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  • We've done one already I think called the ... mentioning the Tiltman break and it's

  • got to the stage, now, where somebody comes and says: "Remind us. What was the

  • Tiltman Break. Why was it so important?" and so on. The Tiltman Break exploited a

  • weakness in any cipher that's based on bitwise exclusive-OR, as indeed all the

  • Tunny traffic exactly was - just that - I suppose I could very briefly - and not

  • using too much notation to frighten computer scientists - but just as

  • a reminder. What happens with exclusive-OR, which I'll denote with a + in a

  • circle. And effectively what happens with it is that if you take a piece of

  • plaintext and you add on to it a key character, what you'll end up with is an

  • enciphered version of that plain character. And it's all done with bitwise

  • exclusive-OR. And if you say: "Well, in what code are these characters expressed?" then,

  • in what we're talking about in the middle 1940s, it was the International

  • Teleprinter Code, five-hole, which had been well known for quite a few years,

  • since the '20s I think. And it was used for telegrams, telex, transatlantic

  • communications and so on. So what happens, then, is if you take something and

  • exclusive-OR it with something else - a 5-hole tape character - you will get

  • encrypted text. If you look at that and then visit the ZigZag Decryption video,

  • where Sean and I've done an even simpler example, you'll find out how

  • zig-zag decryption works. You get a bit of Plaintext#1 one, it predicts Plaintext#2

  • The Plaintext#2 goes on a little bit further and then that predicts a bit

  • more of Plaintext#1. And you flip-flop between the two streams. That's why it's

  • called zig-zag decryption. So, using zig-zag decryption on all of

  • three thousand characters, very early on in this game,

  • the Allies really had got an absolute bonanza here. Because if you then go back

  • and say: "Well, look, we know the plaintext now, we know what ciphertext we received,

  • exclusive-OR tells us that 'plaintext' + 'ciphertext' gives 'key'. We've got

  • 3,000 characters-worth of key, So why was it called the Tiltman break? Well, it

  • was called the Tiltman break because Colonel John Tiltman, who was a

  • mathematician as well as being a military man, knew about the properties

  • and the weaknesses of exclusive-OR. And he knew that under addition, like this,

  • the key would cancel out and you could use this zig-zag techniquea. He did it and it

  • took him 10 days and he was a German expert as well.

  • He had enough mathematics knowledge but was a serious military-German expert.

  • We do make it painfully easy - and we do wave our hands and greatly oversimplify it.

  • You've got to remember that, in real life, what happens is you start zig-zagging and

  • then, suddenly, your German expert says:"Oh dear! I can't see that that's the start

  • of a new German word! Oh dear!" And, in the end, you might get blocked. But not often

  • because what you can then do is look further along the message and see if you

  • can guess another "island" [of plaintext] in the middle. It might be 'geheim'. That was another

  • good word: 'secret'. Why not drag 'geheim' through the D-stream with exclusive-OR

  • and see if you get something looking like 'geheim' at the same place below

  • it, in the other one [e.g. plaintext #2]. So, you got islands of decrypted stuff. And your job was to

  • link the islands and get everything - including the less common German words

  • that had appeared. And in the end Tiltman did it. 10 days it took him. I think it

  • would have taken him a lot less if he had to do it a second time, obviously,

  • because you get the hang of the zigzag technique. So Tiltman had done all this

  • work. But I think, for a month or two in the Research Section, nobody could

  • figure out what on earth sort of machine it was that could be generating stuff

  • that looked like this. So new recruit Bill Tutte, from Cambridge - enrolled for

  • a Chemistry degree, not Mathematics, but very keen on

  • recreational mathematics. He was given the job and he decided that having learned

  • at cipher school that if you think that there could be a periodicity in the

  • cipher then you'd better start looking for what period, what repetition rate it

  • was on . And prior to being put to work on this Tiltman Break he'd worked on a

  • similar cogs-based ciphering machine - a Swedish one called the Hagelin machine.

  • And I think it's fair to say that there's enough similarity there that is:

  • "Oh yeah! maybe it's a cogs machine? Prime numbers of [teeth on the] cogs because we've discovered

  • the prime, or relative prime, of the numbers of [teeth on the] cogs is the magic formula.

