The Ciphertext and Rotor Conundrum

This ciphertext really is almost certainly come from having a number five in the middle and the number one on the right so all we've got to do is to work out what the left rotor is. Just as a very rough color for instance that is, that might be something like there we know e comes up normally Evolet exactly hell and all sorts of things but knowing they known the cross wirings of those two that you're assuming you could work out how the pattern of heavy e's would come out into certain other patterns that would give the game away but only ever-so-slightly would look almost random but not quite. And you had to be trained how to spot the non-randomness what helped a lot of course was when they started building more bombs and even for production work from her three there's no way that the bombs that could build a blast apart were enough they had to start putting them out in other derelict manor houses within about a 20 mile radius. They ended up I think by the beginning 42 with about three of the manor houses full of bombs eventually six by the end of the war.

I think the overall estimates are that there were about 40 or 50 bombs of various sorts in the UK when you added how many of them were built in America because that was the other factor. The plans for all these were handed over to the Americans special relationship all that taken to America and with America not being under daily air raids and having no shortage of raw materials they built I think in the end something approaching a couple of hundred bombs of various sorts.

The interesting story is that in late 42 early 43 I think it was Alan Turing made a journey America and went to see the naval decryption operation and also the the army one as well because there was separate in America not under combined roof as they were at Bletchley. And I think the naval Admirals were really right at the start of the war you know very worried saying we can build this machinery but but you know we're up against it we've got done it's against us he's three out of eight not three out of five now our mathematician people tells us three out of eight turns out to be 336 okay Allen so here's the deal we've got to build 336 of these bombs haven't we.

And now said though you don't you use my bamboo business technique you can sort out which routers you almost certainly have got off the bomb before you ever get on it and then you can make do. I think they thought this was wonderful I think in the end they built I don't know what the compromise was to build somewhere between sixty and a hundred rather than 336 but so high-lead did they think of this technique the Americans that was a very interesting story.

The conditional sequential Bayesian probability bamboo isthmus technique has been classified from then until 2010 that's how sensitive it was. The reason that made it even more sensitive was that it wasn't just used in four-rotor naval enigma where it was important but he fed on into the other machine that we're going to do a separate video about at some stage the well-known Colossus machine that technique was of great use there as well.

One final indication of how they got on top of the problem again from Hugh Alexander with use of the Bamber isms techniques. The sheets and extra bomb time that was the pod everybody wanted bomb time they eventually got enough and what Alexander said I had no idea this took place he said you do realize of course that they weren't all physically in England we had dedicated transatlantic underwater cables between us and the nc our place which was doing naval enigma in the USA so they were very nice.

They didn't have to ship any of their machinery over to us which we wouldn't have never been allowed to do but what we did was we just sent our jobs over to them the ones that we didn't have the bomb time to do we could send them the menu these settings on the bomb plan border to enable you to set up the drums to be of a certain type and in a certain order and ring settings and all that. So the full spec for that menu which we would call program nowadays could be sent over the undersea cable and the result usually came back within an hour and that made a huge difference to the amount of traffic they could get on top of so it's sobering to reflect that just over 70 years ago now it's rather than undersea fiber-optic or anything like that even on good old-fashioned undersea copper cables you were still sending programs into the cryptographic cloud as it were at the other side of the Atlantic.

