference, GOTO (Software Conference), GOTOams, GOTO Amsterdam, Simon Singh, The Code Book, The Simpsons and Their Mathematical Secrets, Big Bang, Fermat's Last Theorem, Trick or Treatment? Alternative Medicine on Trial, Enigma, WWII, Decoding, cryptography, decipher, Cipher Challenge, Second World War Enigma, Computer Science

Id: T59hl2nlrT0

Length: 40min 35sec (2435 seconds)

Published: Mon Jul 11 2016

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Check out this 41 minute talk from GOTO Amsterdam 2016 by Simon Singh - Science Writer based in London. The full talk abstract can be found below:

In "The Code Book", a history of cryptography, the author Simon Singh included ten encrypted messages with a prize of £10,000 for the first person or team to decipher all of them. Thousands of amateur and professional codebreakers took up the Cipher Challenge, but it took over a year before the messages were cracked.

Simon Singh will be talking about how he constructed the Cipher Challenge and how the winners eventually cracked it. He will also be using the Cipher Challenge to give an introduction to the history of cryptography and to demonstrate why encryption is more important today than ever before. The talk will include a demonstration of a genuine Second World War Enigma machine.