  • And he said: "OK the head of the section - Gerry Morgan - has told me that they have reason

  • to believe that one of the cogs in this machine has got 23 teeth on it". So, we've

  • covered in another video how he started looking for 23 but accidentally found 41 [teeth].

  • However there is something following on after that which is intended to

  • randomize it sufficiently well that it will disguise the 41. But it's not been

  • done well enough and occasionally the 41-icity of this is breaking through the murk

  • and convincing us that that's right. So, he announces this to the rest of the

  • Research Section and they go mad for several weeks trying to find out what

  • the [teeth numbers on the ] other streams must be. Because, don't forget, it's teleprinter code. Five

  • streams 1 2 3 4 5 but looks like some kind of two-stage mechanism. There's an

  • initial attempt to encrypt this but then there's a follow-up that's trying

  • to disguise the periodicity of all these wheels. Well after a lot of effort by all

  • the Research Section they cracked it. So here is what happens. You feed in an

  • ordinary teleprinter character into this adaptor. It goes through the first set of

  • wheels which Bill Tutte - in all the things I have read nobody explains why - he decided he

  • would call the first set of wheels the 'chi wheels' The Greek character

  • chi which is written out like that [draws character on paper] and the second set that follows on

  • afterwards, there they are look, here's the first set that is then passed on

  • into a second set of wheels which he called the psi wheels. And there's the

  • character psi. And those psi wheels were meant to give an extra element of

  • disguise as to exactly what it was the chi wheels were doing and to make

  • decryption that bit harder. Chi wheels put out a certain pattern of 1s and

  • 0s which gets exclusive-OR'd with the incoming character. They then all turn on

  • All the chi wheels always move in synchrony, together. But that doesn't get boring

  • because there's different numbers of teeth on these wheels. I mean here on

  • stream 1 there's the famous 41. Next wheel along has got 31 teeth, then 29 26

  • - not prime but relatively prime to all the rest - [then] 23. That first stage encryption

  • then travels onto the psi wheels. But the designers the machine thought it

  • would make it even harder for the Allies if we make it so that the psi wheels don't

  • always move on with every character. Let's put in a 'stutter' mechanism - or at

  • least that's what the decryptors came to call it. Sometimes they move and sometimes

  • they don't. OK that will make it harder?

  • Actually, in the end, it made it easier, as several statisticians pointed out. But that was

  • the way it was and the reason that Bill Tutte was able to prevail, and to see 41,

  • was that the psi-wheel patterns were really bad. And by 'really bad' I mean they

  • left the second set of wheels not rotating for 5. 6, 7 characters

  • on end. Y'know they didn't change the pattern at all! So, you've got this great

  • thing where very clearly it was been exclusive-OR'd in the second stage with

  • the same thing over and over and over again. And if that gets up to 6 or

  • 7 times, it's basically saying [that] it's only a single-stage machine again

  • because the second stage isn't varying fast enough. Bill Tutte

  • said: "Thank heavens for this. We were so lucky in the war. Number one the

  • Tiltman Break: that chap [the machine operator] should not have sent that message again and [thereby] given us

  • 3200 characters of key, potentially. But what really finished

  • them was that they failed to disguise the periodicity of the chi wheels

  • because they had inadequate psi wheel patterns that let great long unaltered stretches

  • come through. And that's what gave us just enough evidence that we could work

  • out that the psi wheels had got 43 47 51 53 59 and so on. So we won't go into

  • the details of precisely how that calamity occurred. Let's just say that

  • whoever was in charge of psi-wheel movements really goofed in the early

  • stages and as Tutte again says, it didn't matter that when we came back

  • later they [had] put their error right and made it better in future. By that time we

  • knew the periodicity of the wheels. So the only worry then was - and another of

  • Bill Tutte's colleagues, and later his PhD supervisor actually, a guy called

  • Shaun Wylie, who was down the hill in Hut 8, with Alan Turing and various other

  • worthies was brought up the hill, along with Jack Good and Donald Michie. People

  • were brought from Hut 8, and Naval Enigma, to help out with Tunny. And Sean Wylie, in

  • one of his writings about this, says: "Do you know the thing that panicked us

  • straight after finding out this wonderful layout of the machine [was] let's

  • hope these wheels were not interchangeable!" Could you imagine if

  • instead of having 41 31, so on, down here, it was possible to pick them out

  • and put them in different slots and permute them, like on Enigma, and he said:

  • 'Thank heavens after analyzing several weeks of traffic we were convinced these

  • things were fixed; it was always going to be 41 31 whatever. So that's one big worry

  • out of the way. So that was more or less the situation that was left then. You'd

  • got this fabulous break - the key subtracted itself out; there was

  • enough indications in there to work out what the periodicity of the wheels was -

  • and they're all relatively prime to each other - but where do we go from here?