"WEBVTTKind: captionsLanguage: enhow do you go about decrypting ciphered traffic that uses these enigma machines can you do by hand and what actually happened at Bletchley Park what historically was the order in which things took place this has been very much prompted by the appearance of the film called the imitation game with Benedict Cumberbatch as Alan Turing afraid these men would only see me down popular at school way two of the first people through the doors of Bletchley Park in September 39 were Alan Turing and his colleague at Cambridge another mathematician called Gordon welchman who I think was a year ahead of Alan Turing actually in taking the master tripod and of course getting there first you will find throughout the story Bletchley Park was full of first-class mathematicians even before war broke out the Allies had had a big success in that a German spy had actually defected before the war started and handed over a military Enigma machine and a starter Enigma code book what better tutorial I think he handed it over to the French Secret Service the French contacted the English who were by that stage had moved to Bletchley Park their chief crypt analyst was a guy called Dylan hogs who'd had a lot of success with this stuff going back to this world war but I mean to cut a long story short the the French and the British initially did they just did not want to do know what to do with this stuff war hadn't yet broken out but fortunately the French I think passed it on and the conditions of great secrecy to the Polish cipher Bureau and we and Bletchley Park owed them a lot because they had a team there led by a very very good mathematician called marian rejewski he spotted straightaway that with all of this system of rotors reflectors plug boards it was basically just running through the permutations so what better way to really get to grips with all of this and all of its possibilities than to have somebody with an expert in what's called the theory of permutation groups and marian rejewski was very good from that point of view they were dealing with machines where there were just three rotors six combinations no choices of three out of five at that stage and that made life a lot simpler a plugboard did come along and the poles originally found that they could invent what you might call by hand methods they used a method of perforated sheets and amazingly by sliding these over one another and perforating them according to the ciphertext that you received but as it became more and more complicated it really did need some machinery and full credit to the poles they realize this and they built a machine called the bomba and with the bomba so long as it was only three wheels so long as the weren't too many cross settings on the plugboard on input and output and so long as the initial message setting was transmitted in a way that got bound by the end of 1938 as the Germans realized it was not very secure essentially you chose a three letter word and you sent it twice and even though it appeared at the other end is six cryptographically mapped symbols you know you might type in ins the german word so it's happening twice once once and it would appear as ljq wxz something like that nevertheless if you knew that those first six letters had to map into a repeated German three-letter word boy did it cut down the number of settings of the Enigma that could possibly have produced that so with all those simplifications and weaknesses the poles are able to make a very good start what really blew them out of the water first of all was tragically being invaded of course by Germany how can you run a cipher Bureau and any sort of operation when your country's being invaded but even prior to that the idea of choosing three out of five before you arranged the three on the spindle as we've seen that led to 60 combination they need not six bombi but 61b how's the question couldn't afford it pressure in Poland was such that they probably never get around to building them anyway handing over of the whole situation as to where the bullish Bambara got to God Bletchley Park off to a flying start I mean clearly they were up against bigger plug boards not just three out of five rotors but looking at the naval stuff coming along as looking like three out of eight the whole idea of machinery was an excellent one but he had to be made even more powerful and robust it was driven by land cheering and of course as we now know he was put on the ideal persons to do it not only was he a theoretical mathematical logician while he was at Princeton he'd actually built hardware he loved soldering relays together making his own little replicas of how his Turing machines might work as people will tell you Alan Hodges in the biography says he was hammer fisted he was enthusiastic but not good is it Sean Wiley is colleague in Hatay said very enthusiastic but he was so clumsy he used to insist on using high voltage so luring ions because they were more efficient and he'd give himself electric shocks and if it wasn't an electric shock making him scream he'd burned himself and no enthusiasm but not the person you would want to build your home computer he said look we've got to do this by building a bomb let's call it a bo MBA partly with a nod in the direction of the polls and saying thank you he drew up a specification of what needed to be done you see this in action in the imitation game I'm designing a machine will allow us to break every message every day incidentally but the good thing of course in the movie is that it doesn't have to produce any results it just has to rotate a lot and look very very impressive thanks to a superb effort what is now the Bletchley Park Museum they've actually rebuilt a bomb and it works but let's just explain that for every vertical column of three in this decryption device the top one here on the bomb corresponds to the rightmost drum the fastest one the middle one corresponds the middle one and the bottom one of the three in any column corresponds to the leftmost drum which was rotating slowest of all essentially what you've got is lots and lots of enigmas in parallel as it were and you can try out different menus as they will call different programs basically saying well you see that enigma replica at the top left I'd like to make the top drum be a type two drum the middle one be a type five in the bottom one be a type three because I think that was the drum ordering and on those drums I'd like to make the ring settings you know where you put your little stud to do the initial offset I'd like to make them reading from the top V a and H can you do that please oh and this is where Turing's ideas came in he said look you know we are going to have to get more and more and more into the idea of decrypting by trying to use known plaintext you know if you're listening in to a certain weather station that's sending out in Enigma code you know that phrases like storm and heavy rain and stuff are going to occur sometimes you wouldn't succeed you know you'd have to give up and so no I think that our idea was wrong we'll have to try something else the fact that enigma never enciphered anything to itself was a huge help if you look at James Grimes video you can see him using pieces of paper tape as it were to show ciphertext and showing some guest plain text underneath it and you slide them along and you keep on trying different and if it's a given position a letter in the ciphertext exactly corresponds to a letter in the plaintext then that cannot be right you can't have an A encrypting as an A so you must keep sliding it along this guest plaintext and you might stand a chance at the places where there are no correspondences there's no places where a letter is encrypted to itself and I think one of the stories told was that they sent out an RAF plane to bomb a crucially important light boy at the mouth of a harbor yeah and then knew which station we'll be reporting that back to headquarters listened to the ciphertext looking for I think it's the German would something like alloy - toner for light boy and if you see something saying you know the light boy has been destroyed wonderful you've got known plaintext now allegedly the house itself was nowhere near big enough to accommodate all of the personnel that were needed it wasn't just Crypt analysts and mathematicians it was service personnel intelligence people Clark's admin all that stuff so as well as occupying the entirety of the house out in the grounds there were various huts and different units with different tasks or in different huts the three-rotor Army and Air Force enigma service was based in her six it was run by Gordon welchman and Turing's near contemporary her Cambridge the bigger problem the much harder problem was naval enigma as we've already discovered naval enigma didn't just choose three rotors out of five H o three rotors out of eight massively complicating things and then doughnuts the head of the German Navy being yet more suspicious and wanting his codes to be super secure introduced the idea of a fourth rotor and I think that was particularly so for the u-boat traffic now that was a much harder problem so for a long time three rotor enigma could almost go into production four-rotor enigma was still at the research stage and for some desperate months I think in late 41 early 42 there was a time when naval ending was off the air completely they just couldn't get into it they couldn't decrypt anything I think they were helped eventually by a pinch which was to get a codebook off a submarine that had been depth charge shattered by depth bombs the stricken reader is abandoned one of dozens that are meeting the same thing and gradually as their skills built up they were more and more successful with naval enigma but I think you could say even right to the end of the war it was always harder than doing the Army and the Air Force stuff so what he came down to then Bletchley was hut 6 3 rotor enigma at 8 navel for rotor or three rotor enigma all done in hut 8 under Alan Turing now when you now look at the imitation game you will notice that it's all centered around Hut eight massive simplification they merge Hut six personnel in with Hut aid personnel they mentioned Hugh Alexander the double British chess champion quite right he was there without insuring in hut 8 they mentioned this wonderful extension to the back of the bomb called a diagonal board which helps a lot it was a bright idea and the implication is given in the imitation game that this was invented by Hugh Alexander no it wasn't it was invented by Gordon welchman of hurt sakes but this is Hollywood for you you have to live with us yes there was a guy called Jack good in cut eight you'll see him in the movie as well he was a very good statistician almost as good as Alan Turing himself and was also good at chess but not as good as you Alexander and yes Joan Clarke it's not an artificial oh we must have a woman in this let's make one oh no she really existed she also had a first class maths degree from Cambridge she went to the women's college noonim but Gordon welchman I think had been one of her tutors or one of her hasn't thought highly over so again spoiler alert inside the imitation game Joan Clarke did not get recruited as a result of doing a crossword puzzle in five minutes and 34 seconds she got recruited because Gordon Welsh weren't around jury knew all about her and just took great care to get