  • Whenever somebody uses the same initial settings

  • which they shouldn't do - they're ordered not to do it - if ever this happens again and

  • gives what Bletchley Park calls a 'depth' - - and you remember the famous,

  • absolutely famous, indicator setting of the Tiltman Break was HQIBPEXEZMUG,

  • 12 characters. Yeah, well, that was how they knew it was worthwhile exclusive

  • or-ing them because the operator, the next time round when he repeated it, sent

  • out this thing [again] saying: 'my settings are HQIBPEXEZMUG'. So, you know it's

  • worthwhile exclusive or-ing them together seeing what you can find out.

  • So, they relied absolutely on the fact that in the early days - and up until mid to late

  • 1942 - the operators were told to send out the Indicator so the other end knew how

  • to set the wheels relative to one another.

  • What they didn't do except very infrequently, thank heavens, was to change

  • what's called the 'patterns' on the wheels. It's probably about time we said a

  • little bit more about that. What I've drawn out for you here on that diagram

  • is the simplest wheel of all with the fewest teeth that was 23. Here is my

  • notional starting point and you can see I've numbered them 01, 02, 03, 04.

  • So, just imagine, that after every exclusive-OR character that

  • contributes, this wheel is moving clockwise around from 6 to 7. And then it

  • moves to position 8 and so on. The dot means this is contributing a 1 when it

  • comes around to the start position. And otherwise it contributes a 0. So these

  • things, the the dots, are called the 'patterns' on the wheels.

  • Now, again, a huge stroke of luck for the Allies. It was such a pain

  • setting up all of these wheels, all 12 of them, with different patterns, and you had

  • a little slider to slide a ratchet up and down, as to whether it was 1 or 0, that

  • the Germans only changed the patterns every month. Phew! that meant that you had

  • one month to try and get depths - you know things where the person had

  • used the same Indicator twice. It may not be as a repeat of the same,

  • exactly same, message. That really was an absolute gift from on high.

  • Typically, though, an operator would say: "I've used HQIBPEXEZMUG, you know, that one

  • [that message] was about 'Parachute dispositions in Salonica' Oh! there's another one here I've got

  • to send which is about when General Katzenzinger next has his leave break.

  • Oh! what Indicator should I use there? Oh well! let's use this one again. They'll never decrypt

  • this it doesn't matter. So, very often, your zigzag was not between two similar

  • messages it was between two very different messages. But at least they'd

  • use the same settings. That, again, explains why you needed German [language] experts around to

  • say: "Oh! y'know, yes, that is the start of something or other [significant] down here".

  • So, that was the name of the game. Hope that the lazy operators give you depths by using

  • the same indicators. Then Bill Tutte came up with an extra method in late '41,

  • I think and said: "I know. Let's try and look for 'near depths' because a slightly less

  • lazy operator would say HQIBPEXEZMUG, we're not going to use

  • the same one twice. I'll only change one of them [Indicator letters]. It's such a faff.

  • Let me just change one of them. Now if only one of those settings was

  • changed and if it happened to be on a first stage chi wheel, Bill Tutte pointed

  • out that from the other four [chi settings] that you knew were the same as the last time, and

  • only one has changed, you can, with some mind-bending

  • attention to complexity and the help of German experts sitting next to you, say

  • it's not ZMUG at the end it's RMUG. So have we got any other messages, from

  • earlier on, that we've part-broken which had R in that position? Who knows?

  • That might help. So, he said, typically you might end up

  • with 20 or 30 possibilities, once you'd propagated this 'R not Z'

  • through all the morass of stuff that you've got. And he said but, yeah, with the

  • help of some really good German [linguist] guys that could work. And that was more

  • evidence, you see, because that could be backtracked into working out what the

  • wheel patterns were a bit more. So I think the feeling in the Research

  • Section was: 'This is OK so long as they keep sending out the Indicator settings'

  • But we need a lot more techniques to get us out of trouble if that isn't the case.

  • Well, everybody knows, of course, that Turing did everything at Bletchley Park.

  • Nobody else was of any importance at all :-) And I hope that one of the things that

  • this set of videos may be doing for you is to emphasize that, very important

  • though he was, he didn't do absolutely everything. One of the problems with the

  • secrecy, particularly in the late 70s and early 80s when this

  • news about Bletchley Park began to trickle out - but a lot was still under

  • the Official Secrets Act - is that some computer scientists, historians and

  • writers very incautiously started saying: "Oh well! If Turing took what the Poles

  • did for Enigma and developed it on, and then did Naval Enigma and got that

  • sorted out, he's such a genius it stands to reason it must have been him running

  • the whole Tunny / Lorentz / Colossus show". No - not true! I think our friend and

  • colleague, Jack Copeland, whose book you see up there, 'Colossus', would be the first

  • to want me to say: "No - Alan Turing had nothing to do with Colossus! Colossus was

  • purely Tommy Flowers." He [Turing] did make a contribution towards the decrypting Tunny effort

  • and it was a very very helpful one.

  • Here we are, in early '42, there's been the Tiltman break. Bill Tutte has worked back

  • from that, and the Research Section helped him to find out the disposition

  • of the wheels on this Tunny ciphering machine. What was the problem? Because

  • every message sent out on that machine had an indicator, showing the start

  • positions of all of the cogwheels. The bigger problem was the worry that the

  • patterns on the wheels - the patterns of 0s and 1s - a lot of people spent a

  • lot of brainpower working back through depths, where people had used the same, you

  • know, Indicator twice, trying to backtrack through the key text into saying: "What

  • does this mean about what the patterns are?" And, in the end, if you gathered

  • enough evidence - and certainly with the Tiltman break there was so much evidence

  • there they really did get the whole thing sorted out. They managed to work

  • out, for that month, exactly what all the wheel patterns must have been. [It] took a lot

  • of people a lot of effort, by hand. But it was done. But the worry was we're gonna

  • more and more be saying: "We want to get the patterns". At the moment we're saved

  • by the fact that we have a month to build up, and analyze, evidence before it

  • changes again. So, you know, let's say for a typical example, start of August, you

  • start collecting evidence as to what this month's patterns must be. You look

  • for depths. You've got all the indicators and by maybe August 20th, or

  • mid-August if you're very lucky, you've got enough evidence to work out

  • what the patterns on the wheels are for this month. Then you go back to all the

  • stuff that was transmitted earlier in the month, that you didn't understand. But

  • now you've got the patterns you can go back and see what the messages were. And

  • so long as the developments in the war are not happening at a breakneck pace

  • then the fact that this intelligence was two weeks old didn't matter too much.

  • Because it was high-quality intelligence. Remember this is Hitler's High Command

  • talking about strategic things, so it was still valuable. Suddenly I think it was

  • late '42 the moment they'd all dreaded. Calamity. Somebody in the German High

  • Command said: "... although it's inconceivable that this is being broken (!) we are idiots

  • if we start sending out stuff we don't need to send out, [i.e.] these Indicator

  • settings. Why not distribute a codebook to everybody and say I'm using wheel

  • patterns [correction: 'wheel settings'] no. 356 today?" That's exactly what they did on Enigma, remember.

  • [The] same argument came out. "Oh they don't understand it. It'll work.

  • It'll be all right". No! no, one step, y'know, belt and braces approach to this,

  • and don't send information that you don't need to. So, there they were then.

  • All of a sudden they didn't know what the Indicator was any more. But they did

  • know when things were being sent in depth because a lazy operator would say,

  • to his opposite number: "I'm using entry no. 356 in the codebook".