hold of her they started building machines with the help of a very talented hardware engineer called doc keen or Harold keen to give his proper name you had to work out the wheel combinations and the wheel ordering first of all you needed BOM time to try them out and in the early days doc keen did his best and made I think bonds that could be used for either three rotor or four row to work at six needed them all the time for production work you know they pretty well knew what the settings were straightforward but they needed bond time when you say production working that is you're talking about just day to day decoded day to day decoding we know we're going to crack this you know we're just set it just send it through just double-check that this is right you know so but you know with the Army and Air Force stuff they were never in any serious doubt that from about late 41 onwards they could do it what you didn't want was the hot eight mob coming in and saying it's our turn on that machine now it's not fair we meant to share these things the problem for Tait you see was that their usage was a lot more speculative it would lead to a lot more failures until you got some idea of what the wheel ordering was and then Alan Turing came up with a really very very bright idea we showed how good a statistician he was what he said was look we could maximize our what's a word payoff from these bombs if only we knew without getting on to the things which wheels were in use at the right in the middle those are the ones that are going to rotate first you know you're feeding your first bit of ciphertext it's the right one that goes around 26 times and then the next one starts move some other time you've done 600 and whatever 26 squared is characters you've seen a fair bit of ciphertext if you take that ciphertext and think that it came from German but with certain wheel settings on the right in the middle but we don't know them yet what do you know from the frequency statistics of letters in German as to how that might give it the give itself away a little bit even in ciphertext depending on exactly what the cross wirings were in the right and the middle rotors in other words could we say that a number one and a number three rotor that we're trying here matches this vague matching process rather better than a number five and number two those of you who know some statistics will realize this is conditional sequential Bayesian probabilities and all that happened when you convoluted as it were arbitrary German texts with this ciphertext is certain little indications would come and they didn't do it on the bomb they did it by another method of sheets and their sheets were made in Banbury you punched holes in sheets and put them over in light box and slid one over the other and you looked at these great long strings of stuff coming out with certain little groupings of letters there that were giving the game away statistically it turned out that it was deadly work you had to concentrate and yet not fall asleep and you had to remember what had gone before you had to try and think what might come up I don't understand all the details but I'm not surprising the slightest to find that the person who was best at spotting this was Hugh Alexander the chess champion and by common consent in hut 8 he was the best probably the next best second equal I think was Jack good also a statistician and a good chess player but I don't play chess but Hugh Alexander was top board or Bletchley Jack good was fourth board right those two but I think she was under thought the world of Joan Clark he thought that possibly Jack with the next-best after him and decoding using this Alan Turing technique which because it used sheets made in Banbury was inevitably given the latinized name of bambor isthmus but it was helpful because if you did it properly you could say we can reduce the time on the bomb when we get on to it because we know that this ciphertext really is almost certainly come from having a number five in the middle and the number one on the right so all we've got to do is to work out what the left rotor is so just as a very rough color for instance that is that might be something like there we know e comes up normally Evolet exactly hell and all sorts of things but knowing they known the cross wirings of those two that you're assuming you could work out how the pattern of heavy e's would come out into certain other patterns that would give the game away but only ever-so-slightly would look almost random but not quite and you had to be trained how to spot the non-randomness what helped a lot of course was when they started building more bombs and even for production work from her three there's no way that the bombs that could build a blast apart were enough they had to start putting them out in other derelict manor houses within about a 20 mile radius they ended up I think by the beginning 42 with about three of the manor houses full of bombs eventually six by the end of the war I think the overall estimates are that there were about 40 or 50 bombs of various sorts in the UK when you added how many of the were it built in America because that was the other factor the plans for all these were handed over to the Americans special relationship all that taken to America and with America not being under daily air raids and having no shortage of raw materials they built I think in the end something approaching a couple of hundred bombs of various sorts and the interesting story is that in late 42 early 43 I think it was Alan Turing made a journey America and went to see the naval decryption operation and also the the army one as well because there was separate in America not under combined roof as they were at Bletchley and I think the naval Admirals were really right at the start of the war you know very worried saying we can build this machinery but but you know we're up against it we've got done it's against us he's three out of eight not three out of five now our mathematician people tells us three out of eight turns out to be 336 okay Allen so here's the deal we've got to build 336 of these bombs haven't we and now said though you don't you use my bamboo business technique you can to sort out which routers you almost certainly have got off the bomb before you ever get on it and then you can make do and I think they thought this was wonderful I think in the end they built I don't know what the compromise was to build somewhere between sixty and a hundred rather than 336 but so high-lead did they think of this technique the Americans that was a very interesting story that conditional sequential Bayesian probability bamboo isthmus technique has been classified from then until 2010 that's how sensitive it was the reason that made it even more sensitive was that it wasn't just used in four-rotor naval enigma where it was important but he fed on into the other machine that we're going to do a separate video about at some stage the well-known Colossus machine that technique was of great use there as well one final indication of how they got on top of the problem again from Hugh Alexander with use of the Bamber isms techniques the sheets and extra bomb time that was the pod everybody wanted bomb time they eventually got enough and what Alexander said I had no idea this took place he said you do realize of course that they weren't all physically in England we had dedicated transatlantic underwater cables between us and the nc our place which was doing naval enigma in the USA so they were very nice we didn't have to ship any of their machinery over to us which we wouldn't have never been allowed to do but what we did was we just sent our jobs over to them the ones that we didn't have the bomb time to do we could send them the menu these settings on the bomb plan border to enable you to set up the drums to be of a certain type and in a certain order and ring settings and all that so the full spec for that menu which we would call program nowadays could be sent over the undersea cable and the result usually came back within an hour and that made a huge difference to the amount of traffic they could get on top of so it's sobering to reflect that just over 70 years ago now it's rather than undersea fiber-optic or anything like that even on good old-fashioned undersea copper cables you were still sending programs into the cryptographic cloud as it were at the other side of the Atlantic suddenly Bob goes ballistic stretches his arms out in front of a display and say you will close this down now ken Thompson and Dennis Ritchie and they were given the Turing awardhow do you go about decrypting ciphered traffic that uses these enigma machines can you do by hand and what actually happened at Bletchley Park what historically was the order in which things took place this has been very much prompted by the appearance of the film called the imitation game with Benedict Cumberbatch as Alan Turing afraid these men would only see me down popular at school way two of the first people through the doors of Bletchley Park in September 39 were Alan Turing and his colleague at Cambridge another mathematician called Gordon welchman who I think was a year ahead of Alan Turing actually in taking the master tripod and of course getting there first you will find throughout the story Bletchley Park was full of first-class mathematicians even before war broke out the Allies had had a big success in that a German spy had actually defected before the war started and handed over a military Enigma machine and a starter Enigma code book what better tutorial I think he handed it over to the French Secret Service the French contacted the English who were by that stage had moved to Bletchley Park their chief crypt analyst was a guy called Dylan hogs who'd had a lot of success with this stuff going back to this world war but I mean to cut a long story short the the French and the British initially did they just did not want to do know what to do with this stuff war hadn't yet broken out but fortunately the French I think passed it on and the conditions of great secrecy to the Polish cipher Bureau and we and Bletchley Park owed them a lot because they had a team there led by a very very good mathematician called marian rejewski he spotted straightaway that with all of this system of rotors reflectors plug boards it was basically just running through the permutations so what better way to really get to grips with all of this and all of its possibilities than to have somebody with an expert in what's called the theory of permutation groups and marian rejewski was very good from that point of view they were dealing with machines where there were just three rotors six combinations no choices of three out of five at that stage and that made life a lot simpler a plugboard did come along and the poles originally found that they could invent what you might call by hand methods they used a method of perforated sheets and amazingly by sliding these over one another and perforating them according to the ciphertext that you received but as it became more and more complicated it really did need some machinery and full credit to the poles they realize this and they built a machine called the bomba and with the bomba so long as it was only three wheels so long as the weren't too many cross settings on the plugboard on input and output and so long as the initial message setting was transmitted in a way that got bound by the