  • And then, a little later on: "I'm still using 356". So you didn't know

  • what [Indicator setting] 356 was, but you knew it was a depth with the same start point. So,

  • the business about exclusive-OR addition and being able, maybe, to do a bit of

  • zig-zagging still applied. But it was [still] a pain not knowing the settings! So this

  • was the time then that by this stage Max Newman - who was one of Turing's tutors

  • remember, at Cambridge, had joined the Research Section and his brief - that he

  • set for himself - was to mechanize wherever possible,.

  • just like they done for Enigma. Bill Tutte came to him, very shyly, he says, one

  • morning and he [Newman] was sitting with the other head of section, Gerry Morgan, I think.

  • So, Max Newman was in charge of mechanization of any sort and he

  • formed a subset called the 'Newmanry' out of the Research Section and then they needed

  • another, much more linguistics-based, section run by a chap called Major Ralph Tester.

  • And that, of course, became the 'Testery'. So, the Testery had a few

  • mathematicians and a lot of linguists. The Newmanry had people who were

  • really concerned with: 'how do we get machines to be able to help us with this?'.

  • Any new technique - any variant on a technique was going to be very helpful.

  • So, Alan Turing, in early 1942, although he wasn't part of the Research Section then,

  • was down in Hut 8 doing Naval Enigma and they we're getting to be very successful, eventually.

  • So he said: "OK, I'm going to take a six-week sabbatical with the

  • Research Section [to] see what I can bring to the party". He did contribute, did Turing, two

  • things which were of enormous strategic help actually. The first, and in the end

  • less useful one, was that he said: "What I'd like to do is to have a rock-solid

  • method that - so long as you've got lots of depths, which we tend to get every

  • month - that you can, by dead-reckoning work out (and we could train people to

  • work out) what the patterns were. It was one that he could get to work. Again you

  • need expert German speakers with you and Bill Tutte said: "Y'know it was

  • wonderful but I could never get it to work. It was a branching explosion

  • of possibilities. And when I said to Turing: 'Well, which one of those do uou take?'

  • "Oh! you take the one that you know in your bones is the right one! "

  • And Tutte said: 'My bones were never good enough! I could never get his method to work.'

  • But he could and his collaborators [could] ! The idea, essentially, was that every

  • wheel has got a different repeat cycle. So, what you're saying is: 'Let's presume

  • that at the start position that tooth and the one next one - let's presume they

  • were 0 and 1 - they were contributing. Then let's say that on the next wheel

  • along and each start position it was 0 or 1, so you can see the binary

  • explosion beginning to take place but then let's go back and say: "No, no that

  • one was 1 1 and that one was 0 1. And then work out what happens 23

  • rotations later on the number 5 wheel, or 41 rotations

  • later on the number 1 wheel. You see it's all perfectly straightforward. You'd

  • have to be aware of the possibilities of they were both the same or they were

  • both different on different periodicities for different wheels. And you combine it

  • all together and everybody's sort of putting cold compresses on their head.

  • But eventually, if you're really persistent and your brain works that way,

  • they did actually succeed. But you had to have enough depths that you knew what

  • the key was. But also I think what came from Turing, and Jack Copeland's book

  • assures me that it was Turing, was the general observation, in all of this work

  • with the Tunny traffic that it was a good idea not just to consider the

  • characters themselves - of plaintext or ciphertext - but how about exclusive-ORing

  • them with the [character] one ahead? Now, just imagine a stream of 5-hole

  • characters, like this, coming down so, you know, it was h a p p y. Now that's your

  • [conceptual] paper tape. Do another one, exactly the same, alongside. But this time just slip

  • it back by one [character]. What would the net effect of that be? You are exclusive-ORing

  • every 5-bit letter with the one ahead of it, to see what happens. Why would you

  • do that? "Ah!" said Turing "because it will make all

  • of these doubled-letter occurrences stand out like a sore thumb". We have

  • referred to these in a previous video. How did they ever get into this traffic?

  • And the answer was: its language structure and the nature of exclusive-OR.