end of 1938 as the Germans realized it was not very secure essentially you chose a three letter word and you sent it twice and even though it appeared at the other end is six cryptographically mapped symbols you know you might type in ins the german word so it's happening twice once once and it would appear as ljq wxz something like that nevertheless if you knew that those first six letters had to map into a repeated German three-letter word boy did it cut down the number of settings of the Enigma that could possibly have produced that so with all those simplifications and weaknesses the poles are able to make a very good start what really blew them out of the water first of all was tragically being invaded of course by Germany how can you run a cipher Bureau and any sort of operation when your country's being invaded but even prior to that the idea of choosing three out of five before you arranged the three on the spindle as we've seen that led to 60 combination they need not six bombi but 61b how's the question couldn't afford it pressure in Poland was such that they probably never get around to building them anyway handing over of the whole situation as to where the bullish Bambara got to God Bletchley Park off to a flying start I mean clearly they were up against bigger plug boards not just three out of five rotors but looking at the naval stuff coming along as looking like three out of eight the whole idea of machinery was an excellent one but he had to be made even more powerful and robust it was driven by land cheering and of course as we now know he was put on the ideal persons to do it not only was he a theoretical mathematical logician while he was at Princeton he'd actually built hardware he loved soldering relays together making his own little replicas of how his Turing machines might work as people will tell you Alan Hodges in the biography says he was hammer fisted he was enthusiastic but not good is it Sean Wiley is colleague in Hatay said very enthusiastic but he was so clumsy he used to insist on using high voltage so luring ions because they were more efficient and he'd give himself electric shocks and if it wasn't an electric shock making him scream he'd burned himself and no enthusiasm but not the person you would want to build your home computer he said look we've got to do this by building a bomb let's call it a bo MBA partly with a nod in the direction of the polls and saying thank you he drew up a specification of what needed to be done you see this in action in the imitation game I'm designing a machine will allow us to break every message every day incidentally but the good thing of course in the movie is that it doesn't have to produce any results it just has to rotate a lot and look very very impressive thanks to a superb effort what is now the Bletchley Park Museum they've actually rebuilt a bomb and it works but let's just explain that for every vertical column of three in this decryption device the top one here on the bomb corresponds to the rightmost drum the fastest one the middle one corresponds the middle one and the bottom one of the three in any column corresponds to the leftmost drum which was rotating slowest of all essentially what you've got is lots and lots of enigmas in parallel as it were and you can try out different menus as they will call different programs basically saying well you see that enigma replica at the top left I'd like to make the top drum be a type two drum the middle one be a type five in the bottom one be a type three because I think that was the drum ordering and on those drums I'd like to make the ring settings you know where you put your little stud to do the initial offset I'd like to make them reading from the top V a and H can you do that please oh and this is where Turing's ideas came in he said look you know we are going to have to get more and more and more into the idea of decrypting by trying to use known plaintext you know if you're listening in to a certain weather station that's sending out in Enigma code you know that phrases like storm and heavy rain and stuff are going to occur sometimes you wouldn't succeed you know you'd have to give up and so no I think that our idea was wrong we'll have to try something else the fact that enigma never enciphered anything to itself was a huge help if you look at James Grimes video you can see him using pieces of paper tape as it were to show ciphertext and showing some guest plain text underneath it and you slide them along and you keep on trying different and if it's a given position a letter in the ciphertext exactly corresponds to a letter in the plaintext then that cannot be right you can't have an A encrypting as an A so you must keep sliding it along this guest plaintext and you might stand a chance at the places where there are no correspondences there's no places where a letter is encrypted to itself and I think one of the stories told was that they sent out an RAF plane to bomb a crucially important light boy at the mouth of a harbor yeah and then knew which station we'll be reporting that back to headquarters listened to the ciphertext looking for I think it's the German would something like alloy - toner for light boy and if you see something saying you know the light boy has been destroyed wonderful you've got known plaintext now allegedly the house itself was nowhere near big enough to accommodate all of the personnel that were needed it wasn't just Crypt analysts and mathematicians it was service personnel intelligence people Clark's admin all that stuff so as well as occupying the entirety of the house out in the grounds there were various huts and different units with different tasks or in different huts the three-rotor Army and Air