  • If you have h a p p y, but you slide the second p up against the first one, on a

  • separate tape, and exclusive-OR them ... anything exclusive-ORd with itself gives

  • you 5 dots [5 zeroes]. Five dots is a very unlikely thing to occur by chance but if

  • you do the 'delta technique', as it was called, it doesn't matter what repeats

  • itself: it could be double 'p'; could be double 'z'; it could be - because I gather

  • that German typewriter operators, like [i.e. 'in common with'] my Dad [who was an English Cipher Clerk]

  • were taught to put in a double space after every full-stop. So a lot of the

  • traffic on Tunny was double spaces and those count as

  • well. So can you see that by delta-ing, as it was called, you are producing a

  • cascade of 0s just because of the way exclusive-OR works. And that message was

  • not lost on Bill Tutte. He said: "Look, the Germans are upping their game all the

  • time. They've really scuppered us, for the moment, by not sending the Indicator. [We've] got

  • to be able to work out what the relative settings of these wheels were, even

  • without the Indicator being given. How do we do that?"

  • And he went in to see Max Newman, the head of his section at that time, and

  • said: "I've got this bright idea - this could work". And I think Newman and Gerry

  • Morgan said: "Well yeah but do you need a depth Bill? >> Tutte: "No, no, this

  • would work on anything, so long as it's [a] sufficiently long message full of

  • ciphertext". I can use the delta method, and statistics, to work out what [the] relative

  • positioning must have been of, shall we say, the first two wheels looking left to right".

  • >> Newman: "Oh!, well how are you going to do that?" >> Tutte: "Well, you rely on the fact that when you

  • delta things together on a per character level you produce far more than probable

  • numbers of 5 dots, which is where two things that are identical have been

  • exclusive-OR'd together. So, on every single stream you're looking at, there

  • will be more dots [for 0s] than crosses [for 1s] and that will be particularly magnified

  • if you do the delta-ing first". And they said: "Well, have you any idea what the

  • skew is between ... you know ..." He said: "About 55 to 45,

  • sometimes, maybe creeping up to 60:40 or whatever". And, I mean, they were all good

  • statisticians. You can imagine. He was bombarded with "what ifs".

  • >> Newman: "Well this is all very well, Bill, but as we all know this could show up and look

  • plausible but actually fade away if you ... " >> Tutte: "Yes! you're going to need LOTS of ciphertext".

  • >> Newman: "How much?" And I think the answer, when you do the analysis, is [that] - to be pretty sure

  • that this isn't a freak result that you're getting - this ratio of ...

  • whatever it's showing up as ... 54 to 46 [say] you need about 2,300 characters to be sure.

  • So you do need long messages. But if you get one that is sufficiently long

  • what it will then ensure for you is that, at the right setting relatively, it will

  • show the 55:45 split. If you presume the wrong setting then randomness takes over

  • it will be closer to 50:50 then to 55;45 or 60:40, or whatever. But, in order to

  • make sure that that distinction between nearly 50:50 and nearly 55:45 is really

  • showing up correctly the Bletchley Park rule was don't rely on anything less

  • than 2,000 characters long, to show this up. But if it does show up then it is

  • odds-on correct that that is the relative positioning of those two [chi wheels].

  • But just imagine: you've got ... if you take wheel #1 and wheel #2 in the chi set, 41 X 31 = 1271

  • relative positions. And, for each one of those relative positions you've got to

  • squirt through at least 2,000 characters of ciphertext. [In total] several million dots and

  • crosses to be analyzed for even one setting of the wheels. Now you realize why

  • mechanization was absolutely essential to start finding the wheel settings

  • correctly. So y'know, Newman was delighted because he more or less said:

  • " ... this just proves what I've been saying, we must mechanize everything we can".

  • [Firstly by] electromechanical Heath Robinson and of course later on [Colossus]. This really made a huge

  • difference that chewing through 3 million possibilities for every pair of

  • streams would be pretty slow on an electromechanical machine but it

  • would be a heck of a lot faster [electronically]. And, of course, that is where it ties into

  • Colossus. Colossus could put these patterns to be searched for on a plug

  • board at the back [of Colossus] and basically just look for them. The thing that

  • Tutte then asked himself is: " ... well it's all about doing these deltas but suppose,

  • just suppose, that the Germans really get their chi wheel patterns so good that

  • actually stream #1 looks like 50:50 stream #2 looks like 50:50. They might be

  • able to disguise each individual stream quite well but would ... ah! think about it though!