Force enigma service was based in her six it was run by Gordon welchman and Turing's near contemporary her Cambridge the bigger problem the much harder problem was naval enigma as we've already discovered naval enigma didn't just choose three rotors out of five H o three rotors out of eight massively complicating things and then doughnuts the head of the German Navy being yet more suspicious and wanting his codes to be super secure introduced the idea of a fourth rotor and I think that was particularly so for the u-boat traffic now that was a much harder problem so for a long time three rotor enigma could almost go into production four-rotor enigma was still at the research stage and for some desperate months I think in late 41 early 42 there was a time when naval ending was off the air completely they just couldn't get into it they couldn't decrypt anything I think they were helped eventually by a pinch which was to get a codebook off a submarine that had been depth charge shattered by depth bombs the stricken reader is abandoned one of dozens that are meeting the same thing and gradually as their skills built up they were more and more successful with naval enigma but I think you could say even right to the end of the war it was always harder than doing the Army and the Air Force stuff so what he came down to then Bletchley was hut 6 3 rotor enigma at 8 navel for rotor or three rotor enigma all done in hut 8 under Alan Turing now when you now look at the imitation game you will notice that it's all centered around Hut eight massive simplification they merge Hut six personnel in with Hut aid personnel they mentioned Hugh Alexander the double British chess champion quite right he was there without insuring in hut 8 they mentioned this wonderful extension to the back of the bomb called a diagonal board which helps a lot it was a bright idea and the implication is given in the imitation game that this was invented by Hugh Alexander no it wasn't it was invented by Gordon welchman of hurt sakes but this is Hollywood for you you have to live with us yes there was a guy called Jack good in cut eight you'll see him in the movie as well he was a very good statistician almost as good as Alan Turing himself and was also good at chess but not as good as you Alexander and yes Joan Clarke it's not an artificial oh we must have a woman in this let's make one oh no she really existed she also had a first class maths degree from Cambridge she went to the women's college noonim but Gordon welchman I think had been one of her tutors or one of her hasn't thought highly over so again spoiler alert inside the imitation game Joan Clarke did not get recruited as a result of doing a crossword puzzle in five minutes and 34 seconds she got recruited because Gordon Welsh weren't around jury knew all about her and just took great care to get hold of her they started building machines with the help of a very talented hardware engineer called doc keen or Harold keen to give his proper name you had to work out the wheel combinations and the wheel ordering first of all you needed BOM time to try them out and in the early days doc keen did his best and made I think bonds that could be used for either three rotor or four row to work at six needed them all the time for production work you know they pretty well knew what the settings were straightforward but they needed bond time when you say production working that is you're talking about just day to day decoded day to day decoding we know we're going to crack this you know we're just set it just send it through just double-check that this is right you know so but you know with the Army and Air Force stuff they were never in any serious doubt that from about late 41 onwards they could do it what you didn't want was the hot eight mob coming in and saying it's our turn on that machine now it's not fair we meant to share these things the problem for Tait you see was that their usage was a lot more speculative it would lead to a lot more failures until you got some idea of what the wheel ordering was and then Alan Turing came up with a really very very bright idea we showed how good a statistician he was what he said was look we could maximize our what's a word payoff from these bombs if only we knew without getting on to the things which wheels were in use at the right in the middle those are the ones that are going to rotate first you know you're feeding your first bit of ciphertext it's the right one that goes around 26 times and then the next one starts move some other time you've done 600 and whatever 26 squared is characters you've seen a fair bit of ciphertext if you take that ciphertext and think that it came from German but with certain wheel settings on the right in the middle but we don't know them yet what do you know from the frequency statistics of letters in German as to how that might give it the give itself away a little bit even in ciphertext depending on exactly what the cross wirings were in the right and the middle rotors in other words could we say that a number one and a number three rotor that we're trying here matches this vague matching process rather better than a number five and number two those of you who know some statistics will realize this is conditional sequential Bayesian probabilities and all that happened when you convoluted as it were arbitrary German texts with this ciphertext is certain little indications would come and they didn't do it on the bomb they did it by another method of sheets and their sheets were made in Banbury you punched holes in sheets and put them over in light box and slid one over the other and you looked at these great long strings of stuff coming out with certain little groupings of letters