  • They're not independent! Because of the fact that we get five dots a huge

  • amount of time - in a delta stream occuring all time, every time there's a double letter,

  • what it means is that the dot-dot combination between #1 and #2 will be

  • more common than dot-cross, cross-dot or even cross-cross. It should be the most

  • common one of the four and they won't be able to disguise that because, you know,

  • there is a correlation between these things and it's particularly so that five

  • dots would be an incredibly [a rather] uncommon thing to occur by chance but it's

  • actually occurring a heck of a lot, because of the nature of exclusive-OR.

  • So, if we do this delta-ing, on whatever, the Germans might be fiendishly clever

  • enough, on any one stream, to be able to hide it, but the chances of them being

  • able to do it across pairs of streams ... it's not gonna happen. So, basically, what you're

  • looking for on stream #1 on stream #2, together, is the occurrence of dot-dot,

  • two dots. Really it ought to be 25% but it won't be. It'll be

  • 55/45 times more common than 25% so it's these little things you can search

  • for. And if you think you've got something looking good after 2300

  • characters of ciphertext, you then say: "Right! Let's correlate stream #2 with stream #3".

  • And then we can find the relative settings of 2 to 3; 3 to 4 etc. So, after

  • only five runs, preferably helped by Colossus - about 12 minutes per run that took -

  • you could zizz through all of these millions of combinations, per relative

  • setting, and say: "That's it! the start settings of the chi wheels are as follows".

  • Of course, that's only the start of the process. So you've got the chi

  • part of the encryption. By the laws of exclusive-OR, if you add that [chi contribution] back

  • into the cipher stream, what will be left over is the psi-wheel contribution. Now,

  • as we found in the early days the psi-wheel settings were dreadful and tended to

  • just let things repeat over and over again.

  • Well, again the Germans had learned from a lot of experience - Oh! and by the way, of

  • course, the number of teeth on the psi wheels was known. So, actually, as a

  • by-hand method to follow on from the de-chi-ing which Colossus will do, then in

  • the first instance a lot of hand effort might go into getting the psi

  • contribution taken away, and revealing the absolute classic plaintext.

  • Now, what's going to happen if you think about it, is that by the time you look

  • at the psi contribution you might see little bits of plaintext showing through.

  • So, you need a German expert again and you need lots and lots and lots of

  • by-hand efforts to say what must the psi wheel settings have been, which when put

  • correctly will cause this to look like plaintext? If the first

  • set of wheels was taken away - the chi contribution; de-chi-ing - what you're now

  • doing is de-psi-ing but of course if it doesn't work it's called "deep sighing" [Joke]

  • >> Sean: [groans loudly] >> DFB: Thank you! Yes, but very largely it was possible to make that final adjustment

  • and get it all backed out and sorted and showing up very clearly. But this really

  • highlights again how immensely lucky the Allies were that the wheel patterns

  • didn't change very often. So, by lots of hard effort - aided by Colossus - we've managed

  • to discover the start settings, even without the Indicator. But you'll have

  • got the impression very clear there's still a lot of by-hand work had to be

  • done to get the full story to appear. And this gave rise to the well-known

  • Bletchley phrase which staggered me when I first saw it ... I couldn't understand it.

  • It said: "Just remember - Colossus time is far more valuable than computer time'

  • In those days a 'computer' was a person! A person who did computation. So, the

  • 'computer time' was the by-hand effort needed to tidy up the story. And you

  • didn't worry that there was hours and hours and hours of that, because the wheel

  • patterns only changed every month. Why it was vital to use Colossus for finding

  • the start settings was that that changed [for] every single message. So, there we go then.

  • That 'Colossus time' is invaluable for finding the start settings of the wheels

  • and is far more precious to you than mere 'human computer' time. It wasn't,

  • believed me, until the 50s and 60s that the use of 'computer', as a person, began to

  • fade away. Even in the late '50s, in the space program, [see the movie 'Hidden Figures'], people using

  • electromechanical calculators were called 'computers'. You had to carefully

  • say: "No, no I mean an electronic computer; I mean a digital computer". It wasn't until

  • the '60s that 'computer' without any prefix came to mean:

  • 'A piece of electronic machinery'.

We've done one already I think called the ... mentioning the Tiltman break and it's

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A2 初級

チューリング、ツッコミ、タニー - コンピュータマニア (Turing, Tutte & Tunny - Computerphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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