there that were giving the game away statistically it turned out that it was deadly work you had to concentrate and yet not fall asleep and you had to remember what had gone before you had to try and think what might come up I don't understand all the details but I'm not surprising the slightest to find that the person who was best at spotting this was Hugh Alexander the chess champion and by common consent in hut 8 he was the best probably the next best second equal I think was Jack good also a statistician and a good chess player but I don't play chess but Hugh Alexander was top board or Bletchley Jack good was fourth board right those two but I think she was under thought the world of Joan Clark he thought that possibly Jack with the next-best after him and decoding using this Alan Turing technique which because it used sheets made in Banbury was inevitably given the latinized name of bambor isthmus but it was helpful because if you did it properly you could say we can reduce the time on the bomb when we get on to it because we know that this ciphertext really is almost certainly come from having a number five in the middle and the number one on the right so all we've got to do is to work out what the left rotor is so just as a very rough color for instance that is that might be something like there we know e comes up normally Evolet exactly hell and all sorts of things but knowing they known the cross wirings of those two that you're assuming you could work out how the pattern of heavy e's would come out into certain other patterns that would give the game away but only ever-so-slightly would look almost random but not quite and you had to be trained how to spot the non-randomness what helped a lot of course was when they started building more bombs and even for production work from her three there's no way that the bombs that could build a blast apart were enough they had to start putting them out in other derelict manor houses within about a 20 mile radius they ended up I think by the beginning 42 with about three of the manor houses full of bombs eventually six by the end of the war I think the overall estimates are that there were about 40 or 50 bombs of various sorts in the UK when you added how many of the were it built in America because that was the other factor the plans for all these were handed over to the Americans special relationship all that taken to America and with America not being under daily air raids and having no shortage of raw materials they built I think in the end something approaching a couple of hundred bombs of various sorts and the interesting story is that in late 42 early 43 I think it was Alan Turing made a journey America and went to see the naval decryption operation and also the the army one as well because there was separate in America not under combined roof as they were at Bletchley and I think the naval Admirals were really right at the start of the war you know very worried saying we can build this machinery but but you know we're up against it we've got done it's against us he's three out of eight not three out of five now our mathematician people tells us three out of eight turns out to be 336 okay Allen so here's the deal we've got to build 336 of these bombs haven't we and now said though you don't you use my bamboo business technique you can to sort out which routers you almost certainly have got off the bomb before you ever get on it and then you can make do and I think they thought this was wonderful I think in the end they built I don't know what the compromise was to build somewhere between sixty and a hundred rather than 336 but so high-lead did they think of this technique the Americans that was a very interesting story that conditional sequential Bayesian probability bamboo isthmus technique has been classified from then until 2010 that's how sensitive it was the reason that made it even more sensitive was that it wasn't just used in four-rotor naval enigma where it was important but he fed on into the other machine that we're going to do a separate video about at some stage the well-known Colossus machine that technique was of great use there as well one final indication of how they got on top of the problem again from Hugh Alexander with use of the Bamber isms techniques the sheets and extra bomb time that was the pod everybody wanted bomb time they eventually got enough and what Alexander said I had no idea this took place he said you do realize of course that they weren't all physically in England we had dedicated transatlantic underwater cables between us and the nc our place which was doing naval enigma in the USA so they were very nice we didn't have to ship any of their machinery over to us which we wouldn't have never been allowed to do but what we did was we just sent our jobs over to them the ones that we didn't have the bomb time to do we could send them the menu these settings on the bomb plan border to enable you to set up the drums to be of a certain type and in a certain order and ring settings and all that so the full spec for that menu which we would call program nowadays could be sent over the undersea cable and the result usually came back within an hour and that made a huge difference to the amount of traffic they could get on top of so it's sobering to reflect that just over 70 years ago now it's rather than undersea fiber-optic or anything like that even on good old-fashioned undersea copper cables you were still sending programs into the cryptographic cloud as it were at the other side of the Atlantic suddenly Bob goes ballistic stretches his arms out in front of a display and say you will close this down now ken Thompson and Dennis Ritchie and they were given the Turing award\n"